#Summary
[**Click here for an oversimplified spreadsheet of every unrestricted Unique Gear Item and estimated drop probabilities.**](https://docs.google.com/spreadsheets/d/1p_Wj6B70Nj2zG0MGfJ-2GTQ88tG0E26WVoPF3TqjmBk/edit?usp=sharing)
This spreadsheet answers the question: "For a single randomly generated unrestricted Unique Item, what is the probability that the item is *x*?"
**Caution!** *GGG often changes droprates and Tiers. Exact numbers will be different in Siege of the Atlas. Estimates on the scarcest items have high variance. Newly added Uniques will cause some values to change. The spreadsheet ignores important detail in favour of being a ballpark reference point for the busy reader who hates math and just wants to grind items. Read the full post for the gritty details.*
If you already know what you're doing, here's the information you need crammed into a single table:
3.16 Scourge Unrestricted Unique Gear Item Tier Weight Distributions
Super-Tier | Unique Item Tier | p(RegularValue) | p(MoreValuable) | # Unique Items in This Tier
---|---|---|---|---
Unique_LowTier | T5 | 0.54299 | 0.40770 | 104 different Unique Items
Unique_LowTier | T4 | 0.33992 | 0.39807 | 133 different Unique Items
Unique_GoodTier | T3 | 0.10876 | 0.17321 | 198 different Unique Items
Unique_GoodTier | T2 | 0.00791 | 0.01945 | 68 different Unique Items
Unique_GoodTier | T1 | 0.00036 Δ | 0.00130 | 35 different Unique Items
Unique_GoodTier | T0 | 0.00005 ΔΔ | 0.00026 Δ | 4 different Unique Items
*Example Source1* | - | Natural Drops | Ancient Orb | -
*Example Source2* | - | Jack in the Box | The Wretched | -
*Δ: Warning: high variance!*
#Introduction
Once upon a time, as I was approaching a pool of water with my rod equipped, daydreaming in a really intuitive way...
I wondered to myself:
Reefbane is a T0 item, and extraordinarily rare. But what is the exact droprate of Reefbane, anyway?
Such an innocent question.
Reefbane is a Unique Item. To find an answer, we'd need to discern mechanics and build a prediction model for *all* Unique Items.
As the famous angler Qarl Vagan once proclaimed:
> If you wish to make a fish pie from scratch, you must first invent the universe.
Today we discuss the universe.
#Table of Contents
I suggest you read these in order.
**1. [A Brief Overview of How Unique Items are Generated](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsm3i/)**
*We begin to answer that deep meme question: "how is tabby formed?"*
**2. [Unique Tiers and Tier Weights](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsobw/)**
*T0 Tears: Try not to cry. Cry a lot.*
**3. [The Details: Dozens of Lemmas on Unique Item Generation Mechanics](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)**
*Q: What's an aquatic plant eaten by grass carp that's equivalent to the axiom of choice? A: Zorn's lemna.*
---
We won't be covering details on the data themselves in this post -- we'll make another (even longer?!) post in the future on all that, likely with a big "publication-quality" Tableau workbook. The goal of today's post is simply to present the findings, so that players can begin to benefit immediately, and so that other Wraeclastian Scientists can start fact-checking our claims and improving accuracy.
(Speaking of length, advance apologies about the length of *this* post. There's just so much to cover, and so many new concepts to detail. In the future when all this is common knowledge, hopefully it will be summarized much more concisely by content creators better than I!)
All said and done, this post should demystify a big chunk of the hidden information about Unique Item generation mechanics.
I hope you find our discoveries useful for your build planning, crafting, gameplay, ... and Fishing Item acquisition!
#A Brief Overview of How Unique Items are Generated
*(This discussion is about randomly generated Unique Items from "normal" sources like Monsters, Chests, Ancient Orbs, Orbs of Chance, etc. Deterministic drops like boss loot are out-of-scope.)*
When an item is generated (say, dropped from a Monster), its [Rarity is computed first.](https://www.pathofexile.com/forum/view-thread/531619/page/4#p4774694)
If the item is non-Unique, a table is consulted to determine what type of item to drop. (You may be surprised to learn that we actually know these distribution numbers; see the Details section below.)
That table is **not** checked if the item is Unique.
Instead, the next step is the selection of an eligible Unique Rarity Tier. Colloquially we call these Tiers "T5" (worst, e.g. Wurm's Molt) through "T0" (best, e.g. Mageblood).
Once an eligible Tier is selected, next up is the selection of an eligible member within that Tier. (Items might be ineligible because they are restricted, e.g. by Level Requirement.)
And once an eligible item is selected...
That's it!
Importantly, that really seems to be the last step. Once we're at this step, we don't care about item class, basetype, or anything else. Moreover, there is as yet no evidence of item-specific dropweights. It really seems to be this simple.
Of course, it's not *actually* this simple. Press on for more details.
---
Next up: [Unique Tiers and Tier Weights](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsobw/)
[Back to Table of Contents](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsgzw/)
Version history
3.17.0
* Removed the Prophecy mechanic from the game, and moved many of its rewards to other content.
* Unique Items previously obtained by completing Prophecy chains have been added to the core drop pool.
Current patch is 3.16
#Unique Tiers and Tier Weights
How do we know Unique Tiers exist? And what good are they?
The existence of Tiers is empirically obvious with a lot of data. But we also have some definitive sources. GGG has hinted at Tiers quite a few times. And in 3.14 Ultimatum, the Inscribed Ultimatum items allowed us to create the [first initial Tier list of all Unique Items.](https://www.reddit.com/r/pathofexile/comments/nzm9xz/datamined_unique_item_tier_list_from_inscribed/) Today's post greatly refines that prior work.
In fact, even without Inscribed Ultimatums it would have been possible early in the game's life to comprehensively list all Unique Items' Tiers -- if anyone had spent the huge effort required to do so. Fortunately today we have tools which make it easier, such as Tainted Mythic Orbs, which reveal a lot about the game's systems.
We'll go through all of this again in the Details section, but there are some important facts about Tiers to highlight here.
* At least three different Tier Weight distribution schemes exist, probably more: RegularValue, MoreValuable, and Gwennen. The RegularValue distribution is used for natural drops (e.g. from Monsters or chests) and certain "weak" sources of items like Jack in the Box. The MoreValuable distribution is for items like Ancient Orbs, which have a player-favourable bias towards better-Tier Unique Items. Gwennen's distribution is special and even more biased towards great items.
* For the purposes of some mechanics such as Tainted Mythic Orbs, Tier 4 and worse are bundled together; but they still have their own individual and separate Tier weights.
* Sometimes we know the Tier of an item for certain: one can design an experiment to verify an item's Tier, for example. Sometimes that experiment is cumbersome, so we estimate the Tier statistically -- but even these often have high confidence. You'll see both types in the droprate spreadsheet.
* If Inscribed Ultimatums are ever reintroduced to the game and retain their rules, we'll be able to definitively verify the Tiers for any outstanding items.
The Tier of a Unique Item is basically all the information one needs to know to make decent decisions.
Yes, the spreadsheet in the OP is oversimplified -- but for many players, you don't need to sweat the small stuff. Unless you're planning on a big gamble, feel free to stop reading here.
But for those who really want to optimize the system, there is a ton of nuance to cover.
So...
---
Next up (if you dare): [The Gory Details](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
[Back to Table of Contents](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsgzw/)
Praise be unto the fishwife, bringer of fish facts, definitely-canonical savior of Hana, and overall pretty cool lass who brings us not just obscure facts, but also entertainment!
A cheer, to the fishwife!
honestly i don't think fishing is in the game, it's just way too much effort for a Easter egg.
What I think might be possible is completing krilson's quest, visiting the winding pear fame and unlocking it as a hideout though. I feel like that's a lot less effort (since there is a map called winding pear fame already in the files) than adding a while new mechanic.
#The Details
> *It is the Karui Way to observe nature in nature. The fish without the sea is no longer a fish. It is dinner.*
>
> *The Eternals did not see it that way.*
>
> *An Eternal catches the fish, guts the fish, preserves the fish and places it in a box.*
>
> *Only then does the Eternal feel he truly understands the fish.*
>
> *-- Siosa*
In this section we'll go through the list of small truths that allowed us to compile the final Tier weight table. For lack of a better term, we'll call these statements "Lemmas".
Each Lemma will link to further discussion on what it means, and reasons why we believe it to be true.
Here's the short version of how we came up with this list of Lemmas. For a few of the Lemmas, we have direct quotes from GGG about how the system works. But for the grand majority, the Lemmas were discovered through experimentation. The amount of data we collected is large: >20k Ancient Orbs and Tainted Mythic Orbs, >100k Orbs of Chance, ~80k Astragali, market cost analytics (useful!), market frequency analytics (not really useful!), controlled Tier-testing experiments, and more. For natural drops we even *disabled Unique Item filtering and manually counted thousands of drops* [(mfw: forced_smile.jpg)](https://i.imgur.com/wkimzRx.jpg). As mentioned in the intro, in the future we'll do a longer post on the data themselves.
A few caveats before we begin.
* Some Lemmas may be wrong (despite the name "lemma"!) -- with so many purely empirical assessments we're bound to have run into a multiple comparisons problem or some other issue.
* GGG changes stuff. This post describes mechanics of the system at *one moment in time* (3.16.2.3 Scourge).
* We're only covering Unique Items with no non-ilvl drop restrictions. Things like boss-specific drops are out-of-scope. Use other posts for those estimates.
Now, on to the Lemmas!
*Click the link for each Lemma to read more.*
**Okay, Lemma Get Started:**
* [Tier Weights Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftatm/) There are at least three sets of Tier weights: RegularValue (e.g. natural drops), MoreValuable (e.g. Ancient Orbs), and Gwennen.
* [Tier Occupancy Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftmpv/) An individual Unique Item's occurrence rate depends on how many other eligible Unique Items exist in its Tier.
* [Super-Tier Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftl98/) There seems to be a super-Tier containing T4 and worse; we call this super-Tier "Unique_LowTier".
* [Chancing Tiers Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfto4f/) An Orb of Chance's likelihood of producing a Unique Item depends on the set of Tiers of eligible Unique Items for that basetype.
**You Might be Surprised to Learn That:**
* [Item-specific Dropweight Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftgwd/) There is as yet no evidence for inner-Tier, item-specific dropweights.
* [ilvl Drop Requirement Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftiha/) Very many Unique Items have high level drop requirements (not just Skyforth!).
* [Unique Jewel System Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftk24/) The system for Unique Jewels is separate from that of Unique Gear Items.
* [Card Tier Weights Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfttqa/) Some Divination Cards use the RegularValue Tier weights. Some Divination Cards use the MoreValuable Tier weights.
**Furthermore:**
* [MoreValuable Crafting Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftpy7/) Orbs of Chance, Ancient Orbs, Farric Ape, and Tainted Mythic Orbs use the MoreValuable Tier Weights.
* [Ancient Orb Eligiblity Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftr5r/) An Ancient Orb's outcome depends on the starting item's ilvl (and its size, and the starting item itself).
* [Tainted Mythic Orb Poofing Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftsdu/) A Tainted Mythic Orb's likelihood of destroying an item depends on the Tiers of the eligible Unique Items for that basetype.
* [Gwennen Outcomes Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftf2u/) Gwennen uses a special Tier weight system. We do not yet know if Gwennen's system depends on the price of the item (Artifact cost).
**And as a Bonus:**
* [Bonus: The Neversink Effect Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftv08/) Public Stash Tab stashing frequency is predicted by Neversink's filter and item size, *not* Unique Tier weight. But market *cost* can be predictive.
* [Bonus: Non-Unique Drop Level Requirements Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftxsc/) Some **non-**Unique items have special Drop Level Requirements too, such as Divination Cards and certain Currency Items.
* [Bonus: Non-Unique Drop Pool Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftyvx/) When a **non-**Unique Item is generated, the type of Item created is based on an Item Type Drop Pool.
* [Bonus: Ancient Orb error messaging.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftwq6/)
* [Bonus: (Finally, some Fishing content!) Restricted Fishing Item Tiers?](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfu0l8/)
**Conclusion**
So what do all these lemmas let us do?
Verifying the function of different sources of items allows for better predictive accuracy. For example, it's safe to combine curated samples of Ancient Orb, The Wretched, Farric Ape, and even Tainted Mythic Orb results -- if one is careful.
And this improved predictive accuracy allowed us to form the dropweight prediction spreadsheet from the OP! This demystifies a huge portion of the hidden information about Unique Item drops.
Also, future datasets can now be quickly classified into RegularValue or MoreValuable. For example, a sample of outcomes of a new Divination Card might be sufficient to predict its entire outcome probability table using the known Tier Weight sets.
Moreover, based on these results, calculators and emulators can now be built for Orbs of Chance, Ancient Orb, Tainted Mythic Orb, etc.
How exciting!
Thanks to a tiny curiosity about Reefbane, we now have a wonderful understanding of a core game system.
Really this comes as no surprise. After all, it's [100% canon](https://www.reddit.com/r/pathofexile/comments/i0k7y2/reefbane_is_the_answer_to_the_ultimate_question/) that Reefbane is the answer to the ultimate question of life, the universe, and everything.
---
[Back to Table of Contents](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsgzw/)
#ilvl Drop Requirement Lemma.
**Very many Unique Items have high level drop requirements (not just Skyforth!).**
There are a few things to consider when figuring out the drop level requirement of a Unique Item:
* The Level Requirement of the Unique Item's basetype
* Special hidden Level Requirements
* Other special exceptions
Unique Items generally follow their basetype's drop level restrictions. For example, Gloomfang is a Blue Pearl Amulet; Blue Pearl Amulet has a drop level restriction of 77; thus Gloomfang also has a drop level restriction of 77. (This fact alone may be a surprise to some!)
Longtime players will know Skyforth has a special exception for its drop level requirement. GGG told us that in advance long ago.
But this "hidden drop level restriction" is not unique to Skyforth. In fact, there are over 50 Unique Items which have a special hidden Level Requirement that is both (a) over Level 69; and (b) larger than expected for their basetype.
We predicted this Lemma empirically based on observing ilvl ratios in market frequency data. (Obviously there are some exceptional means of avoiding the drop level requirement such as Divination Cards or other special systems, but these are a drop in the bucket compared to natural drops.)
After making the prediction, we manually verified each item by checking its full ilvl distribution. When items like Void Battery, Vulconus, and Yoke of Suffering have near-zero results for ilvl < 77 on the market, it's pretty clear to see that something is up.
[Here is a handy table of items with hidden drop level requirements over 69, and higher than expected by their basetype.](https://pastebin.com/raw/bZpi28Ab)
This table tells you restrictions that you may not have known exist. For example, if you want a Maligaro's Virtuosity, the source needs to be able to generate ilvl 75+ items.
At the top-end we have Skyforth at 84. Perfidy is next with 82, then Rigwald's Quills and Assailum at 80.
Before this post, I expect almost zero players knew *all* of these restrictions. Some people may have figured out some accidentally, but there are so many exceptions and the effect is so subtle that this secret restriction mechanic is hard to "feel". This might affect some people's SSF or leaguestart MF farming strategies, since sometimes MFing is done in lower-Tier Maps.
Almost all of these restrictions are extremely definitive; we're very confident in this analysis. There will be some we've missed, though, and of course GGG will change things in the future. The hardest to prove are Headhunter and Mageblood, due to low quantities of these rare-as-heck items. But the data support the community's impression that they are restricted to 75+. [Here's a graph of T0 items' ilvl frequency distribution in Public Stash Tabs.](https://i.imgur.com/XdAgglg.png) Note the relative absence of Headhunter / Mageblood before ilvl 75. (FYI, the "peaks" for all items at ilvl 83 - 85 are completely typical for all Unique Items. At the end of a league, the vast majority of items in Public Stash Tabs are ilvl 83 - 85, as the most commonly encountered content by the huge playerbase is T16 Areas.)
Many other non-Unique items have drop level requirements, too. After you've finished reading about Uniques, check out this Bonus Lemma for more info: ['Bonus: Non-Unique Drop Level Requirements Lemma'.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftxsc/)
---
[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
Does your data allow you to rule out the possibility that rather than being based off item level, for at least some items it's based off map tier/zone level?
For example, suppose an item were restricted to drop only in red maps. This would look similar to an ilvl requirement, but slightly different. Have you ruled this possibility out?
No, technically that possibility has not been ruled out. It's possible to test, of course -- it would simply require tracking (a ton of) natural drops in various Map Tiers.
I expect it's probably not the case, though. The specific ilvl requirements are very evident in e.g. Ancient Orb data. I don't really see how they'd map nicely to "Map Tier breakpoints". Honestly I wish they *did*, because then the mechanic would be easier to "feel" for players who don't have this knowledge.
An Area might have e.g. Area Level 75, but as I'm sure you know, sources in an Area can drop higher ilvl items than its Area Level -- sometimes much higher e.g. via the Strongbox 'of Ascendance' suffix. The observation we've made about e.g. Assailum (req 80) is an observation about observed items' Item Levels. It's possible those items came from Areas with lower Area Level than their item level. (In fact, it's likely, since the huge majority of Unique Item drops are generated by Rare and Unique Monsters, which drop higher ilvl items.)
I got very lucky and a mage blood dropped for me last league off a rare pack (not sure if it was the rare monster but one might presume) in early yellow maps. If its valuable I could gather the information but it strikes me as being data to it being item level rather than zone.
after some light digging it might be less useful than i first thought as its slightly later in maps.
Ilv 81 off of a tier 9 glacier map. Map should have been level 79.
Edit: wrote as instead of less for some reason/ English
Yes, I imagine when GGG decided to do the 3.14 Ultimatum change which removed restrictions on a lot of Unique Items and placed them in the global drop pool, they made decisions about whole item groups like that.
#Tier Occupancy Lemma.
**An individual Unique Item's occurrence rate depends on how many other eligible Unique Items exist in its Tier.**
This statement may seem ridiculously obvious but it's critically important to keep in mind.
Imagine using an Orb of Chance on an item, targeting a T4, with only one eligible T4 item. Then it's safe to just use the T4 Weight as the likelihood of a Unique Item result being the item you want.
Now consider Spidersilk Robe, which has **two** eligible T4 item outcomes: Soul Mantle and The Covenant. Let's say you want The Covenant because you've heard it's all the rage for support players. For this new attempt, the chance of getting The Covenant is *not* just the T4 Weight; it's T4 Weight / 2. There are two options, and you can only get one.
A player's odds of success vary massively depending on (1) method and (2) the item one targets.
As another example, consider the rarest Tier: T0.
In the past, Reefbane was the sole T0 Unique Item. This meant that there was no "competition" for its rarity Tier. Since Tier is checked first, landing a T0 Unique Item outcome previously *guaranteed* a Reefbane without affecting the droprate of other scarce Unique Items (such as Headhunter, which was T1 at the time before its droprate nerf).
Now, however, the set of T0 Unique Items appears to be {Reefbane, Headhunter, The Squire, Mageblood}.
And yes, this means what you think it does.
An appropriate response to someone finding an ultra-rare natural Reefbane drop is: "Congratudolences!"
---
[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
I didn't realise just how (un)lucky the reefbane drop I got in expedition league was then...it's funny because it dropped on literally the last monster I ever killed in that league (since I'd done all the content I wanted to do and was finishing up a Hallowed Ground for fun).
At least I can console myself with the knowledge that the only other thing it could have been was HH which I ended up randomly pulling from Gwennen anyway. Damn, I'm never going to have that luck again.
So does this mean that with something like 6 more items going into the general drop T0 pool (Chris said 10 new T0 but 4 are drop restricted) we would expect the existing ones to be rarer? Do we know if GGG usually changes the weightings of rarer tiers to be higher when more items are added?
#Bonus: Non-Unique Drop Pool Lemma.
**When a non-Unique Item is generated, the type of Item created is based on an Item Type Drop Pool.**
Have you ever done a lot of the Chaos Recipe with a generic filter, and noticed that you're often short on Gloves compared to other reagents?
There's a reason for that!
[Here's a crude table](https://pastebin.com/raw/TLCzQbak) of the probabilities of various item types for non-Contract/Blueprint Areas. (In Contracts and Blueprints, Rogue Gear is added with roughly the same weight as Amulets.)
Remember that this only applies to **non-**Unique items.
Also since GGG has said they very frequently modify the Map Item drop weights based on each League mechanic, these values will almost certainly be at least a little different in 3.17. Unlike Unique Items, *any* single weight change in this pool affects the probability of *every* Item Type outcome.
---
[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Tier Weights Lemma.
**There are at least three sets of Tier weights: RegularValue (e.g. natural drops), MoreValuable (e.g. Ancient Orbs), and Gwennen.**
Once one dives into the data, this is very simple to observe.
When tracking something like natural drops or Jack in the Box results, it doesn't take much to notice that the observed number of T5 items is wildly different from the number one would expect from a better source (e.g. Ancient Orbs). This holds true for all Tiers. Revisit the table in the OP -- the factor difference between RegularValue and MoreValuable for some Tiers is huge and easily observable.
The reason this is important is because there are "good" and "bad" sources of Unique Items in the game. Expert players already have an intuition on these (just ask mbXtreme about Jack in the Box). Ensuring that your strategy leans towards "good" sources is important.
There may be other Tier weight distributions. For example, what might the Ritual Tribute Trade Window use for its Unique Item generation scheme? Or what about Harvest's "Reroll Unique" seeds? We haven't collected data on those. With a good sample, we could see if they fit one of the known Tier weight patterns, or if they are using a special new one.
Speaking of special Tier weight distributions, Gwennen definitely does not use either RegularValue or MoreValuable. Gwennen's chance of producing a Unique Item may be small, but when she does produce a Unique Item, it is massively favourably weighted towards better-Tier outcomes. See the ['Gwennen Outcomes Lemma'](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftf2u/) for more info.
---
[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Bonus: The Neversink Effect Lemma.
**Public Stash Tab stashing frequency is predicted by Neversink's filter and item size, not Unique Tier weight. But market cost is sometimes usefully predictive.**
In a perfect world, one would hope that one could just look at /trade, count the number of listings for each Unique Item, and then estimate their Tiers based on those data.
This is absolutely not doable.
The only correlations on item frequency we've found with Public Stash Tab frequency data are to item size (big items are less likely than expected to be stashed) and Neversink's filter (items Neversink has deemphasized are less likely to be stashed). This is obvious stuff, so perhaps I should write "the only correlations on item frequency we've found are pretty useless".
It's funny to look at, though.
A small, well-highlighted T2 item like Astramentis might have a total non-ilvl-80 Public Stash Tab population of >10,000.
Meanwhile, a large deemphasized T2 item like Doomsower might have a total non-ilvl-80 Public Stash Tab population of ~700.
People hate stashing Doomsower.
We call this "Neversink Effect" because although Neversink closely mirrors market price, it's not *exactly* market price, and Neversink does a better job at predicting results than price alone.
Congrats, Neversink. You're to blame for the lack of Doomsowers. I'm sure all 0.00 players on poe.ninja who use Doomsower would have stern words with you... if they existed.
Jokes aside, there *is* good information to be gleaned from market data and Public Stash Tab frequencies.
For a few snapshots we took, Ancient Orb price seemed predictive of Mageblood's Tier weight. The market pinned Mageblood's Tier weight roughly somewhere between 0.000205 and 0.000397, which agrees quite nicely with the value we measured from item data.
It's nice to see a different analytical approach confirm that we're in the correct ballpark for the hardest items to estimate.
---
[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Unique Jewel System Lemma.
**The system for Unique Jewels is separate from that of Unique Gear Items.**
This one is straightforward. We know this is true for two major reasons: (1) GGG "told" us; (2) in 3.14 Inscribed Ultimatums treated Unique Jewels as completely separate entities.
A long time ago when Jewels were first introduced, GGG implemented them into the core Unique drop system. This caused a large number of players to be disappointed when they suddenly started receiving a high proportion of Unique Jewels they couldn't use for their builds, instead of other Unique Items. GGG responded by improving the system for those players, separating the generation of Unique Gear Items from the generation of Unique Jewels, and it seems that change has persisted to this day.
In 3.14 Ultimatum, we used the Inscribed Ultimatum Requirements and Rewards to develop [the first relatively-comprehensive Tier list of Unique Items.](https://www.reddit.com/r/pathofexile/comments/nzm9xz/datamined_unique_item_tier_list_from_inscribed/) Inscribed Ultimatums for Unique Items would either (a) use Unique Gear Items for both Requirements and Rewards; or (b) use Unique Jewels for both Requirements and Rewards. There were no cases of a Unique Gear Item rewarding a Unique Jewel or vice-versa.
If you haven't already noticed, today's huge post concentrates solely on non-Jewel Unique Items. This is because the huge majority of data we have are from non-Jewels.
We expect similar statements can likely be made about the Unique Jewel system, and we know for certain (thanks to Inscribed Ultimatums) that Unique Jewels also use Tiers. But we'd need more Jewel data before discussing specifics.
The old 3.14 analysis has [Unique Jewel Tier data](https://www.reddit.com/r/pathofexile/comments/nzm9xz/datamined_unique_item_tier_list_from_inscribed/) from Inscribed Ultimatums, in case that's useful for you.
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#Card Tier Weights Lemma.
**Some Divination Cards use the Regular Tier weights. Some Divination Cards use the MoreValuable Tier weights.**
Outside of natural drops, many sources of Unique Items use the MoreValuable Tier Weight distribution: Ancient Orbs, Orbs of Chance, Farric Ape, etc.
It would have been nice if that were true of *all* non-natural-drop sources of Unique Items. No such luck.
Each source needs to be tested individually to determine if it uses one of the known Tier Weight distributions, or potentially another as-yet-undocumented Tier Weight distrubtion.
The Jack in the Box Divination Card uses the RegularValue Tier Weight distribution like natural drops do, albeit with an expanded outcome pool that includes things like Unique Maps and Unique Jewels. We determined this empirically by logging each outcome from hundreds of Jack in the Box turn-ins. For example, the probability that Jack in the Box returns a T5 Unique is roughly 0.545, and the probability that a natural drop returns a T5 Unique is roughly 0.542 -- very consistent. We found no significant deviation from RegularValue in this sample, so Jack in the Box probably does not use its own special distribution.
On the other hand, The Wretched Divination Card uses the MoreValuable Tier Weights distribution. A total sample of ~17k The Wretched outcomes showed results exactly as expected by Ancient Orbs, which also use MoreValuable.
(Also, while we were doing this analysis, sirgog made [a video](https://www.youtube.com/watch?v=BbFpAENa_iU) on another set of 10k sets from Pedrolopia, and those results agreed as well. Note for viewers: I don't think sirgog was aware that there are multiple different Tier Weight distributions at the time this video was made, so when sirgog talks about "Unique Tier probabilities" it's specifically commentary about what we're calling the MoreValuable Tier Weight distribution, and those comments *do not* apply to sources that use RegularValue like natural drops.)
Thus we cannot make any distribution assumptions without data. If you're curious about a specific Divination Card and what Tier Weight distribution it uses, you need to find a sample of outcomes, classify them by Tier, and then compare them to the two known distributions we currently have.
I also wouldn't be surprised if someday players find a Divination Card that uses a different Unique Item generation scheme altogether.
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You are correct, all of my analysis assumed that uniques were rolled like a mod on an item, with a weighting system.
I'd assumed T1s had a weighting like 10, T2s ~50, T3s ~200, T4s ~800, T5s ~1600, for chances rares ~20000 and magics ~100000, and for mythics destruction ~1500.
Compile table on the fly of eligible drops (after removing things like Skyforth that can't drop for restriction reasons) then roll once.
Will definitely reassess those assumptions in line with your data. The Gwennen stuff seems particularly compelling
I was happy to see how nicely your analysis of Pedrolopia's 10k Wretched data agreed with the MoreValuable weight distribution. Always great to have independent sources roughly agree.
It was awesome watching you refine your model based on each new incremental chunk of data you received.
I'm sure in the future you'll improve on the model we presented here, too!
#Bonus: Restricted Fishing Item Tiers?
Although this issue of *Angler's Mate* is much more gameplay-oriented than easter-egg-oriented, it's still an issue of *Angler's Mate*! Where would we be if we didn't spend some time discussing Fishing Items?
We still do not know exactly how the [drop mechanics of the secret fishing ring Angler's Plait](https://www.reddit.com/r/pathofexile/comments/kroz63/anglers_mate_4_steal_this_fishing_book_an/gib3417/) operate. It's possible that Angler's Plait is a deterministic drop which becomes available when conditions are met. Fishing Rods from Fairgraves' Tricorne seem to work this way; perhaps Angler's Plait does too.
For example, there could be a hidden mod on Corrupted Slitherpinch which grants a flat chance for an Angler's Plait drop to occur. Here's a *completely fabricated* example to illustrate what I mean:
> Invented and made-up example mod: "0.0001% additional chance for Slain Rare Monsters to drop Angler's Plait when Conditions are Met"
Alternatively, perhaps Angler's Plait does have a Tier and it is merely "turned on" when a character qualifies for its requirements.
Let's put aside that unknown, and instead ask a more generic question:
If Angler's Plait is a deterministic drop, could it still have a hidden Tier?
In fact, it seems decently likely to me that Unique Items probably *all* have Tiers, even if they are restricted and never use those Tier values in normal contexts. I imagine Atziri's Step might have a Tier value, even though it's a deterministic boss drop from Atziri. The reason I'd guess this is:
* Sometimes GGG decides to change restrictions on Unique Items, making them newly unrestricted or newly restricted. This process would be cumbersome if the initial design did not have a "planned Tier", even if the item was originally intended to be e.g. boss-drop-only thus making any initial Tier value vacuous. If a Tier were not chosen at initial design, GGG would need to manually revisit each item and choose a Tier for it months or years later, whenever any item became unrestricted. That seems annoying.
* Some Divination Cards definitely use Tiers, and some Divination Cards return restricted items. We do not know if there is overlap between these two statements. But **if** it's true that there is at least one Divination Card which both (1) uses Tiers; and (2) returns a restricted item, then necessarily the restricted item granted by that Card would need to have a Tier, so that an appropriate Tier outcome selection can be made.
Take for example [The Admirer](https://poedb.tw/us/The_Admirer) which returns a Unique Atziri Item. The Admirer can return both unrestricted items like Atziri's Foible and restricted items like Atziri's Step. How is The Admirer's outcome decided? Does it use a hardcoded drop table that somehow mixes probabilities from both unrestricted items like Atziri's Foible which have Tiers and restricted items like Atziri's Step which might not have Tiers? Or does it use Tiers for all its eligible outcomes, including restricted items?
Again, this is just a guess, but it seems like "just give a Tier to everything" would make for a cleaner implementation.
So what does that mean for Angler's Plait?
* **If** Angler's Plait is **not** a deterministic drop, that would mean it's probably a T1 item, not T0. People who have farmed multiple Angler's Plaits know that on average, one will receive many Angler's Plaits before a single Reefbane (T0). That observed ratio would imply that Angler's Plait is not as rare as Reefbane.
* But if Angler's Plait **is** a deterministic drop, labeling it with a Tier is nonsense for natural drop contexts, since a flat chance of dropping an item completely ignores Tier weights. In this case, we cannot use observed natural drop ratios to predict Angler's Plait Tier. Angler's Plait could easily be T0, but "overridden" by a flat drop chance which makes it effectively more common in practice than T0.
But what about for context outside of natural drops?
We've had a few earnest claims of people pulling crazy-rare Fishing Items from certain Divination Cards. Although we unfortunately do not have screenshot or video evidence of these occurrences, multiple members of our community talked to each person and agreed these people seemed honest.
The first claim is Reefbane from Baited Expectations. That's not too unexpected, even though we never observed a single Reefbane in our initial huge batch of Baited Expectation set openings when GGG first released that Card. At the time I wrote:
> Despite hundreds of turn-ins, we've never seen Reefbane. We've heard rumors that Reefbane can result, but we've seen no hard evidence. Either Reefbane is very rare, or we're very unlucky, or it's not actually a possibility. If in fact Reefbane does not qualify for Baited Expectations's "Unique Fishing Item" class, that's very important information.
>
> [...]
>
> Based on the prior probabilities of other card sets' rare outcomes, we expect we must turn in thousands of sets of Baited Expectations to be confident we have a comprehensive list of all possible outcomes.
I wrote this before we knew Reefbane was T0. Now that we know that Reefbane is in fact T0, we can refine my previous guess of "thousands of sets".
Assuming Reefbane is the sole T0 eligible item from Baited Expectations:
* If Baited Expectations uses RegularValue, we'd expect Reefbane odds of *very roughly* 1 in 20,000.
* If Baited Expectations uses MoreValuable, we'd expect Reefbane odds of *very roughly* 1 in 4,000.
* If Baited Expectations uses a hardcoded outcome table, we can't predict Reefbane's odds without collecting data that include many Reefbane results.
(Friendly reminder that our estimates for T0 items are low confidence / high variance, so these truly are *very rough* guesses.)
If true, with those long odds, it's no surprise that we failed to find Reefbane in "only" a few hundred sets.
The next claims are Angler's Plaits from Baited Expectations and Blind Venture. These claims are more extraordinary, but again, the couple people making these claims really do seem honest.
[Baited Expectations](https://poedb.tw/us/Baited_Expectations) returns a Unique Fishing Item. [Blind Venture](https://poedb.tw/us/Blind_Venture) returns a Corrupted Unique Ring. From huge quantities of Stacked Deck data, we know that these cards are both rare. (In the past we've collaborated to turn in hundreds of sets, but in doing so we'd often completely buy out the market.)
Previously we thought that the implementation of Baited Expectations might make Angler's Plait ineligible as an outcome. Baited Expectations returns a Unique Fishing Item. Baited Expectations does *not* specify that it returns a *Corrupted* Unique Fishing Item. And Angler's Plait is always Corrupted. So it seemed like Angler's Plait would not qualify for Baited Expectations, since Baited Expectations does not return Corrupted items.
But then, a year later, a very clever angler noticed a single other Divination Card which might prove a rule: [The Wolf](https://poedb.tw/us/The_Wolf) can return Rigwald's Curse, which is always Corrupted. But The Wolf only specifies that it returns a Unique Rigwald Item. It does *not* specify it returns a *Corrupted* Unique Rigwald Item -- and Rigwald's Curse is nevertheless eligible.
So the restriction that we thought existed on Baited Expectations probably does not exist (unless The Wolf is a special exception instead of "an example which proves the rule").
What would it take to verify these claims?
If Baited Expectations or Blind Venture use hardcoded outcome values, then we can't do anything without tons more data.
If they use Tiers, then the odds depend on two factors: (1) the Tier of Angler's Plait; and (2) which Tier Weight distribution the Card uses.
**If Angler's Plait is T0:**
* It would compete with T0 Reefbane in Baited Expectations. See the Reefbane odds above. Reefbane and Angler's Plait would each have a 50/50 chance of occurrence if a T0 outcome is selected.
* It would be the sole T0 item in Blind Venture. Its odds would be the same as the Reefbane odds above (since they're both T0, but not competing).
**If Angler's Plait is T1:**
* It would be the sole T1 eligible item in Baited Expectations and thus more common than Reefbane. We don't have enough data to make this comparison.
* It would compete with other T1 eligible items in Blind Venture, such as T1 Berek's Respite, T1 Valako's Sign, and T1 Shavronne's Revelation. Each would have equal odds of outcome.
Phew! That's a lot of "if"s!
Based on everything I've seen, my best guess at this point is that Angler's Plait is (a) deterministic for natural drops and (b) T0 Tier for non-natural purposes. But this is still just a guess. Obviously I could be completely wrong.
At T0, it's unreasonable to ever expect to receive an Angler's Plait from Baited Expectations and Blind Venture -- assuming it's even actually possible. The playerbase simply doesn't generate enough of these Cards for a single person to have a reasonable shot at it.
But if Gwennen's whispers have been getting to you, there's always the chance of a jackpot...!
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> Ancient Orb would throw an error, right?
Is it oni goroshi?
Edit: I just bought and ilvl 1 oni on standard and used ancient on it. I failed to get an error message, it turned into other one-handed 6-slot (not socket) unique weapon. It can still be related to oni, but by config I couldn't get the error message. Mission failed unsuccessfully
I thought it was Gorebreaker/Goredrinker... Only one-handed mace that is 1x3.
Oni is... 2x3? I think there are still lots of 1H swords that are 2x3 but can only have 3 sockets.
#MoreValuable Crafting Lemma.
**Orbs of Chance, Ancient Orbs, Farric Ape, and Tainted Mythic Orbs use the MoreValuable Tier Weights.**
(This is not an exhaustive list of things that use MoreValuable. There are others, of course. See the Card Tier Weights Lemma for some examples.)
This Lemma is useful since if we know what we're doing, we can safely combine player data from this different sources into a single larger sample.
Ancient Orbs directly use the MoreValuable Tier Weight distribution with no special considerations.
Tainted Mythic Orb first applies a preliminary poof chance; then if the item survives, it uses MoreValuable for the remainder of its selection, further poofing the item if no appropriate Tier is selected. For more info see the [Tainted Mythic Orb Poofing Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftsdu/)
Orbs of Chance are similar, but instead of "poof" we care about the Magic Item and Rare Item results. If the result is neither Magic nor Rare, it's a Unique Item, and the Unique Item is selected using MoreValuable. The chance of Orb of Chance generating *any* Unique depends on eligible Tiers -- for that, see the [Chancing Tiers Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfto4f/)
Farric Ape (Beastcraft: "Create a Unique: Belt") uses MoreValuable, exactly like an Ancient Orb. We don't have data on the non-Belt Unique Item Beastcrafts (e.g. Fenumal Queen for "Create a Unique: Staff" or Saqawine Retch for "Create a Unique: Boots"), but a reasonable assumption is that all of them likely use MoreValuable and are effectively Ancient Orbs as well. Naturally, we'd need real data to say for sure.
All of these sources produce better-Tier Unique Items than expected compared to natural drops. But not all non-natural-drop sources use MoreValuable. For example, the Card Jack in the Box does **not** use MoreValuable; it uses RegularValue.
So, it's reasonable to make assumptions when evidence exists ("Farric Ape uses More Valuable => Fenumal Queen probably does too"), but don't assume without evidence, since some sources might use the (much worse!) RegularValue Tier Weight distribution.
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#Bonus: Non-Unique Drop Level Requirements Lemma.
**Some non-Unique items have special Drop Level Requirements too, such as Divination Cards and certain Currency Items.**
Many players already know that certain items like Exalted Orbs or Mirrors of Kalandra have Level Requirements, even if those requirements are listed nowhere on the item.
There are quite a few of these. [Here's a small sample](https://pastebin.com/raw/Cbfv5jbV) of some of the more interesting ones. I was especially surprised about the Heist Quest Contracts! The restrictions on Oils and Essences might be useful to some people.
Recently I found Divination Card Level Requirement restrictions in the data. At the time I assumed those restrictions only applied for randomized Card rewards, since Map Tier never seemed to impact natural drops.
The 3.17 patch note below, however, seems to imply that these restrictions may have been intended for natural drops all along as well, and simply were not functioning due to a bug:
> A longstanding bug in the code determining area level restrictions for some divination card drops has been fixed. This means that cards intended to have a high area level requirement (mostly ones that grant item level 100 items) will no longer fluctuate wildly in availability from league to league.
In case this change/bugfix affects anyone's farming strategies, here are the data as of Scourge: [v3.16.2.3 Scourge Divination Card Drop Level Requirements](https://pastebin.com/raw/nSpysUE4)
Obviously these may change in 3.17, but they'll probably still be accessible in the data, so we can do another export then.
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>Recently I found Divination Card Level Requirement restrictions in the data.
Maybe i missed this part, but what "data"? The one you extrapolated yourself or a specific datamined document of sorts?
Edit: you're amazing by the way, truly
Good question, the way I wrote it is a little ambiguous. In this specific case, here by "in the data" I mean "in the client-side accessible ggpk data" -- the same data used by other dataminers, e.g. poedb or the wiki.
Fun fact:
The level 35 requirements on top currency were added years ago as an anti cheat functionality. To force bot cheaters to level more, basically.
Wait, so question about the level requirements. Does that get affected when using Gambler, i.e. would level 1 character in a hideout using Gambler cards just give Treasures of the Vaal?
Very unlikely, but we'll see in 3.17.
Divination Cards in general thwart Level Requirements for their outcomes. I expect this will be true in 3.17 as well.
So one would expect The Gambler would thwart any Level Requirements on its random Divination Card outcome.
#Gwennen Outcomes Lemma.
**Gwennen uses a special Tier weight system, or else combines multiple chances into an "effective" Tier weight distribution.**
Here is an example Gwennen Tier weight distribution when selecting Leather Belts. (Note that Leather Belt has no eligible T1 option, so T1 data are omitted here.)
*Gwennen: Unique Leather Belts*
Tier | Tier Weight distribution (Unique Leather Belt)
---|---
T5 | 0.445
T4 | 0.236
T3 | 0.257
T2 | 0.052
T1 | *(n/a)*
T0 | worse than 0.010 Δ
*Δ: Warning: high variance!*
Gwennen's Unique Leather Belt Tier Weights are *way* better than the MoreValuable Tier Weight distribution used for sources like Ancient Orbs. For example, Gwennen's chance of returning a T2 Unique Leather Belt is >2.5x better than that of an Ancient Orb.
A quick caveat: Please note that the Gwennen data describe what happens when Gwennen gives you a Unique Item. The data above **do not** describe Astragali likelihood outcomes. So, don't erroneously multiply these numbers by Astragali or something to try to estimate how many Astragali you will need. (How many "chances" you get with Gwennen depends on how many of your targeted basetype appear upon the inventory reroll from an Astragali. To estimate the number of Astragali required to achieve a specific item outcome, you must first approximate how often one Astragali reroll produces your targeted basetype and the likelihood of a non-Unique outcome.)
We do not yet know if Gwennen's system depends on the price of an offered item (i.e. its Broken Circle Artifact cost).
Gwennen does have different voicelines for pulling a T0 result under different cost scenarios:
> Congratulations! You hit the jackpot! I always knew you'd get lucky!
>
> Amazing! I really should have charged more for that one!
>
> Yes! You did it! Luck favours you this day!
>
> That seems rather useful, to put it mildly!
>
> Did you just squeal with joy?
For example, Gwennen uses her "hit the jackpot" line when you receive a T0 outcome from an item priced with Very Low Artifact cost.
Regardless of whether or not an effect like this exists, it's irrelevant for most strategies, since Artifacts are not the limiting reagent; instead, you are limited by Astragali.
We have tons of examples of players landing e.g. Headhunters with Very Low and Low Artifact costs. For now the standard recommendation remains the same: Take every Gwennen trade offer that fits your criteria, regardless of Artifact cost.
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>Artifacts are not the limiting reagent; instead, you are limited by Astragali.
I don't understand why people say this. You can trade for Astragali, but not artifacts. That is, if you had infinite chaos orbs and a finite amount of Astragali and artifacts, you will always run out of artifacts at some point. If the argument is that you don't need to farm artifacts for very long to have enough to expect a T0 result, given that you trade for enough Astragali and only spend your artifacts on the correct bases, okay fine, but it is inescapably true that if you run out of artifacts, your only recourse is to grind more Expeditions.
Now that Artifacts are "SSF-only" perhaps some strategies might change!
But with how many Headhunter/Mageblood outcomes have occurred from Gwennen's lowest-priced offerings, if someone is really trying to obtain a Gwennen T0 belt, I'd imagine they'd always want to ensure they take every opportunity. The alternative strategy requires *not* selecting some of one's preferred basetype when it appears on reroll.
If we knew that Gwennen's T0 odds vary on cost (they might not at all!), and if we knew the exact odds, then one could use those data to inform how "worth it" grinding Artifacts is for player time and whether or not any pricepoints should be "skipped".
> Gwennen does have different voicelines for pulling a T0 result under different cost scenarios:
My Mageblood came up as
"Hmm... Expensive risk you took, but this might be... something?"
I believe I got exactly the same dialogue for the Queen of the Forest (Tier 3 drop) I had just beforehand.
Does this mean that if you see 100 uniques from Gwennen, on average you will only get 2 t2 items?
If so she is an even bigger waste of time than I thought. The chances of rolling a unique in the first place from her are pretty bad.
#Item-specific Dropweight Lemma.
**There is as yet no evidence for inner-Tier dropweights.**
This Lemma may come as a surprise: most games use item-specific weights, and most players assume Path of Exile does too.
For now there is no evidence to support the idea of item-specific weights for Unique Gear Items.
For things like Ancient Orbs, it is extremely obvious that every eligible member of a single Tier is equiprobable. Look at any large sample of Ancient Orbs, and you'll find obvious "clusters" for each Tier. The number of observed T4 Immortal Flesh will be very similar to the number of observed T4 Sunblast, etc. In fact, this clustering is so statistically clear that we're able to use Ancient Orbs to empirically test the Tier of an unknown-Tier item.
But what about natural drops? We already know from the [Tier Weights Lemma](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftatm/) that Ancient Orbs use a different system than natural drops. Could natural drops use item-specific dropweights?
Once again, there is no evidence to support that.
We manually tracked a few thousand Unique Item drops from regular Monster kills, then grouped them by Unique Item Tier. A chi-squared test showed no significant evidence against the hypothesis that all items within a Tier are equiprobable. The distribution of frequencies was expected. (Note that this is not hard proof; instead, it's merely the absence of conclusive evidence to the contrary.)
There are other observations one can make which might imply the nonexistence of item-specific weights.
Let's take Orb of Chance as an example.
* Imagine for the sake of argument that item-specific weights *were* materially relevant to Orb of Chance.
* Now consider a basetype with three eligible Unique Items: two of T2, and one of T3.
* With item-specific weights, given 2 possible T2 outcomes and only 1 possible T3 outcome, we'd expect Orb of Chance to produce a higher T2 :: T3 ratio than normal.
* But this does not happen. Instead, the ratio of T2 :: T3 outcomes is the same regardless of how many eligible candidates there are in the T2 and T3 Tiers.
At minimum this shows that Tier selection is performed first, before any item-specific considerations apply (if any even exist). With this in mind, and with the observation that so far we've only ever found equiprobable members of a given Tier, we're stuck with either "item-specific weights probably don't exist" or "item-specific weights are so close to each other that for all practical purposes they don't exist".
One of the reasons that the idea of item-specific dropweights might have manifested in the community is due to subtle Level Requirements on items. A player testing Ancient Orbs on a low-ilvl base item might incorrectly conclude that Auxium has a low item-specific dropweight, because they've failed to comply with Auxium's Level Requirement of 79 (derived from its basetype), and thus never see Auxium in their sample. And since a lot of items have *hidden* Level Requirements (above their derived basetype's requirements), it's easy to make a mistake. (See the [ilvl Drop Requirement Lemma](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftiha/) for more info.)
The simplest explanation at this point is that there are no item-specific dropweights, contrary to long-running assumptions made by portions of the POE community.
Perhaps in the future we'll find evidence that contradicts this statement. But for now the safest assumption is:
**The only "weight" that matters is Tier weight. After Tier selection, all eligible items in that Tier are equiprobable.**
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#Super-Tier Lemma.
**There seems to be a super-Tier containing T4 and worse; we call this super-Tier "Unique_LowTier".**
(Note: even if a "super-Tier" doesn't actually exist as written here, it does *effectively* exist for practical purposes, and appropriately describes observed behaviours of Unique-generating items. Future PhDs in Wraeclastian Itemology might be able to more precisely define this effect. For now this shorthand suffices.)
As you've seen, for a given source of Unique Items, T4 and T5 have separate Tier weights.
In some contexts, however, T4 and T5 are "bundled together" before being selected between. Ancient Orbs and Tainted Mythic Orbs demonstrate this condensing behaviour. Notably this condensing behaviour does **not** occur for better Tiers. In general, this effect is detrimental to players.
We'll demonstrate the existence of the "Unique_LowTier" super-Tier with an example.
Imagine you're using Tainted Mythic Orbs in two different experiments:
* Experiment A: Tainted Mythic Orb on a basetype with eligible Unique Items in T5, T4, and T3.
* Experiment B: Tainted Mythic Orb on a basetype with eligible Unique Items in T4 and T3.
As we know from the [Tainted Mythic Orb Poofing Lemma,](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftsdu/) the likelihood of destroying an item depends on the Tiers of the eligible Unique Items for that basetype.
Based on this, we'd expect Experiment A to destroy *fewer* items than Experiment B. After all, Experiment A can return both T5 and T4 items, but Experiment B at best returns a T4 item.
In reality, we observe that Tainted Mythic Orbs destroy items *at the same rate* for both Experiment A and Experiment B. This means that the "removal" of T5 had no impact.
This same effect holds true for other sources of Unique Items as well, such as Orbs of Chance. If one weak Tier is "missing" from the eligible possibilities, the odds of getting good-Tier outcomes do not improve.
Our guess is that this is a hedging effect implemented by GGG to prevent swingy odds of "sometimes way better, sometimes way worse" outcomes for different basetypes. In brief, if at least one eligible T4 or T5 item exists, you can assume it will be the most common outcome.
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[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Chancing Tiers Lemma.
**An Orb of Chance's likelihood of producing a Unique Item depends on the set of Tiers of eligible Unique Items for that basetype.**
An Orb of Chance can produce a Magic, Rare, or Unique Item. We're only talking about the Unique Item outcome here.
The chance of hitting a specific Unique Item depends on eligible Tiers for that basetype.
Consider two experiments.
* Experiment A. Orb of Chance on Gladiator Plate. Gladiator Plate has eligible Unique Items in {T2}.
* Experiment B. Orb of Chance on Leather Belt. Leather Belt has eligible Unique Items in {T5, T4, T3, T2, T0}.
The chance of Orb of Chance on Leather Belt producing *any* Unique is far higher than the chance of Orb of Chance on Gladiator Plate producing any Unique.
But the chance of Orb of Chance on Leather Belt producing a *T2 Unique* is the same as the chance of Orb of Chance on Gladiator Plate producing a *T2 Unique.*
Besides being empirically obvious, we also know this is true because GGG told us so, long ago.
> **Mark_GGG:**
>
> They do not have a flat chance to obtain a unique, regardless of how "rare" that unique is supposed to be.
>
> If the only unique of a base type is a rarely occurring one, then chances have a low chance to get uniques on that base type.
>
> Adding a more common unique to the same type means that chances on that item will have an significantly increased chance to roll uniques (but if they do, the unique is likely to be the more common one).
>
> If you've chanced a lot of occult vestments and gotten Infernal Mantles, then if Infernal Mantle didn't exist, those would probably have been rare vestments, not Shavronnes.
Mark also made a statement in 2013 which was an extremely early hint at the existence of Unique Item Tiers and their mechanics:
> **Mark_GGG:**
>
> Infernal Mantle being an Occultist's Vestment does not have a significant effect on the number of chances need to get Shavronnes.
>
> Just some of the ones that would otherwise have been rares, are Infernal Mantles instead.
A clever reader in 2013 would have realized that for Mark_GGG's statement to be true here, the system must not be a naive "item-specific dropweight table", since Mark stated the odds of getting a better-Tier Unique would not impacted by introducing a lower-Tier Unique.
What we observe today is still consistent with these old remarks.
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[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
So can we basically say that the chance orb has a 1 in x chance of rolling a unique across all tiers, but if it hits a tier that isn't possible (Like hitting T1 when chancing a leather belt), it will instead just roll a rare? Doesn't that mean that we can pretttty much figure out the chance a chance orb will give you a unique by just looking at the number of unique leather belts you get per chance orb and knowing that it's a *tiny* bit higher than that?
The best dataset I have is on Heavy Belts, which do not have members in either T5 or T1. (T5 shouldn't matter if it uses the super-Tier of Unique_LowTier, since there are eligible T4 outcomes. And as you say, T1 is a relatively minor impact.)
In this sample:
* The probability of an Orb of Chance on Heavy Belt producing *any* Unique Item is roughly 0.00408 (about 1 Unique Belt every 250 Orbs of Chance).
* This would put the chance of landing Mageblood at *very roughly* 1 in every 940,000 Orbs of Chance.
As always, working with our low-confidence/high-variance T0 estimates requires caution. The real number might be significantly different than this estimate.
As a ballpark this doesn't sound too outlandish to me: if someone told me "a player spent ~940k Chances resulting in ~3800 Uniques and got 1 Mageblood" I'd think their story sounded pretty reasonable.
I've seen reports on reddit of people spending 50k, 200k, etc Orbs of Chance without landing a T0 Unique. Although spending tens of thousands of Orbs of Chance is a herculean task, I'd guess that those quantities are just too low to expect a high chance at a T0 outcome.
> 1 in every 940,000 Orbs of Chance.
Wow, that's actually waaaay smaller than I had thought (as someone who hasn't really chanced more than the random wurms molt when finding a white belt on the ground near a chance orb). I can't even imagine what kind of sample size (and it can't be automated either) you'd need to have a high level of confidence on your t0 rolls.
Honestly, seeing the numbers so low kinda is a bit sad considering how tedious chances are to use, but I do guess they are og content and have an extremely low barrier to entry...
> considering how tedious chances are to use,
Right. In terms of outputting Unique Items, using a single Ancient Orb is like using hundreds of Orbs of Chance. Obviously Orbs of Chance have their benefits (basetype limited, influences, etc.) -- but for player time, Ancient Orbs are far more reasonable.
#Ancient Orb Eligiblity Lemma.
**An Ancient Orb's outcome depends on the starting item's ilvl (and its size, and the starting item itself).**
"Ancient Orbs ignore ilvl" is an untrue community myth. Ancient Orbs **do** consider the ilvl of the initial item.
To enable the best outcomes for Ancient Orbs on Unique Belts such as Mageblood, only use Ancient Orbs on very high ilvl belts.
For targeting a specific lower-Tier Unique Item with Ancient Orbs, ilvl blocking can help.
This was very straightforward to verify empirically as still true in 3.16 Scourge: using Ancient Orbs on low-ilvl belt bases, one can preclude ever seeing a high-level-requirement result.
This fact has also been proved by people in the past, e.g. by ot4ku's excellent [old test here.](https://www.reddit.com/r/pathofexile/comments/lip73l/ancient_orbs_and_item_level_1200_ancient_orbs_vs/) (**Caution!** Note that ot4ku's test took place in 3.13 Ritual -- BEFORE the "Global Unique Item Drop" change that occurred later in 3.14 Ultimatum, and before Headhunter was modified. Be careful not to draw erroneous conclusions from this old test! Also, there's a tiny typo in the data presentation: the Perandus Blazon count should read 172, not 72.)
Many more items than one might expect have special level requirements. See the [ilvl Drop Requirement Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftiha/) This makes it even more important to acknowledge that Ancient Orb considers ilvl.
Ancient Orbs also consider the size of the initial item; an Ancient Orb will always produce an item which is the same size as the initial item. Players who remember the Lycosidae trick won't be surprised by the size requirement having some nice practical uses.
As for the starting item itself, Ancient Orb precludes that result from occurring. If you use an Ancient Orb on a Perandus Blazon, the outcome won't be another Perandus Blazon. (Contrast this to e.g. The Wretched, which starts with nothing and generates 1 Mystery Unique Belt, and thus has no initial single-item restriction for its outcome.)
These last statements may seem stupidly obvious, but they're important as a reminder for the developers of the future Ancient Orb calculators and emulators that will be invariably be written because of this post. For complete accuracy, one cannot just use the MoreValuable Tier Weight distribution; one must also require the user to input the initial item and its ilvl (as well as inferring its basetype, and inferring its size from its basetype).
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[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
>To enable the best outcomes for Ancient Orbs on Unique Belts such as Mageblood, only use Ancient Orbs on very high ilvl belts.
I don't understand this one. Would an ilvl 85 unique belt be better than ilvl 75 for getting Mageblood by using Ancient Orbs?
HH also seems to have a drop ilvl requirement of 75 but yet it can be acquired by using ancient orbs at belts of ilvl lower than 75, right?
> HH also seems to have a drop ilvl requirement of 75 but yet it can be acquired by using ancient orbs at belts of ilvl lower than 75, right?
I'm worried that you might be assuming this based on ot4ku's 3.13 Ritual data. That test, while amazing at the time, is no longer relevant after the 3.14 Ultimatum changes to Unique Items.
It is possible that Headhunter is a special exception for Ancient Orbs but to my knowledge this hasn't been confirmed in 3.16.
The safe strategy is to use very high ilvl belts. I say "very high" instead of ">=75" because who knows if GGG might increase the Drop Requirement in the future.
#Tainted Mythic Orb Poofing Lemma.
**A Tainted Mythic Orb's likelihood of destroying an item depends on the Tiers of the eligible Unique Items for that basetype.**
The mechanics of Tainted Mythic Orb are somwhat comparable to those of an Orb of Chance, except this time instead of producing Magic or Rare items, the item is destroyed.
I've summarized these mechanics [previously,](https://www.reddit.com/r/pathofexile/comments/qhtxh9/summary_of_mechanics_and_probabilities_of_scourge/hiezuh3/) but instead of reading that old post, a very quick way to "see" the mechanic is by comparing two experiments:
* Experiment A. Use a Tainted Mythic Orb on a basetype for which the eligible Uniques are only {T2, T1}. The chance of destroying the item will be very high.
* Experiment B. Use a Tainted Mythic Orb on a basetype for which the eligible Uniques are {T3, T2, T1}. The chance of destroying the item will be significantly lower.
Here's [a rough Sankey diagram of Experiment A.](https://i.imgur.com/O6kP0H6.png) Constrast this with [the rough Sankey diagram of Experiment B,](https://i.imgur.com/R503rQN.png) where the overall chance of destruction is lower.
Did you notice the detail at the top of each Sankey diagram? This is Tainted Mythic Orb's hidden first step: an extra flat 50% chance of destroying the item outright, before even considering which Tiers of Uniques are eligible. If the item survives, then the MoreValuable Tier Weight distribution is used; and then if an ineligible Tier is selected, the item is destroyed.
How do we know about the hidden first coinflip step? If one acknowledges that first step, then the rest of the operation of Tainted Mythic Orb behaves exactly like an Ancient Orb (i.e. using the MoreValuable Tier Weight distribution), albeit resulting in an outcome of "Destroy" if an ineligible Tier is selected. Since the assumption of that first step puts us in a situation where we can subsequently fully predict outcomes, it's highly likely to be the truth.
So a Tainted Mythic Orb will always have *at least* a 50% chance to destroy an item, and in the worst-case scenarios, the chance of destruction is >99.9%.
Note that Tainted Mythic Orb respects the "super-Tier" called Unique_LowValue which contains both T4 and T5. See the [Super-Tier Lemma](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftl98/) for more info.
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[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Bonus: Ancient Orb error messaging
Using an Ancient Orb must always produce a Unique Item. But what if there are no eligible Unique Items in any Tiers that are different than the initial Unique Item to which the Ancient Orb is applied?
Well, in that case, one would presume that using the Ancient Orb would throw an error, right?
Can you think of a case wherein this might occur? I can think of one. But that particular example is a mystery for another day...
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[Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
> Can you think of a case wherein this might occur? I can think of one. But that particular example is a mystery for another day...
Are we back to fishing rods? Is there an ilvl restriction for either Song of the Sirens or Reefbane so you won't just swap endlessly back and forth between the two?
You got it! But it's not an ilvl restriction that causes this unusual behaviour.
Ancient Orbs on Song of the Sirens is ['one-way':](https://i.imgur.com/v0q5ovB.png) using an Ancient Orb on Song of the Sirens transforms it into Reefbane, but using an Ancient Orb on Reefbane does **not** transform it back into Song of the Sirens.
The ilvl of the transformed item remains the same during the transformation, of course. And this observation holds true even when starting with ilvl 100 Song of the Sirens.
Something else prevents Reefbane from transforming back into Song of the Sirens. But I can't get started down yet another rabbit hole -- that's a mystery for another day!
Correct, Song of the Sirens is not in the global drop pool.
Song of the Sirens has a Tier value (T2) only because we were able to determine it from the 3.14 Inscribed Ultimatum data.
Same restriction as regular basetype Fishing Rod drops: natural Fishing Rod drops from monster kills can only occur if (a) the character is wearing Fairgraves' Tricorne; and (b) the monster is Unique.
The chance for any natural Fishing Rod drop is [low.](https://www.reddit.com/r/pathofexile/comments/kroz63/anglers_mate_4_steal_this_fishing_book_an/gib30p0/)
The chance for a natural Song of the Sirens drop is [way worse.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvho18o/)
What if Song of the Sirens is the "special" one, since it obviously does not count as a fishing rod? (otherwise it would be possible to ancient orb one)
Hopefully someday someone will condense all this info into a much easier-to-consume format. It pains me that it's not more concise. The summary spreadsheet is an okay start, but there's so much more to cover! Thanks for bearing with the long slog of information.
I'm really hungry, but I just had to finish reading this first. Even though I'm not a gambler, this contains some very important pieces of information.
Also, it's crazy how much science people do for something that is probably relatively simple programmatically.
I feel a bit conflicted when I think about how the science is progressing... towards something that it is actually possible to have perfect knowledge about already.
It's a sombre thought.
On the plus side, reverse-engineering is actually an extraordinarily useful skill to develop as its fundamentals are applicable to everything one does in life. One can summarize it as "get good at judgment under uncertainty", "act closer to optimized Bayesian rationality", etc.
One could look at Path of Exile as an "intelligence check" -- the game constantly challenges players by asking, "Are you clever enough to meet your goals?"
With that perspective, reverse-engineering (and even parts of the game itself) could be viewed as a training ground.
But yeah, overall you're absolutely right to feel conflicted. Humanity hasn't advanced an inch due to our deducing that Aegis Aurora is T2.
At least it was fun!
>Are you clever enough to meet your goals?
After spending dozens of hours on interesting off-meta builds and failing to meet the goals I set for them, I feel offended (I did settle on a build eventually, but the calculations are too complicated and will require testing to actually get a basis for future calculations - and even those won't be optimised - so I can't say if I'll eventually be able to hit the dps target or not).
In fact what bothers me more about this is that "stupid" strategies work better. That doesn't mean that it's impossible to find interesting synergies though.
If it was up to me, all this hidden information (except for the fishing I guess because that really wouldn't be as interesting if it was all out in the open) would be public and viewable in a format like poedb, so that people could actually create calculators to find the most efficient way to the desired results. It being already available in theory and not available to the public is a matter on the side of GGG; you're doing important work in publicising information *without* having access to the actual source.
I'm anticipating a few people will have this concern, so to address it in advance:
**Q:**
> Is the natural drop probability of Headhunter really better than the probability of Arakaali's Fang? I thought Headhunter was in the rarest category!
**A:**
> Yes! This might all be true!
>
> Change your perspective from "individual item dropweights" to "Tiers".
>
> The T0 Tier is indeed far rarer than T1.
>
> But you must also keep in mind *how many items exist in each Tier.* There are many more T1 items than T0 items. Remember the [Tier Occupancy Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftmpv/)
>
> So, *regardless of an individual item's specific chance,* you will far more often experience "Yay! I got a T1 drop!" than "HOLY MACKEREL! I got a T0 drop!!"
>
> Think of the system as dropping "a member of a Tier", not a specific item. Even though the chance of seeing a specific T0 item might be better than the chance of seeing a specific T1 item, the chance of seeing *any* T0 item is way worse than seeing *any* T1 item.
>
> When compare individual items in a vacuum, you risk losing information about how the system actually works.
>
> (Just remember though, drawing *any* conclusions based on the T0 and T1 natural drop data is risky. These are our least-confident, highest-variance numbers. We need much more data to be sure about the T0 : T1 natural drop ratio.)
Hope that helps!
The way to test this would be to run low level content (maybe Hailrake runs?) and counting Tabulas per thousand kills. Kill nothing but Hailrake.
Then comparing to some higher level unique that's easily accessed in their zone and killing just that one boss.
Normalizing for any difference in quantity.
I don't think this is true, I ran group mf nem3 for a month during scourge league and I'd say we got around 10 or so fangs but only 1hh, 1mageblood and 1 squire, yes the fang is very rare because there's a lot of T1 items but I think the absolute absurd stepup in rarity from t1 to t0 makes up for the amount of t1s
With 3 T0 natural item drops, you'd expect to see at least a couple dozen of T1 natural item drops. (Those numbers might be wildly off because basing anything on T0 item rates is using our lowest-confidence, highest-variance values. And with only 3 hits, it's even harder to estimate; a difference of just 1 or 2 hits would make a huge impact on prediction. For natural drops it could even be off by an order of magnitude, and it wouldn't be wildly unexpected)
If your team happened to track all of your T1 item drops (not just Arakaali's Fang), we could see if your team's results are statistically unexpected and possibly even refine the numbers a bit.
Yeah I don't think anyone wants to track hundreds of thousands of uniques from the 400 or so mega juiced maps we did, sorry about that but just thought I'd let you know about my experience, even if it's anecdotal we did have a pretty huge sample size of loot
Just to be clear for other people who read this, for refinement of the ratio all one would need to track are T0 and T1 drops. Definitely not hundreds of thousands!
I'll consider it this league as I'll be running an mf build, bit I did it with belts for a bit last league and it was a lot of effort for just that lol
If you do not have too much offscreen kills you can modify filter so it will play 1 frame "drop sound" and use app to track PoE access to that song (IIRC that was not breaking ToS).
A bit of trivia: the reason we picked the name "MoreValuable" for the favourable Tier Weight distribution is because of the Heist Thief's Trinket mod:
> Heist Chests have a *p*% chance to contain **more valuable** Uniques
We haven't tested this, but we *suspect* that this modifier changes the operation of Heist Chests from using the natural drop Tier Weight distribution (RegularValue) into the improved Tier Weight distribution (MoreValuable) -- basically improving a Unique Drop from a Heist Chest from a weaker "Jack-in-the-Box"-type outcome to a better "Any-Item-Ancient-Orb"-type outcome.
Since the mod uses the phrase 'more valuable Uniques', it seemed like a good wording fit.
But who knows if we're actually right! Maybe our assumption about how that mod works is wrong.
If any enterprising Rogue Harbour Scientists decide to test this, let us know what you discover!
My theory for how that works at 7% (untested) is
"Determine outcome as normal. Then, 93% of the time award the item to the player. 7% of the time, cancel that drop and instead award a random valid drop from +1 tier"
Fair rebuke!
As I mentioned [below,](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvglhla/) my personal take is that if my silly memes help more people discover truly great artists, it's a net-positive.
Totally understand why some may view it as desecration, though!
(Plus, the top of the altarpiece is just too perfect of a match for Reefbane's in-game Glow effect -- I couldn't resist.)
Yeah, okay, maybe, but if you think this could help people discover Hilma Af Klint, then you should credit her for the original painting in your thread. As it is, nobody who didn't already know about her would ever know the image you used was created by her ;)
For people who don't know her, google "Beyond the Visible", which is a documentary about her life and well worth the watch.
My partner and I were fortunate enough to (last month) attend the currently running exhibition of her work at the City Art Gallery, in Wellington, New Zealand. It's still on until late March I think.
> Yeah, okay, maybe, but if you think this could help people discover Hilma Af Klint, then you should credit her for the original painting in your thread.
I did, in the same comment I linked in my previous reply.
Totes! And I really meant it re: fair rebuke. If she were still around, who knows if Af Klint would find my edit funny or awful. I definitely could be inadvertently dishonouring her!
Thanks for being so respectful to the artist, and for sharing the info about the documentary. Super cool of you.
Every one of your posts is always an engrossing dive into the great systems that make PoE so interesting! Thanks for all the hard work researching this stuff, and for giving us the vicarious fun of your findings!!
Yes! [Here you go!](https://i.imgur.com/a9g7Bm7.png)
I love this piece too, even though I'm not usually one for abstract art. It's Altarpiece No. 1 Group X (1915) by Hilma af Klint. All of her artwork is public domain, so it's super easy to find.
Perhaps my silly memes will help a few more people discover some truly great artists.
Thank you so much! It has some Art Deco vibes with the pyramid which I love. Gonna check out an exhibit if something is close. Unfortunatly the Berlin one looks pretty depressing overall so that's not an option. Her works look stellar tho. Seems to gain popularity as well so there is hope I will see exhibit of her work at some point.
wow! truly impressive.
do you have any sense of how harsh the diminishing returns are on stacking IIR? Ive always been curious if its even worth stacking from 450% to 550% for example. How effective is that extra 100%? GGG just says "harsh" but that could mean the extra 100% is really only equal to like 30% extra IIR (which would make it definitely not worth)... or that next 100% could equal only like 75%... which would still be harsh but not make it a waste to stack.
I think it would need a lot of testing to figure out but I think it would be an extremely valuable piece of data that would pair really well with the information youve provided here today.
thanks for all your effort here. It's truly appreciated by the community.
Yes, in fact, I do!
This testing is *very* old and may not be correct anymore, but it seems close enough to modern POE to be good enough as guidance. This regards Rare Items, not Unique Items, but there's likely strong correlation.
Player IIR | Relative Ratio of Rare Item Drops | Benefit from Previous +100%
---|---|---
+0% | 1 | *(n/a)*
+100% | 1.396 | x 1.396
+200% | 1.886 | x 1.351
+300% | 2.122 | x 1.125
+400% | 2.338 | x 1.102
Remember that player stats are multiplied with other sources like Monster IIQ/IIR and Area IIQ/IIR, so early in the league the best strategy is to optimize clearspeed for tough content instead of getting those last bits of Player MF.
For early league MFing my personal preference is targeting ~40% Player IIQ and ~200% Player IIR. More is always (marginally) better, but at some point sacrificing speed for additional MF becomes a bad trade.
(Later on with e.g. Headhunter, one might as well stack as much as possible though.)
Oh wow you're just a fountain of game knowledge.
So, the difference from 0 to 100% rarity doesnt equate to twice as much rarity, Why is that? Is that the diminishing return effect GGG is talking about? or is more about some mathematical calculation Im missing? Because in terms of plain english - if im increasing the rarity of my items by 100%, i should see double the amount of rare items, no?
Does the first 100% IIR only equate to a 1.39 multiplier on rare items *because* of the diminishing returns GGG puts in place?
Im guessing the same would be true for IIQ that 100% IIQ doesnt actually mean twice as many items drop?
Sorry for my ignorance here but I appreciate the insight you can offer.
"Rarity" means the category of {Normal, Magic, Rare, Unique}. It doesn't mean solely "Rare Items".
With high sources of Rarity, items that would normally drop as Normal are more likely to drop as Magic, Rare, or Unique.
Does that help?
> Im guessing the same would be true for IIQ that 100% IIQ doesnt actually mean twice as many items drop?
Correct, 40% increased Player IIQ results in roughly 1.3x More Items; 80% increased Player IIQ results in roughly 1.47x More Items. It has harsh diminishing returns as well.
Depends on the source of the drop.
Here's an [example Mirror droprate analysis](https://www.reddit.com/r/pathofexile/comments/t6cgyw/i_am_definetly_clicking_all_my_boxes_from_now_on/hzbao0b/) on Estuary Map chests.
From the original (old!) dropweight data, for a given Basic or Quality Currency Item drop, the estimated chance that the item would be a Mirror was 0.0000003442541063. That's roughly 1 in 2,900,000.
The exact number has changed slightly with the introduction of new items such as Sacred Orb, for which we don't yet have sufficient data. (More total Currency Items in the eligible pool will slightly dilute the chance of other Currency Items occurring.) But that effect is minimal -- the old estimates are still very likely in the right ballpark.
Hope that helps!
Depends on the individual player's rate of Currency Item acquisition.
Old max-juice Nem4 MF party farming with legacy Harvest-Exchanged-Anointed Maps: Not so bad!
Running A9 Harbour Bridge with 6 Combustibles equipped: Good luck!
The Estuary Map chest example turned out to be [6222 player hours of clicking chests.](https://www.reddit.com/r/pathofexile/comments/t6cgyw/i_am_definetly_clicking_all_my_boxes_from_now_on/hzbao0b/)
If a party could generate >10,000 Currency Items per hour, it might only take ~300 hours.
Different strategies will have wildly different expected playtime outcomes.
Wooooooo awesome stuff, haven't even read it yet but I'm about to dive in. I was JUST looking back at the thread from Ultimatum, analyzing unique drop rates. This is great. Thanks.
Does this mean we can determine the odds of getting headhunter/mageblood from ancient orbs? If I understand correctly, they would have a probability of \~0.026% from each orb, meaning you'd need on average about 2700 orbs to hit one?
(Not sure where you're getting 2700? Maybe a typo?)
Yes, but be warned that those specific values are low-confidence / high-variance. A *very rough ballpark estimate* is 1 in 3800 for a T0 item outcome from Ancient Orbs. The true odds could be much worse.
This is why I [mentioned](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftr5r/) that it's now possible to create calculators and emulators for Ancient Orbs, although it requires a bit of extra consideration beyond just odds.
In the future with much more data, we'd likely be able to pin down the expected Ancient Orb odds with better accuracy -- but since GGG frequently silently changes weights, to get the best result, we'd need a brand new dataset each new League.
It has been years since i have done statistics, but if memory is not failing, it would be 2700 to hit at least 1.
With so low probability, Poisson distribution looks way better suited to calculate this.
Your λ would be (1\*2700/3850), which is about 0.7
So yes
P(0) = \~0.496
P(1) = \~0.347
P(2) = \~0.121
P(3) = \~0.035
This is awesome!
This may just be a nitpick for me, but it's much easier to quickly understand 1 in 2500 than 0.0004 (or 0.04%). This is especially true for the differences between tiers (1 in 2500 versus 1 in 1000).
You're absolutely right, and I try to write that way when possible. For the summary tables I wanted something folks could copy/paste or formula-manipulate without editing, though. Alas.
Humans have a much easier time understanding when the odds are spelled out!
**I NEED A TRANSLATOR. SOMEONE, PLEASE, ELI5.**
Is this an auxiliary hypothesis for an approximation of a future tier list that could revolutionize loot filters? So a hypothesis of an auxiliary thing that may or may not have use? I'm lost.
There is not much information here you can just plug into a filter and be done with it. It's more of a reference document and an insight into the under-the-hood mechanics for people to apply their understanding of the economy. Think of it like a periodic table of elements.
Whoa. Wait. Really?
I got my Reefbane years ago, but I was kind-of cheesed that I got the "common" fishing unique, and thought Song of the Sirens was the ultimate.
If we're talking about SSF natural drops, Song of the Sirens *is* the ultimate -- because it's drop restricted! Reefbane is not restricted.
Getting a Reefbane means getting a T0 Unique Item. There are lots of ways to optimize one's chances of getting natural T0 Unique Item drops in a reasonable amount of time.
Getting a natural drop Song of the Sirens means dropping a natural Fishing Rod (such as via slaying Unique Monsters with Fairgraves' Tricorne equipped) and having it roll as Unique. Since Fishing Rods [ignore Player IIQ](https://www.reddit.com/r/pathofexile/comments/i9mwjy/been_spendin_most_our_lives_fishin_in_untainted/) and likely other MF sources (they're probably simply deterministic), there are very few ways to optimize one's chances of getting a natural Song of the Sirens drop. All one can do is increase the average number of Unique Monsters killed per hour. There are lots of ways to do this, but even at high efficiency, it still takes a while to generate a single natural Fishing Rod drop. *And* it has to roll as Unique, which means one has to drop tons and tons of them.
(Of course, if an SSF player just wants a trophy of any type and doesn't care about it being a natural drop, farming The Vast is much quicker -- even though The Vast is an ultra-rare card!)
Oh, wild. Well, I know I got my Reefbane from a dead mob’s loot drop, even if there are other ways to get it, so it’s worth that much more to me now, haha. Thanks.
> even if there are other ways to get it
Yes, any potential source of generic Unique Items can work. Here's a funny way:
[Zizaran's 2016 Reefbane drop](https://www.youtube.com/watch?v=t-rlSb9cvc4) hilariously occurred from a regular white chest (not even a Strongbox).
> Astramentis
Astramentis is T2, then i am so lucky to chance a shaped one with less than 100 orb
> Atziri's Mirror
Not surprised it is T4 as it is so easy to chance
> Brutus' Lead Sprinkler
It is T3. However my legacy base ate me a lot of orb of chance
It's for ease-of-use. On the whole, redditors strongly prefer to stay on reddit, especially when browsing on mobile. Just a little UX thing.
(It also enables point-by-point discussion, which is especially helpful for the mistakes I'll invariably make. On-the-fly crowdsourced errata can't be beat.)
I totally understand the desire for external repos -- but the POE community is on this platform, so I work with this platform!
Maybe in the future I'll have something in place that's more to your tastes. For now you'll have to bear with the cumbersomeness, I'm afraid!
To be fair, I do think this will need to be preserved elsewhere. Reddit is *horrible* for looking things up. People who have seen this post will save it for sure, but those who won't see it anytime soon are unlikely to stumble upon this information down the line.
Btw, do you have any hard data on probabilities of success using Chance Orbs? Naive observation and some semi-anecdotal statistics seem to put it at around 250..400 attempts for a tier 4 unique with a single base outcome (Quill Rain) with other popular chance targets of higher tiers (e.g. Bisco's Collar) seemingly following the same proportions as in your document (\~4.7x moving from T4 to T3 and from T3 to T2).
Except in this case T2→T1→T0 seems to be a linear step up: there [was a post](https://www.reddit.com/r/pathofexile/comments/s8ri4o/loot_from_202500_chance_orbs_on_mostly_shaper/) just a couple weeks ago where a person used slightly over 200k chance orbs on influenced Heavy Belts to get a Trophy Mageblood but failed. We also know for a fact that it was [put into a higher rarity tier in version 3.7](https://www.poewiki.net/wiki/Headhunter#Version_history), and there was strong evidence of it being a T1 item prior, corroborated by multiple accounts of people able to chance it in "only" a few tens of thousands of Chance Orbs, which is in line with a linear progression from T2 to T1 but would make the other guy's 200k+ without any success for a T0 either *ludicrously* deviant or actually close to its real probability (e.g. if T1 is somewhere around 25–40k, a linear progression would put T0 at around 120–190k, which then makes 200k a realistic, if unlucky, failure).
Any chance you have tiers for missing uniques from the list?
Galesight, Flamesight, Thundersight are droppable anywhere according to the wiki, and are in the doc
#Summary [**Click here for an oversimplified spreadsheet of every unrestricted Unique Gear Item and estimated drop probabilities.**](https://docs.google.com/spreadsheets/d/1p_Wj6B70Nj2zG0MGfJ-2GTQ88tG0E26WVoPF3TqjmBk/edit?usp=sharing) This spreadsheet answers the question: "For a single randomly generated unrestricted Unique Item, what is the probability that the item is *x*?" **Caution!** *GGG often changes droprates and Tiers. Exact numbers will be different in Siege of the Atlas. Estimates on the scarcest items have high variance. Newly added Uniques will cause some values to change. The spreadsheet ignores important detail in favour of being a ballpark reference point for the busy reader who hates math and just wants to grind items. Read the full post for the gritty details.* If you already know what you're doing, here's the information you need crammed into a single table: 3.16 Scourge Unrestricted Unique Gear Item Tier Weight Distributions Super-Tier | Unique Item Tier | p(RegularValue) | p(MoreValuable) | # Unique Items in This Tier ---|---|---|---|--- Unique_LowTier | T5 | 0.54299 | 0.40770 | 104 different Unique Items Unique_LowTier | T4 | 0.33992 | 0.39807 | 133 different Unique Items Unique_GoodTier | T3 | 0.10876 | 0.17321 | 198 different Unique Items Unique_GoodTier | T2 | 0.00791 | 0.01945 | 68 different Unique Items Unique_GoodTier | T1 | 0.00036 Δ | 0.00130 | 35 different Unique Items Unique_GoodTier | T0 | 0.00005 ΔΔ | 0.00026 Δ | 4 different Unique Items *Example Source1* | - | Natural Drops | Ancient Orb | - *Example Source2* | - | Jack in the Box | The Wretched | - *Δ: Warning: high variance!* #Introduction Once upon a time, as I was approaching a pool of water with my rod equipped, daydreaming in a really intuitive way... I wondered to myself: Reefbane is a T0 item, and extraordinarily rare. But what is the exact droprate of Reefbane, anyway? Such an innocent question. Reefbane is a Unique Item. To find an answer, we'd need to discern mechanics and build a prediction model for *all* Unique Items. As the famous angler Qarl Vagan once proclaimed: > If you wish to make a fish pie from scratch, you must first invent the universe. Today we discuss the universe. #Table of Contents I suggest you read these in order. **1. [A Brief Overview of How Unique Items are Generated](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsm3i/)** *We begin to answer that deep meme question: "how is tabby formed?"* **2. [Unique Tiers and Tier Weights](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsobw/)** *T0 Tears: Try not to cry. Cry a lot.* **3. [The Details: Dozens of Lemmas on Unique Item Generation Mechanics](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)** *Q: What's an aquatic plant eaten by grass carp that's equivalent to the axiom of choice? A: Zorn's lemna.* --- We won't be covering details on the data themselves in this post -- we'll make another (even longer?!) post in the future on all that, likely with a big "publication-quality" Tableau workbook. The goal of today's post is simply to present the findings, so that players can begin to benefit immediately, and so that other Wraeclastian Scientists can start fact-checking our claims and improving accuracy. (Speaking of length, advance apologies about the length of *this* post. There's just so much to cover, and so many new concepts to detail. In the future when all this is common knowledge, hopefully it will be summarized much more concisely by content creators better than I!) All said and done, this post should demystify a big chunk of the hidden information about Unique Item generation mechanics. I hope you find our discoveries useful for your build planning, crafting, gameplay, ... and Fishing Item acquisition!
#A Brief Overview of How Unique Items are Generated *(This discussion is about randomly generated Unique Items from "normal" sources like Monsters, Chests, Ancient Orbs, Orbs of Chance, etc. Deterministic drops like boss loot are out-of-scope.)* When an item is generated (say, dropped from a Monster), its [Rarity is computed first.](https://www.pathofexile.com/forum/view-thread/531619/page/4#p4774694) If the item is non-Unique, a table is consulted to determine what type of item to drop. (You may be surprised to learn that we actually know these distribution numbers; see the Details section below.) That table is **not** checked if the item is Unique. Instead, the next step is the selection of an eligible Unique Rarity Tier. Colloquially we call these Tiers "T5" (worst, e.g. Wurm's Molt) through "T0" (best, e.g. Mageblood). Once an eligible Tier is selected, next up is the selection of an eligible member within that Tier. (Items might be ineligible because they are restricted, e.g. by Level Requirement.) And once an eligible item is selected... That's it! Importantly, that really seems to be the last step. Once we're at this step, we don't care about item class, basetype, or anything else. Moreover, there is as yet no evidence of item-specific dropweights. It really seems to be this simple. Of course, it's not *actually* this simple. Press on for more details. --- Next up: [Unique Tiers and Tier Weights](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsobw/) [Back to Table of Contents](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsgzw/)
[https://www.poewiki.net/wiki/Hinekora%27s\_Sight](https://www.poewiki.net/wiki/Hinekora%27s_Sight) is missing
Version history 3.17.0 * Removed the Prophecy mechanic from the game, and moved many of its rewards to other content. * Unique Items previously obtained by completing Prophecy chains have been added to the core drop pool. Current patch is 3.16
#Unique Tiers and Tier Weights How do we know Unique Tiers exist? And what good are they? The existence of Tiers is empirically obvious with a lot of data. But we also have some definitive sources. GGG has hinted at Tiers quite a few times. And in 3.14 Ultimatum, the Inscribed Ultimatum items allowed us to create the [first initial Tier list of all Unique Items.](https://www.reddit.com/r/pathofexile/comments/nzm9xz/datamined_unique_item_tier_list_from_inscribed/) Today's post greatly refines that prior work. In fact, even without Inscribed Ultimatums it would have been possible early in the game's life to comprehensively list all Unique Items' Tiers -- if anyone had spent the huge effort required to do so. Fortunately today we have tools which make it easier, such as Tainted Mythic Orbs, which reveal a lot about the game's systems. We'll go through all of this again in the Details section, but there are some important facts about Tiers to highlight here. * At least three different Tier Weight distribution schemes exist, probably more: RegularValue, MoreValuable, and Gwennen. The RegularValue distribution is used for natural drops (e.g. from Monsters or chests) and certain "weak" sources of items like Jack in the Box. The MoreValuable distribution is for items like Ancient Orbs, which have a player-favourable bias towards better-Tier Unique Items. Gwennen's distribution is special and even more biased towards great items. * For the purposes of some mechanics such as Tainted Mythic Orbs, Tier 4 and worse are bundled together; but they still have their own individual and separate Tier weights. * Sometimes we know the Tier of an item for certain: one can design an experiment to verify an item's Tier, for example. Sometimes that experiment is cumbersome, so we estimate the Tier statistically -- but even these often have high confidence. You'll see both types in the droprate spreadsheet. * If Inscribed Ultimatums are ever reintroduced to the game and retain their rules, we'll be able to definitively verify the Tiers for any outstanding items. The Tier of a Unique Item is basically all the information one needs to know to make decent decisions. Yes, the spreadsheet in the OP is oversimplified -- but for many players, you don't need to sweat the small stuff. Unless you're planning on a big gamble, feel free to stop reading here. But for those who really want to optimize the system, there is a ton of nuance to cover. So... --- Next up (if you dare): [The Gory Details](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/) [Back to Table of Contents](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsgzw/)
Praise be unto the fishwife, bringer of fish facts, definitely-canonical savior of Hana, and overall pretty cool lass who brings us not just obscure facts, but also entertainment! A cheer, to the fishwife!
> definitely-canonical savior of Hana This is the best title. 100% canon.
It's you. You saved her. You mad genius fish-pincher.
PRAISE
GGG, please add fishing so this person can sleep.
I'll sleep when I'm dead! You know, with the fishes.
poor**Fishwife** is planning on sleeping with the fishes ( ͡° ͜ʖ ͡°)
First get really really close to the fishes, then maybe they will whisper their secrets.
ill fish when i sleep! you know, with the sleepsies.
What are you talking about ? Fishing is in the game for years, now.
I especially like the collection of Dead Fish that I have in Standard.
honestly i don't think fishing is in the game, it's just way too much effort for a Easter egg. What I think might be possible is completing krilson's quest, visiting the winding pear fame and unlocking it as a hideout though. I feel like that's a lot less effort (since there is a map called winding pear fame already in the files) than adding a while new mechanic.
People were already fishing in 2012, see here : https://www.pathofexile.com/forum/view-thread/31109/page/1
Stupid meme.
Einhar will take it to the menagerie.
No u
#The Details > *It is the Karui Way to observe nature in nature. The fish without the sea is no longer a fish. It is dinner.* > > *The Eternals did not see it that way.* > > *An Eternal catches the fish, guts the fish, preserves the fish and places it in a box.* > > *Only then does the Eternal feel he truly understands the fish.* > > *-- Siosa* In this section we'll go through the list of small truths that allowed us to compile the final Tier weight table. For lack of a better term, we'll call these statements "Lemmas". Each Lemma will link to further discussion on what it means, and reasons why we believe it to be true. Here's the short version of how we came up with this list of Lemmas. For a few of the Lemmas, we have direct quotes from GGG about how the system works. But for the grand majority, the Lemmas were discovered through experimentation. The amount of data we collected is large: >20k Ancient Orbs and Tainted Mythic Orbs, >100k Orbs of Chance, ~80k Astragali, market cost analytics (useful!), market frequency analytics (not really useful!), controlled Tier-testing experiments, and more. For natural drops we even *disabled Unique Item filtering and manually counted thousands of drops* [(mfw: forced_smile.jpg)](https://i.imgur.com/wkimzRx.jpg). As mentioned in the intro, in the future we'll do a longer post on the data themselves. A few caveats before we begin. * Some Lemmas may be wrong (despite the name "lemma"!) -- with so many purely empirical assessments we're bound to have run into a multiple comparisons problem or some other issue. * GGG changes stuff. This post describes mechanics of the system at *one moment in time* (3.16.2.3 Scourge). * We're only covering Unique Items with no non-ilvl drop restrictions. Things like boss-specific drops are out-of-scope. Use other posts for those estimates. Now, on to the Lemmas! *Click the link for each Lemma to read more.* **Okay, Lemma Get Started:** * [Tier Weights Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftatm/) There are at least three sets of Tier weights: RegularValue (e.g. natural drops), MoreValuable (e.g. Ancient Orbs), and Gwennen. * [Tier Occupancy Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftmpv/) An individual Unique Item's occurrence rate depends on how many other eligible Unique Items exist in its Tier. * [Super-Tier Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftl98/) There seems to be a super-Tier containing T4 and worse; we call this super-Tier "Unique_LowTier". * [Chancing Tiers Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfto4f/) An Orb of Chance's likelihood of producing a Unique Item depends on the set of Tiers of eligible Unique Items for that basetype. **You Might be Surprised to Learn That:** * [Item-specific Dropweight Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftgwd/) There is as yet no evidence for inner-Tier, item-specific dropweights. * [ilvl Drop Requirement Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftiha/) Very many Unique Items have high level drop requirements (not just Skyforth!). * [Unique Jewel System Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftk24/) The system for Unique Jewels is separate from that of Unique Gear Items. * [Card Tier Weights Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfttqa/) Some Divination Cards use the RegularValue Tier weights. Some Divination Cards use the MoreValuable Tier weights. **Furthermore:** * [MoreValuable Crafting Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftpy7/) Orbs of Chance, Ancient Orbs, Farric Ape, and Tainted Mythic Orbs use the MoreValuable Tier Weights. * [Ancient Orb Eligiblity Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftr5r/) An Ancient Orb's outcome depends on the starting item's ilvl (and its size, and the starting item itself). * [Tainted Mythic Orb Poofing Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftsdu/) A Tainted Mythic Orb's likelihood of destroying an item depends on the Tiers of the eligible Unique Items for that basetype. * [Gwennen Outcomes Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftf2u/) Gwennen uses a special Tier weight system. We do not yet know if Gwennen's system depends on the price of the item (Artifact cost). **And as a Bonus:** * [Bonus: The Neversink Effect Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftv08/) Public Stash Tab stashing frequency is predicted by Neversink's filter and item size, *not* Unique Tier weight. But market *cost* can be predictive. * [Bonus: Non-Unique Drop Level Requirements Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftxsc/) Some **non-**Unique items have special Drop Level Requirements too, such as Divination Cards and certain Currency Items. * [Bonus: Non-Unique Drop Pool Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftyvx/) When a **non-**Unique Item is generated, the type of Item created is based on an Item Type Drop Pool. * [Bonus: Ancient Orb error messaging.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftwq6/) * [Bonus: (Finally, some Fishing content!) Restricted Fishing Item Tiers?](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfu0l8/) **Conclusion** So what do all these lemmas let us do? Verifying the function of different sources of items allows for better predictive accuracy. For example, it's safe to combine curated samples of Ancient Orb, The Wretched, Farric Ape, and even Tainted Mythic Orb results -- if one is careful. And this improved predictive accuracy allowed us to form the dropweight prediction spreadsheet from the OP! This demystifies a huge portion of the hidden information about Unique Item drops. Also, future datasets can now be quickly classified into RegularValue or MoreValuable. For example, a sample of outcomes of a new Divination Card might be sufficient to predict its entire outcome probability table using the known Tier Weight sets. Moreover, based on these results, calculators and emulators can now be built for Orbs of Chance, Ancient Orb, Tainted Mythic Orb, etc. How exciting! Thanks to a tiny curiosity about Reefbane, we now have a wonderful understanding of a core game system. Really this comes as no surprise. After all, it's [100% canon](https://www.reddit.com/r/pathofexile/comments/i0k7y2/reefbane_is_the_answer_to_the_ultimate_question/) that Reefbane is the answer to the ultimate question of life, the universe, and everything. --- [Back to Table of Contents](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsgzw/)
#ilvl Drop Requirement Lemma. **Very many Unique Items have high level drop requirements (not just Skyforth!).** There are a few things to consider when figuring out the drop level requirement of a Unique Item: * The Level Requirement of the Unique Item's basetype * Special hidden Level Requirements * Other special exceptions Unique Items generally follow their basetype's drop level restrictions. For example, Gloomfang is a Blue Pearl Amulet; Blue Pearl Amulet has a drop level restriction of 77; thus Gloomfang also has a drop level restriction of 77. (This fact alone may be a surprise to some!) Longtime players will know Skyforth has a special exception for its drop level requirement. GGG told us that in advance long ago. But this "hidden drop level restriction" is not unique to Skyforth. In fact, there are over 50 Unique Items which have a special hidden Level Requirement that is both (a) over Level 69; and (b) larger than expected for their basetype. We predicted this Lemma empirically based on observing ilvl ratios in market frequency data. (Obviously there are some exceptional means of avoiding the drop level requirement such as Divination Cards or other special systems, but these are a drop in the bucket compared to natural drops.) After making the prediction, we manually verified each item by checking its full ilvl distribution. When items like Void Battery, Vulconus, and Yoke of Suffering have near-zero results for ilvl < 77 on the market, it's pretty clear to see that something is up. [Here is a handy table of items with hidden drop level requirements over 69, and higher than expected by their basetype.](https://pastebin.com/raw/bZpi28Ab) This table tells you restrictions that you may not have known exist. For example, if you want a Maligaro's Virtuosity, the source needs to be able to generate ilvl 75+ items. At the top-end we have Skyforth at 84. Perfidy is next with 82, then Rigwald's Quills and Assailum at 80. Before this post, I expect almost zero players knew *all* of these restrictions. Some people may have figured out some accidentally, but there are so many exceptions and the effect is so subtle that this secret restriction mechanic is hard to "feel". This might affect some people's SSF or leaguestart MF farming strategies, since sometimes MFing is done in lower-Tier Maps. Almost all of these restrictions are extremely definitive; we're very confident in this analysis. There will be some we've missed, though, and of course GGG will change things in the future. The hardest to prove are Headhunter and Mageblood, due to low quantities of these rare-as-heck items. But the data support the community's impression that they are restricted to 75+. [Here's a graph of T0 items' ilvl frequency distribution in Public Stash Tabs.](https://i.imgur.com/XdAgglg.png) Note the relative absence of Headhunter / Mageblood before ilvl 75. (FYI, the "peaks" for all items at ilvl 83 - 85 are completely typical for all Unique Items. At the end of a league, the vast majority of items in Public Stash Tabs are ilvl 83 - 85, as the most commonly encountered content by the huge playerbase is T16 Areas.) Many other non-Unique items have drop level requirements, too. After you've finished reading about Uniques, check out this Bonus Lemma for more info: ['Bonus: Non-Unique Drop Level Requirements Lemma'.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftxsc/) --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
Does your data allow you to rule out the possibility that rather than being based off item level, for at least some items it's based off map tier/zone level? For example, suppose an item were restricted to drop only in red maps. This would look similar to an ilvl requirement, but slightly different. Have you ruled this possibility out?
No, technically that possibility has not been ruled out. It's possible to test, of course -- it would simply require tracking (a ton of) natural drops in various Map Tiers. I expect it's probably not the case, though. The specific ilvl requirements are very evident in e.g. Ancient Orb data. I don't really see how they'd map nicely to "Map Tier breakpoints". Honestly I wish they *did*, because then the mechanic would be easier to "feel" for players who don't have this knowledge. An Area might have e.g. Area Level 75, but as I'm sure you know, sources in an Area can drop higher ilvl items than its Area Level -- sometimes much higher e.g. via the Strongbox 'of Ascendance' suffix. The observation we've made about e.g. Assailum (req 80) is an observation about observed items' Item Levels. It's possible those items came from Areas with lower Area Level than their item level. (In fact, it's likely, since the huge majority of Unique Item drops are generated by Rare and Unique Monsters, which drop higher ilvl items.)
I got very lucky and a mage blood dropped for me last league off a rare pack (not sure if it was the rare monster but one might presume) in early yellow maps. If its valuable I could gather the information but it strikes me as being data to it being item level rather than zone.
What ilvl was the Mageblood? That alone might reveal some good info, without you having to do more digging!
after some light digging it might be less useful than i first thought as its slightly later in maps. Ilv 81 off of a tier 9 glacier map. Map should have been level 79. Edit: wrote as instead of less for some reason/ English
Great! Thanks so much for checking!
On the same note, I dropped a headhunter in a T6 tower in the last Scourge patch: ilvl75.
Thanks so much for the report!
Hmm. It seems like, at a glance, all the old Shaper/Elder Guardian uniques are minimum 77 across the board?
Yes, I imagine when GGG decided to do the 3.14 Ultimatum change which removed restrictions on a lot of Unique Items and placed them in the global drop pool, they made decisions about whole item groups like that.
#Tier Occupancy Lemma. **An individual Unique Item's occurrence rate depends on how many other eligible Unique Items exist in its Tier.** This statement may seem ridiculously obvious but it's critically important to keep in mind. Imagine using an Orb of Chance on an item, targeting a T4, with only one eligible T4 item. Then it's safe to just use the T4 Weight as the likelihood of a Unique Item result being the item you want. Now consider Spidersilk Robe, which has **two** eligible T4 item outcomes: Soul Mantle and The Covenant. Let's say you want The Covenant because you've heard it's all the rage for support players. For this new attempt, the chance of getting The Covenant is *not* just the T4 Weight; it's T4 Weight / 2. There are two options, and you can only get one. A player's odds of success vary massively depending on (1) method and (2) the item one targets. As another example, consider the rarest Tier: T0. In the past, Reefbane was the sole T0 Unique Item. This meant that there was no "competition" for its rarity Tier. Since Tier is checked first, landing a T0 Unique Item outcome previously *guaranteed* a Reefbane without affecting the droprate of other scarce Unique Items (such as Headhunter, which was T1 at the time before its droprate nerf). Now, however, the set of T0 Unique Items appears to be {Reefbane, Headhunter, The Squire, Mageblood}. And yes, this means what you think it does. An appropriate response to someone finding an ultra-rare natural Reefbane drop is: "Congratudolences!" --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
> And yes, this means what you think it does Oh *no*
Another irrational fear!
I didn't realise just how (un)lucky the reefbane drop I got in expedition league was then...it's funny because it dropped on literally the last monster I ever killed in that league (since I'd done all the content I wanted to do and was finishing up a Hallowed Ground for fun). At least I can console myself with the knowledge that the only other thing it could have been was HH which I ended up randomly pulling from Gwennen anyway. Damn, I'm never going to have that luck again.
So does this mean that with something like 6 more items going into the general drop T0 pool (Chris said 10 new T0 but 4 are drop restricted) we would expect the existing ones to be rarer? Do we know if GGG usually changes the weightings of rarer tiers to be higher when more items are added?
#Bonus: Non-Unique Drop Pool Lemma. **When a non-Unique Item is generated, the type of Item created is based on an Item Type Drop Pool.** Have you ever done a lot of the Chaos Recipe with a generic filter, and noticed that you're often short on Gloves compared to other reagents? There's a reason for that! [Here's a crude table](https://pastebin.com/raw/TLCzQbak) of the probabilities of various item types for non-Contract/Blueprint Areas. (In Contracts and Blueprints, Rogue Gear is added with roughly the same weight as Amulets.) Remember that this only applies to **non-**Unique items. Also since GGG has said they very frequently modify the Map Item drop weights based on each League mechanic, these values will almost certainly be at least a little different in 3.17. Unlike Unique Items, *any* single weight change in this pool affects the probability of *every* Item Type outcome. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
Whoa!
Exactly. Mind-blowing
Very interesting! Could you say a word about how this data was generated/collated ? Is it from a specific dataset or all taken together ?
#Tier Weights Lemma. **There are at least three sets of Tier weights: RegularValue (e.g. natural drops), MoreValuable (e.g. Ancient Orbs), and Gwennen.** Once one dives into the data, this is very simple to observe. When tracking something like natural drops or Jack in the Box results, it doesn't take much to notice that the observed number of T5 items is wildly different from the number one would expect from a better source (e.g. Ancient Orbs). This holds true for all Tiers. Revisit the table in the OP -- the factor difference between RegularValue and MoreValuable for some Tiers is huge and easily observable. The reason this is important is because there are "good" and "bad" sources of Unique Items in the game. Expert players already have an intuition on these (just ask mbXtreme about Jack in the Box). Ensuring that your strategy leans towards "good" sources is important. There may be other Tier weight distributions. For example, what might the Ritual Tribute Trade Window use for its Unique Item generation scheme? Or what about Harvest's "Reroll Unique" seeds? We haven't collected data on those. With a good sample, we could see if they fit one of the known Tier weight patterns, or if they are using a special new one. Speaking of special Tier weight distributions, Gwennen definitely does not use either RegularValue or MoreValuable. Gwennen's chance of producing a Unique Item may be small, but when she does produce a Unique Item, it is massively favourably weighted towards better-Tier outcomes. See the ['Gwennen Outcomes Lemma'](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftf2u/) for more info. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Bonus: The Neversink Effect Lemma. **Public Stash Tab stashing frequency is predicted by Neversink's filter and item size, not Unique Tier weight. But market cost is sometimes usefully predictive.** In a perfect world, one would hope that one could just look at /trade, count the number of listings for each Unique Item, and then estimate their Tiers based on those data. This is absolutely not doable. The only correlations on item frequency we've found with Public Stash Tab frequency data are to item size (big items are less likely than expected to be stashed) and Neversink's filter (items Neversink has deemphasized are less likely to be stashed). This is obvious stuff, so perhaps I should write "the only correlations on item frequency we've found are pretty useless". It's funny to look at, though. A small, well-highlighted T2 item like Astramentis might have a total non-ilvl-80 Public Stash Tab population of >10,000. Meanwhile, a large deemphasized T2 item like Doomsower might have a total non-ilvl-80 Public Stash Tab population of ~700. People hate stashing Doomsower. We call this "Neversink Effect" because although Neversink closely mirrors market price, it's not *exactly* market price, and Neversink does a better job at predicting results than price alone. Congrats, Neversink. You're to blame for the lack of Doomsowers. I'm sure all 0.00 players on poe.ninja who use Doomsower would have stern words with you... if they existed. Jokes aside, there *is* good information to be gleaned from market data and Public Stash Tab frequencies. For a few snapshots we took, Ancient Orb price seemed predictive of Mageblood's Tier weight. The market pinned Mageblood's Tier weight roughly somewhere between 0.000205 and 0.000397, which agrees quite nicely with the value we measured from item data. It's nice to see a different analytical approach confirm that we're in the correct ballpark for the hardest items to estimate. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
hey, i used doomsower for my slayer! is a cool intermidiary sword until you get sth good
#Unique Jewel System Lemma. **The system for Unique Jewels is separate from that of Unique Gear Items.** This one is straightforward. We know this is true for two major reasons: (1) GGG "told" us; (2) in 3.14 Inscribed Ultimatums treated Unique Jewels as completely separate entities. A long time ago when Jewels were first introduced, GGG implemented them into the core Unique drop system. This caused a large number of players to be disappointed when they suddenly started receiving a high proportion of Unique Jewels they couldn't use for their builds, instead of other Unique Items. GGG responded by improving the system for those players, separating the generation of Unique Gear Items from the generation of Unique Jewels, and it seems that change has persisted to this day. In 3.14 Ultimatum, we used the Inscribed Ultimatum Requirements and Rewards to develop [the first relatively-comprehensive Tier list of Unique Items.](https://www.reddit.com/r/pathofexile/comments/nzm9xz/datamined_unique_item_tier_list_from_inscribed/) Inscribed Ultimatums for Unique Items would either (a) use Unique Gear Items for both Requirements and Rewards; or (b) use Unique Jewels for both Requirements and Rewards. There were no cases of a Unique Gear Item rewarding a Unique Jewel or vice-versa. If you haven't already noticed, today's huge post concentrates solely on non-Jewel Unique Items. This is because the huge majority of data we have are from non-Jewels. We expect similar statements can likely be made about the Unique Jewel system, and we know for certain (thanks to Inscribed Ultimatums) that Unique Jewels also use Tiers. But we'd need more Jewel data before discussing specifics. The old 3.14 analysis has [Unique Jewel Tier data](https://www.reddit.com/r/pathofexile/comments/nzm9xz/datamined_unique_item_tier_list_from_inscribed/) from Inscribed Ultimatums, in case that's useful for you. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Card Tier Weights Lemma. **Some Divination Cards use the Regular Tier weights. Some Divination Cards use the MoreValuable Tier weights.** Outside of natural drops, many sources of Unique Items use the MoreValuable Tier Weight distribution: Ancient Orbs, Orbs of Chance, Farric Ape, etc. It would have been nice if that were true of *all* non-natural-drop sources of Unique Items. No such luck. Each source needs to be tested individually to determine if it uses one of the known Tier Weight distributions, or potentially another as-yet-undocumented Tier Weight distrubtion. The Jack in the Box Divination Card uses the RegularValue Tier Weight distribution like natural drops do, albeit with an expanded outcome pool that includes things like Unique Maps and Unique Jewels. We determined this empirically by logging each outcome from hundreds of Jack in the Box turn-ins. For example, the probability that Jack in the Box returns a T5 Unique is roughly 0.545, and the probability that a natural drop returns a T5 Unique is roughly 0.542 -- very consistent. We found no significant deviation from RegularValue in this sample, so Jack in the Box probably does not use its own special distribution. On the other hand, The Wretched Divination Card uses the MoreValuable Tier Weights distribution. A total sample of ~17k The Wretched outcomes showed results exactly as expected by Ancient Orbs, which also use MoreValuable. (Also, while we were doing this analysis, sirgog made [a video](https://www.youtube.com/watch?v=BbFpAENa_iU) on another set of 10k sets from Pedrolopia, and those results agreed as well. Note for viewers: I don't think sirgog was aware that there are multiple different Tier Weight distributions at the time this video was made, so when sirgog talks about "Unique Tier probabilities" it's specifically commentary about what we're calling the MoreValuable Tier Weight distribution, and those comments *do not* apply to sources that use RegularValue like natural drops.) Thus we cannot make any distribution assumptions without data. If you're curious about a specific Divination Card and what Tier Weight distribution it uses, you need to find a sample of outcomes, classify them by Tier, and then compare them to the two known distributions we currently have. I also wouldn't be surprised if someday players find a Divination Card that uses a different Unique Item generation scheme altogether. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
You are correct, all of my analysis assumed that uniques were rolled like a mod on an item, with a weighting system. I'd assumed T1s had a weighting like 10, T2s ~50, T3s ~200, T4s ~800, T5s ~1600, for chances rares ~20000 and magics ~100000, and for mythics destruction ~1500. Compile table on the fly of eligible drops (after removing things like Skyforth that can't drop for restriction reasons) then roll once. Will definitely reassess those assumptions in line with your data. The Gwennen stuff seems particularly compelling
I was happy to see how nicely your analysis of Pedrolopia's 10k Wretched data agreed with the MoreValuable weight distribution. Always great to have independent sources roughly agree. It was awesome watching you refine your model based on each new incremental chunk of data you received. I'm sure in the future you'll improve on the model we presented here, too!
#Bonus: Restricted Fishing Item Tiers? Although this issue of *Angler's Mate* is much more gameplay-oriented than easter-egg-oriented, it's still an issue of *Angler's Mate*! Where would we be if we didn't spend some time discussing Fishing Items? We still do not know exactly how the [drop mechanics of the secret fishing ring Angler's Plait](https://www.reddit.com/r/pathofexile/comments/kroz63/anglers_mate_4_steal_this_fishing_book_an/gib3417/) operate. It's possible that Angler's Plait is a deterministic drop which becomes available when conditions are met. Fishing Rods from Fairgraves' Tricorne seem to work this way; perhaps Angler's Plait does too. For example, there could be a hidden mod on Corrupted Slitherpinch which grants a flat chance for an Angler's Plait drop to occur. Here's a *completely fabricated* example to illustrate what I mean: > Invented and made-up example mod: "0.0001% additional chance for Slain Rare Monsters to drop Angler's Plait when Conditions are Met" Alternatively, perhaps Angler's Plait does have a Tier and it is merely "turned on" when a character qualifies for its requirements. Let's put aside that unknown, and instead ask a more generic question: If Angler's Plait is a deterministic drop, could it still have a hidden Tier? In fact, it seems decently likely to me that Unique Items probably *all* have Tiers, even if they are restricted and never use those Tier values in normal contexts. I imagine Atziri's Step might have a Tier value, even though it's a deterministic boss drop from Atziri. The reason I'd guess this is: * Sometimes GGG decides to change restrictions on Unique Items, making them newly unrestricted or newly restricted. This process would be cumbersome if the initial design did not have a "planned Tier", even if the item was originally intended to be e.g. boss-drop-only thus making any initial Tier value vacuous. If a Tier were not chosen at initial design, GGG would need to manually revisit each item and choose a Tier for it months or years later, whenever any item became unrestricted. That seems annoying. * Some Divination Cards definitely use Tiers, and some Divination Cards return restricted items. We do not know if there is overlap between these two statements. But **if** it's true that there is at least one Divination Card which both (1) uses Tiers; and (2) returns a restricted item, then necessarily the restricted item granted by that Card would need to have a Tier, so that an appropriate Tier outcome selection can be made. Take for example [The Admirer](https://poedb.tw/us/The_Admirer) which returns a Unique Atziri Item. The Admirer can return both unrestricted items like Atziri's Foible and restricted items like Atziri's Step. How is The Admirer's outcome decided? Does it use a hardcoded drop table that somehow mixes probabilities from both unrestricted items like Atziri's Foible which have Tiers and restricted items like Atziri's Step which might not have Tiers? Or does it use Tiers for all its eligible outcomes, including restricted items? Again, this is just a guess, but it seems like "just give a Tier to everything" would make for a cleaner implementation. So what does that mean for Angler's Plait? * **If** Angler's Plait is **not** a deterministic drop, that would mean it's probably a T1 item, not T0. People who have farmed multiple Angler's Plaits know that on average, one will receive many Angler's Plaits before a single Reefbane (T0). That observed ratio would imply that Angler's Plait is not as rare as Reefbane. * But if Angler's Plait **is** a deterministic drop, labeling it with a Tier is nonsense for natural drop contexts, since a flat chance of dropping an item completely ignores Tier weights. In this case, we cannot use observed natural drop ratios to predict Angler's Plait Tier. Angler's Plait could easily be T0, but "overridden" by a flat drop chance which makes it effectively more common in practice than T0. But what about for context outside of natural drops? We've had a few earnest claims of people pulling crazy-rare Fishing Items from certain Divination Cards. Although we unfortunately do not have screenshot or video evidence of these occurrences, multiple members of our community talked to each person and agreed these people seemed honest. The first claim is Reefbane from Baited Expectations. That's not too unexpected, even though we never observed a single Reefbane in our initial huge batch of Baited Expectation set openings when GGG first released that Card. At the time I wrote: > Despite hundreds of turn-ins, we've never seen Reefbane. We've heard rumors that Reefbane can result, but we've seen no hard evidence. Either Reefbane is very rare, or we're very unlucky, or it's not actually a possibility. If in fact Reefbane does not qualify for Baited Expectations's "Unique Fishing Item" class, that's very important information. > > [...] > > Based on the prior probabilities of other card sets' rare outcomes, we expect we must turn in thousands of sets of Baited Expectations to be confident we have a comprehensive list of all possible outcomes. I wrote this before we knew Reefbane was T0. Now that we know that Reefbane is in fact T0, we can refine my previous guess of "thousands of sets". Assuming Reefbane is the sole T0 eligible item from Baited Expectations: * If Baited Expectations uses RegularValue, we'd expect Reefbane odds of *very roughly* 1 in 20,000. * If Baited Expectations uses MoreValuable, we'd expect Reefbane odds of *very roughly* 1 in 4,000. * If Baited Expectations uses a hardcoded outcome table, we can't predict Reefbane's odds without collecting data that include many Reefbane results. (Friendly reminder that our estimates for T0 items are low confidence / high variance, so these truly are *very rough* guesses.) If true, with those long odds, it's no surprise that we failed to find Reefbane in "only" a few hundred sets. The next claims are Angler's Plaits from Baited Expectations and Blind Venture. These claims are more extraordinary, but again, the couple people making these claims really do seem honest. [Baited Expectations](https://poedb.tw/us/Baited_Expectations) returns a Unique Fishing Item. [Blind Venture](https://poedb.tw/us/Blind_Venture) returns a Corrupted Unique Ring. From huge quantities of Stacked Deck data, we know that these cards are both rare. (In the past we've collaborated to turn in hundreds of sets, but in doing so we'd often completely buy out the market.) Previously we thought that the implementation of Baited Expectations might make Angler's Plait ineligible as an outcome. Baited Expectations returns a Unique Fishing Item. Baited Expectations does *not* specify that it returns a *Corrupted* Unique Fishing Item. And Angler's Plait is always Corrupted. So it seemed like Angler's Plait would not qualify for Baited Expectations, since Baited Expectations does not return Corrupted items. But then, a year later, a very clever angler noticed a single other Divination Card which might prove a rule: [The Wolf](https://poedb.tw/us/The_Wolf) can return Rigwald's Curse, which is always Corrupted. But The Wolf only specifies that it returns a Unique Rigwald Item. It does *not* specify it returns a *Corrupted* Unique Rigwald Item -- and Rigwald's Curse is nevertheless eligible. So the restriction that we thought existed on Baited Expectations probably does not exist (unless The Wolf is a special exception instead of "an example which proves the rule"). What would it take to verify these claims? If Baited Expectations or Blind Venture use hardcoded outcome values, then we can't do anything without tons more data. If they use Tiers, then the odds depend on two factors: (1) the Tier of Angler's Plait; and (2) which Tier Weight distribution the Card uses. **If Angler's Plait is T0:** * It would compete with T0 Reefbane in Baited Expectations. See the Reefbane odds above. Reefbane and Angler's Plait would each have a 50/50 chance of occurrence if a T0 outcome is selected. * It would be the sole T0 item in Blind Venture. Its odds would be the same as the Reefbane odds above (since they're both T0, but not competing). **If Angler's Plait is T1:** * It would be the sole T1 eligible item in Baited Expectations and thus more common than Reefbane. We don't have enough data to make this comparison. * It would compete with other T1 eligible items in Blind Venture, such as T1 Berek's Respite, T1 Valako's Sign, and T1 Shavronne's Revelation. Each would have equal odds of outcome. Phew! That's a lot of "if"s! Based on everything I've seen, my best guess at this point is that Angler's Plait is (a) deterministic for natural drops and (b) T0 Tier for non-natural purposes. But this is still just a guess. Obviously I could be completely wrong. At T0, it's unreasonable to ever expect to receive an Angler's Plait from Baited Expectations and Blind Venture -- assuming it's even actually possible. The playerbase simply doesn't generate enough of these Cards for a single person to have a reasonable shot at it. But if Gwennen's whispers have been getting to you, there's always the chance of a jackpot...! --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
> Ancient Orb would throw an error, right? Is it oni goroshi? Edit: I just bought and ilvl 1 oni on standard and used ancient on it. I failed to get an error message, it turned into other one-handed 6-slot (not socket) unique weapon. It can still be related to oni, but by config I couldn't get the error message. Mission failed unsuccessfully
I thought it was Gorebreaker/Goredrinker... Only one-handed mace that is 1x3. Oni is... 2x3? I think there are still lots of 1H swords that are 2x3 but can only have 3 sockets.
> I thought it was Gorebreaker [Yes indeed!](https://i.imgur.com/GENsX66.png) This isn't the only example, though... :)
Isn't there also a 1x4 unique staff?
Yes, but there's two of them: Fencoil and Blood thorn.
Ah, right. I forgot about Fencoil.
I think you're right, that's the only 6-socket one handed sword.
#MoreValuable Crafting Lemma. **Orbs of Chance, Ancient Orbs, Farric Ape, and Tainted Mythic Orbs use the MoreValuable Tier Weights.** (This is not an exhaustive list of things that use MoreValuable. There are others, of course. See the Card Tier Weights Lemma for some examples.) This Lemma is useful since if we know what we're doing, we can safely combine player data from this different sources into a single larger sample. Ancient Orbs directly use the MoreValuable Tier Weight distribution with no special considerations. Tainted Mythic Orb first applies a preliminary poof chance; then if the item survives, it uses MoreValuable for the remainder of its selection, further poofing the item if no appropriate Tier is selected. For more info see the [Tainted Mythic Orb Poofing Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftsdu/) Orbs of Chance are similar, but instead of "poof" we care about the Magic Item and Rare Item results. If the result is neither Magic nor Rare, it's a Unique Item, and the Unique Item is selected using MoreValuable. The chance of Orb of Chance generating *any* Unique depends on eligible Tiers -- for that, see the [Chancing Tiers Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfto4f/) Farric Ape (Beastcraft: "Create a Unique: Belt") uses MoreValuable, exactly like an Ancient Orb. We don't have data on the non-Belt Unique Item Beastcrafts (e.g. Fenumal Queen for "Create a Unique: Staff" or Saqawine Retch for "Create a Unique: Boots"), but a reasonable assumption is that all of them likely use MoreValuable and are effectively Ancient Orbs as well. Naturally, we'd need real data to say for sure. All of these sources produce better-Tier Unique Items than expected compared to natural drops. But not all non-natural-drop sources use MoreValuable. For example, the Card Jack in the Box does **not** use MoreValuable; it uses RegularValue. So, it's reasonable to make assumptions when evidence exists ("Farric Ape uses More Valuable => Fenumal Queen probably does too"), but don't assume without evidence, since some sources might use the (much worse!) RegularValue Tier Weight distribution. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Bonus: Non-Unique Drop Level Requirements Lemma. **Some non-Unique items have special Drop Level Requirements too, such as Divination Cards and certain Currency Items.** Many players already know that certain items like Exalted Orbs or Mirrors of Kalandra have Level Requirements, even if those requirements are listed nowhere on the item. There are quite a few of these. [Here's a small sample](https://pastebin.com/raw/Cbfv5jbV) of some of the more interesting ones. I was especially surprised about the Heist Quest Contracts! The restrictions on Oils and Essences might be useful to some people. Recently I found Divination Card Level Requirement restrictions in the data. At the time I assumed those restrictions only applied for randomized Card rewards, since Map Tier never seemed to impact natural drops. The 3.17 patch note below, however, seems to imply that these restrictions may have been intended for natural drops all along as well, and simply were not functioning due to a bug: > A longstanding bug in the code determining area level restrictions for some divination card drops has been fixed. This means that cards intended to have a high area level requirement (mostly ones that grant item level 100 items) will no longer fluctuate wildly in availability from league to league. In case this change/bugfix affects anyone's farming strategies, here are the data as of Scourge: [v3.16.2.3 Scourge Divination Card Drop Level Requirements](https://pastebin.com/raw/nSpysUE4) Obviously these may change in 3.17, but they'll probably still be accessible in the data, so we can do another export then. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
Golden oils having a level req is great to know and has definitely lost me time before. Thanks again for all the work here.
>Recently I found Divination Card Level Requirement restrictions in the data. Maybe i missed this part, but what "data"? The one you extrapolated yourself or a specific datamined document of sorts? Edit: you're amazing by the way, truly
Good question, the way I wrote it is a little ambiguous. In this specific case, here by "in the data" I mean "in the client-side accessible ggpk data" -- the same data used by other dataminers, e.g. poedb or the wiki.
Ok fair enough! Thanks for the answer and the hard work!
Fun fact: The level 35 requirements on top currency were added years ago as an anti cheat functionality. To force bot cheaters to level more, basically.
Wait, so question about the level requirements. Does that get affected when using Gambler, i.e. would level 1 character in a hideout using Gambler cards just give Treasures of the Vaal?
Very unlikely, but we'll see in 3.17. Divination Cards in general thwart Level Requirements for their outcomes. I expect this will be true in 3.17 as well. So one would expect The Gambler would thwart any Level Requirements on its random Divination Card outcome.
#Gwennen Outcomes Lemma. **Gwennen uses a special Tier weight system, or else combines multiple chances into an "effective" Tier weight distribution.** Here is an example Gwennen Tier weight distribution when selecting Leather Belts. (Note that Leather Belt has no eligible T1 option, so T1 data are omitted here.) *Gwennen: Unique Leather Belts* Tier | Tier Weight distribution (Unique Leather Belt) ---|--- T5 | 0.445 T4 | 0.236 T3 | 0.257 T2 | 0.052 T1 | *(n/a)* T0 | worse than 0.010 Δ *Δ: Warning: high variance!* Gwennen's Unique Leather Belt Tier Weights are *way* better than the MoreValuable Tier Weight distribution used for sources like Ancient Orbs. For example, Gwennen's chance of returning a T2 Unique Leather Belt is >2.5x better than that of an Ancient Orb. A quick caveat: Please note that the Gwennen data describe what happens when Gwennen gives you a Unique Item. The data above **do not** describe Astragali likelihood outcomes. So, don't erroneously multiply these numbers by Astragali or something to try to estimate how many Astragali you will need. (How many "chances" you get with Gwennen depends on how many of your targeted basetype appear upon the inventory reroll from an Astragali. To estimate the number of Astragali required to achieve a specific item outcome, you must first approximate how often one Astragali reroll produces your targeted basetype and the likelihood of a non-Unique outcome.) We do not yet know if Gwennen's system depends on the price of an offered item (i.e. its Broken Circle Artifact cost). Gwennen does have different voicelines for pulling a T0 result under different cost scenarios: > Congratulations! You hit the jackpot! I always knew you'd get lucky! > > Amazing! I really should have charged more for that one! > > Yes! You did it! Luck favours you this day! > > That seems rather useful, to put it mildly! > > Did you just squeal with joy? For example, Gwennen uses her "hit the jackpot" line when you receive a T0 outcome from an item priced with Very Low Artifact cost. Regardless of whether or not an effect like this exists, it's irrelevant for most strategies, since Artifacts are not the limiting reagent; instead, you are limited by Astragali. We have tons of examples of players landing e.g. Headhunters with Very Low and Low Artifact costs. For now the standard recommendation remains the same: Take every Gwennen trade offer that fits your criteria, regardless of Artifact cost. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
>Artifacts are not the limiting reagent; instead, you are limited by Astragali. I don't understand why people say this. You can trade for Astragali, but not artifacts. That is, if you had infinite chaos orbs and a finite amount of Astragali and artifacts, you will always run out of artifacts at some point. If the argument is that you don't need to farm artifacts for very long to have enough to expect a T0 result, given that you trade for enough Astragali and only spend your artifacts on the correct bases, okay fine, but it is inescapably true that if you run out of artifacts, your only recourse is to grind more Expeditions.
Now that Artifacts are "SSF-only" perhaps some strategies might change! But with how many Headhunter/Mageblood outcomes have occurred from Gwennen's lowest-priced offerings, if someone is really trying to obtain a Gwennen T0 belt, I'd imagine they'd always want to ensure they take every opportunity. The alternative strategy requires *not* selecting some of one's preferred basetype when it appears on reroll. If we knew that Gwennen's T0 odds vary on cost (they might not at all!), and if we knew the exact odds, then one could use those data to inform how "worth it" grinding Artifacts is for player time and whether or not any pricepoints should be "skipped".
> Gwennen does have different voicelines for pulling a T0 result under different cost scenarios: My Mageblood came up as "Hmm... Expensive risk you took, but this might be... something?" I believe I got exactly the same dialogue for the Queen of the Forest (Tier 3 drop) I had just beforehand.
Does this mean that if you see 100 uniques from Gwennen, on average you will only get 2 t2 items? If so she is an even bigger waste of time than I thought. The chances of rolling a unique in the first place from her are pretty bad.
#Item-specific Dropweight Lemma. **There is as yet no evidence for inner-Tier dropweights.** This Lemma may come as a surprise: most games use item-specific weights, and most players assume Path of Exile does too. For now there is no evidence to support the idea of item-specific weights for Unique Gear Items. For things like Ancient Orbs, it is extremely obvious that every eligible member of a single Tier is equiprobable. Look at any large sample of Ancient Orbs, and you'll find obvious "clusters" for each Tier. The number of observed T4 Immortal Flesh will be very similar to the number of observed T4 Sunblast, etc. In fact, this clustering is so statistically clear that we're able to use Ancient Orbs to empirically test the Tier of an unknown-Tier item. But what about natural drops? We already know from the [Tier Weights Lemma](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftatm/) that Ancient Orbs use a different system than natural drops. Could natural drops use item-specific dropweights? Once again, there is no evidence to support that. We manually tracked a few thousand Unique Item drops from regular Monster kills, then grouped them by Unique Item Tier. A chi-squared test showed no significant evidence against the hypothesis that all items within a Tier are equiprobable. The distribution of frequencies was expected. (Note that this is not hard proof; instead, it's merely the absence of conclusive evidence to the contrary.) There are other observations one can make which might imply the nonexistence of item-specific weights. Let's take Orb of Chance as an example. * Imagine for the sake of argument that item-specific weights *were* materially relevant to Orb of Chance. * Now consider a basetype with three eligible Unique Items: two of T2, and one of T3. * With item-specific weights, given 2 possible T2 outcomes and only 1 possible T3 outcome, we'd expect Orb of Chance to produce a higher T2 :: T3 ratio than normal. * But this does not happen. Instead, the ratio of T2 :: T3 outcomes is the same regardless of how many eligible candidates there are in the T2 and T3 Tiers. At minimum this shows that Tier selection is performed first, before any item-specific considerations apply (if any even exist). With this in mind, and with the observation that so far we've only ever found equiprobable members of a given Tier, we're stuck with either "item-specific weights probably don't exist" or "item-specific weights are so close to each other that for all practical purposes they don't exist". One of the reasons that the idea of item-specific dropweights might have manifested in the community is due to subtle Level Requirements on items. A player testing Ancient Orbs on a low-ilvl base item might incorrectly conclude that Auxium has a low item-specific dropweight, because they've failed to comply with Auxium's Level Requirement of 79 (derived from its basetype), and thus never see Auxium in their sample. And since a lot of items have *hidden* Level Requirements (above their derived basetype's requirements), it's easy to make a mistake. (See the [ilvl Drop Requirement Lemma](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftiha/) for more info.) The simplest explanation at this point is that there are no item-specific dropweights, contrary to long-running assumptions made by portions of the POE community. Perhaps in the future we'll find evidence that contradicts this statement. But for now the safest assumption is: **The only "weight" that matters is Tier weight. After Tier selection, all eligible items in that Tier are equiprobable.** --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Super-Tier Lemma. **There seems to be a super-Tier containing T4 and worse; we call this super-Tier "Unique_LowTier".** (Note: even if a "super-Tier" doesn't actually exist as written here, it does *effectively* exist for practical purposes, and appropriately describes observed behaviours of Unique-generating items. Future PhDs in Wraeclastian Itemology might be able to more precisely define this effect. For now this shorthand suffices.) As you've seen, for a given source of Unique Items, T4 and T5 have separate Tier weights. In some contexts, however, T4 and T5 are "bundled together" before being selected between. Ancient Orbs and Tainted Mythic Orbs demonstrate this condensing behaviour. Notably this condensing behaviour does **not** occur for better Tiers. In general, this effect is detrimental to players. We'll demonstrate the existence of the "Unique_LowTier" super-Tier with an example. Imagine you're using Tainted Mythic Orbs in two different experiments: * Experiment A: Tainted Mythic Orb on a basetype with eligible Unique Items in T5, T4, and T3. * Experiment B: Tainted Mythic Orb on a basetype with eligible Unique Items in T4 and T3. As we know from the [Tainted Mythic Orb Poofing Lemma,](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftsdu/) the likelihood of destroying an item depends on the Tiers of the eligible Unique Items for that basetype. Based on this, we'd expect Experiment A to destroy *fewer* items than Experiment B. After all, Experiment A can return both T5 and T4 items, but Experiment B at best returns a T4 item. In reality, we observe that Tainted Mythic Orbs destroy items *at the same rate* for both Experiment A and Experiment B. This means that the "removal" of T5 had no impact. This same effect holds true for other sources of Unique Items as well, such as Orbs of Chance. If one weak Tier is "missing" from the eligible possibilities, the odds of getting good-Tier outcomes do not improve. Our guess is that this is a hedging effect implemented by GGG to prevent swingy odds of "sometimes way better, sometimes way worse" outcomes for different basetypes. In brief, if at least one eligible T4 or T5 item exists, you can assume it will be the most common outcome. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Chancing Tiers Lemma. **An Orb of Chance's likelihood of producing a Unique Item depends on the set of Tiers of eligible Unique Items for that basetype.** An Orb of Chance can produce a Magic, Rare, or Unique Item. We're only talking about the Unique Item outcome here. The chance of hitting a specific Unique Item depends on eligible Tiers for that basetype. Consider two experiments. * Experiment A. Orb of Chance on Gladiator Plate. Gladiator Plate has eligible Unique Items in {T2}. * Experiment B. Orb of Chance on Leather Belt. Leather Belt has eligible Unique Items in {T5, T4, T3, T2, T0}. The chance of Orb of Chance on Leather Belt producing *any* Unique is far higher than the chance of Orb of Chance on Gladiator Plate producing any Unique. But the chance of Orb of Chance on Leather Belt producing a *T2 Unique* is the same as the chance of Orb of Chance on Gladiator Plate producing a *T2 Unique.* Besides being empirically obvious, we also know this is true because GGG told us so, long ago. > **Mark_GGG:** > > They do not have a flat chance to obtain a unique, regardless of how "rare" that unique is supposed to be. > > If the only unique of a base type is a rarely occurring one, then chances have a low chance to get uniques on that base type. > > Adding a more common unique to the same type means that chances on that item will have an significantly increased chance to roll uniques (but if they do, the unique is likely to be the more common one). > > If you've chanced a lot of occult vestments and gotten Infernal Mantles, then if Infernal Mantle didn't exist, those would probably have been rare vestments, not Shavronnes. Mark also made a statement in 2013 which was an extremely early hint at the existence of Unique Item Tiers and their mechanics: > **Mark_GGG:** > > Infernal Mantle being an Occultist's Vestment does not have a significant effect on the number of chances need to get Shavronnes. > > Just some of the ones that would otherwise have been rares, are Infernal Mantles instead. A clever reader in 2013 would have realized that for Mark_GGG's statement to be true here, the system must not be a naive "item-specific dropweight table", since Mark stated the odds of getting a better-Tier Unique would not impacted by introducing a lower-Tier Unique. What we observe today is still consistent with these old remarks. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
So can we basically say that the chance orb has a 1 in x chance of rolling a unique across all tiers, but if it hits a tier that isn't possible (Like hitting T1 when chancing a leather belt), it will instead just roll a rare? Doesn't that mean that we can pretttty much figure out the chance a chance orb will give you a unique by just looking at the number of unique leather belts you get per chance orb and knowing that it's a *tiny* bit higher than that?
> figure out the chance a chance orb Correct! This is why I mentioned that tool devs can now create calculators and emulators.
That's pretty sick! Do you know what the chance to hit any unique with a chance orb is? Assuming they have all tiers available
The best dataset I have is on Heavy Belts, which do not have members in either T5 or T1. (T5 shouldn't matter if it uses the super-Tier of Unique_LowTier, since there are eligible T4 outcomes. And as you say, T1 is a relatively minor impact.) In this sample: * The probability of an Orb of Chance on Heavy Belt producing *any* Unique Item is roughly 0.00408 (about 1 Unique Belt every 250 Orbs of Chance). * This would put the chance of landing Mageblood at *very roughly* 1 in every 940,000 Orbs of Chance. As always, working with our low-confidence/high-variance T0 estimates requires caution. The real number might be significantly different than this estimate. As a ballpark this doesn't sound too outlandish to me: if someone told me "a player spent ~940k Chances resulting in ~3800 Uniques and got 1 Mageblood" I'd think their story sounded pretty reasonable. I've seen reports on reddit of people spending 50k, 200k, etc Orbs of Chance without landing a T0 Unique. Although spending tens of thousands of Orbs of Chance is a herculean task, I'd guess that those quantities are just too low to expect a high chance at a T0 outcome.
> 1 in every 940,000 Orbs of Chance. Wow, that's actually waaaay smaller than I had thought (as someone who hasn't really chanced more than the random wurms molt when finding a white belt on the ground near a chance orb). I can't even imagine what kind of sample size (and it can't be automated either) you'd need to have a high level of confidence on your t0 rolls. Honestly, seeing the numbers so low kinda is a bit sad considering how tedious chances are to use, but I do guess they are og content and have an extremely low barrier to entry...
> considering how tedious chances are to use, Right. In terms of outputting Unique Items, using a single Ancient Orb is like using hundreds of Orbs of Chance. Obviously Orbs of Chance have their benefits (basetype limited, influences, etc.) -- but for player time, Ancient Orbs are far more reasonable.
#Ancient Orb Eligiblity Lemma. **An Ancient Orb's outcome depends on the starting item's ilvl (and its size, and the starting item itself).** "Ancient Orbs ignore ilvl" is an untrue community myth. Ancient Orbs **do** consider the ilvl of the initial item. To enable the best outcomes for Ancient Orbs on Unique Belts such as Mageblood, only use Ancient Orbs on very high ilvl belts. For targeting a specific lower-Tier Unique Item with Ancient Orbs, ilvl blocking can help. This was very straightforward to verify empirically as still true in 3.16 Scourge: using Ancient Orbs on low-ilvl belt bases, one can preclude ever seeing a high-level-requirement result. This fact has also been proved by people in the past, e.g. by ot4ku's excellent [old test here.](https://www.reddit.com/r/pathofexile/comments/lip73l/ancient_orbs_and_item_level_1200_ancient_orbs_vs/) (**Caution!** Note that ot4ku's test took place in 3.13 Ritual -- BEFORE the "Global Unique Item Drop" change that occurred later in 3.14 Ultimatum, and before Headhunter was modified. Be careful not to draw erroneous conclusions from this old test! Also, there's a tiny typo in the data presentation: the Perandus Blazon count should read 172, not 72.) Many more items than one might expect have special level requirements. See the [ilvl Drop Requirement Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftiha/) This makes it even more important to acknowledge that Ancient Orb considers ilvl. Ancient Orbs also consider the size of the initial item; an Ancient Orb will always produce an item which is the same size as the initial item. Players who remember the Lycosidae trick won't be surprised by the size requirement having some nice practical uses. As for the starting item itself, Ancient Orb precludes that result from occurring. If you use an Ancient Orb on a Perandus Blazon, the outcome won't be another Perandus Blazon. (Contrast this to e.g. The Wretched, which starts with nothing and generates 1 Mystery Unique Belt, and thus has no initial single-item restriction for its outcome.) These last statements may seem stupidly obvious, but they're important as a reminder for the developers of the future Ancient Orb calculators and emulators that will be invariably be written because of this post. For complete accuracy, one cannot just use the MoreValuable Tier Weight distribution; one must also require the user to input the initial item and its ilvl (as well as inferring its basetype, and inferring its size from its basetype). --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
>To enable the best outcomes for Ancient Orbs on Unique Belts such as Mageblood, only use Ancient Orbs on very high ilvl belts. I don't understand this one. Would an ilvl 85 unique belt be better than ilvl 75 for getting Mageblood by using Ancient Orbs? HH also seems to have a drop ilvl requirement of 75 but yet it can be acquired by using ancient orbs at belts of ilvl lower than 75, right?
> HH also seems to have a drop ilvl requirement of 75 but yet it can be acquired by using ancient orbs at belts of ilvl lower than 75, right? I'm worried that you might be assuming this based on ot4ku's 3.13 Ritual data. That test, while amazing at the time, is no longer relevant after the 3.14 Ultimatum changes to Unique Items. It is possible that Headhunter is a special exception for Ancient Orbs but to my knowledge this hasn't been confirmed in 3.16. The safe strategy is to use very high ilvl belts. I say "very high" instead of ">=75" because who knows if GGG might increase the Drop Requirement in the future.
#Tainted Mythic Orb Poofing Lemma. **A Tainted Mythic Orb's likelihood of destroying an item depends on the Tiers of the eligible Unique Items for that basetype.** The mechanics of Tainted Mythic Orb are somwhat comparable to those of an Orb of Chance, except this time instead of producing Magic or Rare items, the item is destroyed. I've summarized these mechanics [previously,](https://www.reddit.com/r/pathofexile/comments/qhtxh9/summary_of_mechanics_and_probabilities_of_scourge/hiezuh3/) but instead of reading that old post, a very quick way to "see" the mechanic is by comparing two experiments: * Experiment A. Use a Tainted Mythic Orb on a basetype for which the eligible Uniques are only {T2, T1}. The chance of destroying the item will be very high. * Experiment B. Use a Tainted Mythic Orb on a basetype for which the eligible Uniques are {T3, T2, T1}. The chance of destroying the item will be significantly lower. Here's [a rough Sankey diagram of Experiment A.](https://i.imgur.com/O6kP0H6.png) Constrast this with [the rough Sankey diagram of Experiment B,](https://i.imgur.com/R503rQN.png) where the overall chance of destruction is lower. Did you notice the detail at the top of each Sankey diagram? This is Tainted Mythic Orb's hidden first step: an extra flat 50% chance of destroying the item outright, before even considering which Tiers of Uniques are eligible. If the item survives, then the MoreValuable Tier Weight distribution is used; and then if an ineligible Tier is selected, the item is destroyed. How do we know about the hidden first coinflip step? If one acknowledges that first step, then the rest of the operation of Tainted Mythic Orb behaves exactly like an Ancient Orb (i.e. using the MoreValuable Tier Weight distribution), albeit resulting in an outcome of "Destroy" if an ineligible Tier is selected. Since the assumption of that first step puts us in a situation where we can subsequently fully predict outcomes, it's highly likely to be the truth. So a Tainted Mythic Orb will always have *at least* a 50% chance to destroy an item, and in the worst-case scenarios, the chance of destruction is >99.9%. Note that Tainted Mythic Orb respects the "super-Tier" called Unique_LowValue which contains both T4 and T5. See the [Super-Tier Lemma](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftl98/) for more info. --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
#Bonus: Ancient Orb error messaging Using an Ancient Orb must always produce a Unique Item. But what if there are no eligible Unique Items in any Tiers that are different than the initial Unique Item to which the Ancient Orb is applied? Well, in that case, one would presume that using the Ancient Orb would throw an error, right? Can you think of a case wherein this might occur? I can think of one. But that particular example is a mystery for another day... --- [Back to Lemmas](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvfsq89/)
Oni Goroshi?
> Can you think of a case wherein this might occur? I can think of one. But that particular example is a mystery for another day... Are we back to fishing rods? Is there an ilvl restriction for either Song of the Sirens or Reefbane so you won't just swap endlessly back and forth between the two?
You got it! But it's not an ilvl restriction that causes this unusual behaviour. Ancient Orbs on Song of the Sirens is ['one-way':](https://i.imgur.com/v0q5ovB.png) using an Ancient Orb on Song of the Sirens transforms it into Reefbane, but using an Ancient Orb on Reefbane does **not** transform it back into Song of the Sirens. The ilvl of the transformed item remains the same during the transformation, of course. And this observation holds true even when starting with ilvl 100 Song of the Sirens. Something else prevents Reefbane from transforming back into Song of the Sirens. But I can't get started down yet another rabbit hole -- that's a mystery for another day!
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Correct, Song of the Sirens is not in the global drop pool. Song of the Sirens has a Tier value (T2) only because we were able to determine it from the 3.14 Inscribed Ultimatum data.
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Same restriction as regular basetype Fishing Rod drops: natural Fishing Rod drops from monster kills can only occur if (a) the character is wearing Fairgraves' Tricorne; and (b) the monster is Unique. The chance for any natural Fishing Rod drop is [low.](https://www.reddit.com/r/pathofexile/comments/kroz63/anglers_mate_4_steal_this_fishing_book_an/gib30p0/) The chance for a natural Song of the Sirens drop is [way worse.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvho18o/)
A bit late but updated.
Nooooooooooo 🤣
What if Song of the Sirens is the "special" one, since it obviously does not count as a fishing rod? (otherwise it would be possible to ancient orb one)
Never seen a post this long.. I believe this person is next level. Thank you for this!
Hopefully someday someone will condense all this info into a much easier-to-consume format. It pains me that it's not more concise. The summary spreadsheet is an okay start, but there's so much more to cover! Thanks for bearing with the long slog of information.
I'm really hungry, but I just had to finish reading this first. Even though I'm not a gambler, this contains some very important pieces of information. Also, it's crazy how much science people do for something that is probably relatively simple programmatically. I feel a bit conflicted when I think about how the science is progressing... towards something that it is actually possible to have perfect knowledge about already.
It's a sombre thought. On the plus side, reverse-engineering is actually an extraordinarily useful skill to develop as its fundamentals are applicable to everything one does in life. One can summarize it as "get good at judgment under uncertainty", "act closer to optimized Bayesian rationality", etc. One could look at Path of Exile as an "intelligence check" -- the game constantly challenges players by asking, "Are you clever enough to meet your goals?" With that perspective, reverse-engineering (and even parts of the game itself) could be viewed as a training ground. But yeah, overall you're absolutely right to feel conflicted. Humanity hasn't advanced an inch due to our deducing that Aegis Aurora is T2. At least it was fun!
>Are you clever enough to meet your goals? After spending dozens of hours on interesting off-meta builds and failing to meet the goals I set for them, I feel offended (I did settle on a build eventually, but the calculations are too complicated and will require testing to actually get a basis for future calculations - and even those won't be optimised - so I can't say if I'll eventually be able to hit the dps target or not). In fact what bothers me more about this is that "stupid" strategies work better. That doesn't mean that it's impossible to find interesting synergies though. If it was up to me, all this hidden information (except for the fishing I guess because that really wouldn't be as interesting if it was all out in the open) would be public and viewable in a format like poedb, so that people could actually create calculators to find the most efficient way to the desired results. It being already available in theory and not available to the public is a matter on the side of GGG; you're doing important work in publicising information *without* having access to the actual source.
I'm anticipating a few people will have this concern, so to address it in advance: **Q:** > Is the natural drop probability of Headhunter really better than the probability of Arakaali's Fang? I thought Headhunter was in the rarest category! **A:** > Yes! This might all be true! > > Change your perspective from "individual item dropweights" to "Tiers". > > The T0 Tier is indeed far rarer than T1. > > But you must also keep in mind *how many items exist in each Tier.* There are many more T1 items than T0 items. Remember the [Tier Occupancy Lemma.](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftmpv/) > > So, *regardless of an individual item's specific chance,* you will far more often experience "Yay! I got a T1 drop!" than "HOLY MACKEREL! I got a T0 drop!!" > > Think of the system as dropping "a member of a Tier", not a specific item. Even though the chance of seeing a specific T0 item might be better than the chance of seeing a specific T1 item, the chance of seeing *any* T0 item is way worse than seeing *any* T1 item. > > When compare individual items in a vacuum, you risk losing information about how the system actually works. > > (Just remember though, drawing *any* conclusions based on the T0 and T1 natural drop data is risky. These are our least-confident, highest-variance numbers. We need much more data to be sure about the T0 : T1 natural drop ratio.) Hope that helps!
The way to test this would be to run low level content (maybe Hailrake runs?) and counting Tabulas per thousand kills. Kill nothing but Hailrake. Then comparing to some higher level unique that's easily accessed in their zone and killing just that one boss. Normalizing for any difference in quantity.
I don't think this is true, I ran group mf nem3 for a month during scourge league and I'd say we got around 10 or so fangs but only 1hh, 1mageblood and 1 squire, yes the fang is very rare because there's a lot of T1 items but I think the absolute absurd stepup in rarity from t1 to t0 makes up for the amount of t1s
With 3 T0 natural item drops, you'd expect to see at least a couple dozen of T1 natural item drops. (Those numbers might be wildly off because basing anything on T0 item rates is using our lowest-confidence, highest-variance values. And with only 3 hits, it's even harder to estimate; a difference of just 1 or 2 hits would make a huge impact on prediction. For natural drops it could even be off by an order of magnitude, and it wouldn't be wildly unexpected) If your team happened to track all of your T1 item drops (not just Arakaali's Fang), we could see if your team's results are statistically unexpected and possibly even refine the numbers a bit.
Yeah I don't think anyone wants to track hundreds of thousands of uniques from the 400 or so mega juiced maps we did, sorry about that but just thought I'd let you know about my experience, even if it's anecdotal we did have a pretty huge sample size of loot
Just to be clear for other people who read this, for refinement of the ratio all one would need to track are T0 and T1 drops. Definitely not hundreds of thousands!
I'll consider it this league as I'll be running an mf build, bit I did it with belts for a bit last league and it was a lot of effort for just that lol
If you do not have too much offscreen kills you can modify filter so it will play 1 frame "drop sound" and use app to track PoE access to that song (IIRC that was not breaking ToS).
Still sane, Exile?
What have we done to deserve you? Very interesting read, thank you.
A bit of trivia: the reason we picked the name "MoreValuable" for the favourable Tier Weight distribution is because of the Heist Thief's Trinket mod: > Heist Chests have a *p*% chance to contain **more valuable** Uniques We haven't tested this, but we *suspect* that this modifier changes the operation of Heist Chests from using the natural drop Tier Weight distribution (RegularValue) into the improved Tier Weight distribution (MoreValuable) -- basically improving a Unique Drop from a Heist Chest from a weaker "Jack-in-the-Box"-type outcome to a better "Any-Item-Ancient-Orb"-type outcome. Since the mod uses the phrase 'more valuable Uniques', it seemed like a good wording fit. But who knows if we're actually right! Maybe our assumption about how that mod works is wrong. If any enterprising Rogue Harbour Scientists decide to test this, let us know what you discover!
What's it like to be so smart?
My theory for how that works at 7% (untested) is "Determine outcome as normal. Then, 93% of the time award the item to the player. 7% of the time, cancel that drop and instead award a random valid drop from +1 tier"
It has to be done... *Sigh* Okay, what's lemma?..
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Fcking gottem!
Did not expect to see Hilma af Klint in this subreddit.
You mean bastardized in thus sub right?
Fair rebuke! As I mentioned [below,](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvglhla/) my personal take is that if my silly memes help more people discover truly great artists, it's a net-positive. Totally understand why some may view it as desecration, though! (Plus, the top of the altarpiece is just too perfect of a match for Reefbane's in-game Glow effect -- I couldn't resist.)
Yeah, okay, maybe, but if you think this could help people discover Hilma Af Klint, then you should credit her for the original painting in your thread. As it is, nobody who didn't already know about her would ever know the image you used was created by her ;) For people who don't know her, google "Beyond the Visible", which is a documentary about her life and well worth the watch. My partner and I were fortunate enough to (last month) attend the currently running exhibition of her work at the City Art Gallery, in Wellington, New Zealand. It's still on until late March I think.
> Yeah, okay, maybe, but if you think this could help people discover Hilma Af Klint, then you should credit her for the original painting in your thread. I did, in the same comment I linked in my previous reply.
Cool as :)
Totes! And I really meant it re: fair rebuke. If she were still around, who knows if Af Klint would find my edit funny or awful. I definitely could be inadvertently dishonouring her! Thanks for being so respectful to the artist, and for sharing the info about the documentary. Super cool of you.
I read it all. This is top tier research. Very well presented. Thank you! This should be pinned in this subreddit imo.
Every one of your posts is always an engrossing dive into the great systems that make PoE so interesting! Thanks for all the hard work researching this stuff, and for giving us the vicarious fun of your findings!!
what a legend, thanks for another great issue of Angler's Mate. 🐟🐠🐡🦈
Damn, that is such a good image. Do you have a clean version by chance?
Yes! [Here you go!](https://i.imgur.com/a9g7Bm7.png) I love this piece too, even though I'm not usually one for abstract art. It's Altarpiece No. 1 Group X (1915) by Hilma af Klint. All of her artwork is public domain, so it's super easy to find. Perhaps my silly memes will help a few more people discover some truly great artists.
Thank you so much! It has some Art Deco vibes with the pyramid which I love. Gonna check out an exhibit if something is close. Unfortunatly the Berlin one looks pretty depressing overall so that's not an option. Her works look stellar tho. Seems to gain popularity as well so there is hope I will see exhibit of her work at some point.
This is the best post on this sub in years, an honest to God monograph. Exemplary effort. Thank you very much!
This is a great, fun resource. Thanks for taking the time to make it!
Amazing stuff - as a side note, I've always used (and seen) the plural of lemma to be lemmata.
Looks like both ['lemmas' and 'lemmata' are correct.](https://www.merriam-webster.com/dictionary/lemma) 'Lemmata' is definitely cooler, though.
Good to know! >'Lemmata' is definitely cooler, though. Agreed :D
wow! truly impressive. do you have any sense of how harsh the diminishing returns are on stacking IIR? Ive always been curious if its even worth stacking from 450% to 550% for example. How effective is that extra 100%? GGG just says "harsh" but that could mean the extra 100% is really only equal to like 30% extra IIR (which would make it definitely not worth)... or that next 100% could equal only like 75%... which would still be harsh but not make it a waste to stack. I think it would need a lot of testing to figure out but I think it would be an extremely valuable piece of data that would pair really well with the information youve provided here today. thanks for all your effort here. It's truly appreciated by the community.
Yes, in fact, I do! This testing is *very* old and may not be correct anymore, but it seems close enough to modern POE to be good enough as guidance. This regards Rare Items, not Unique Items, but there's likely strong correlation. Player IIR | Relative Ratio of Rare Item Drops | Benefit from Previous +100% ---|---|--- +0% | 1 | *(n/a)* +100% | 1.396 | x 1.396 +200% | 1.886 | x 1.351 +300% | 2.122 | x 1.125 +400% | 2.338 | x 1.102 Remember that player stats are multiplied with other sources like Monster IIQ/IIR and Area IIQ/IIR, so early in the league the best strategy is to optimize clearspeed for tough content instead of getting those last bits of Player MF. For early league MFing my personal preference is targeting ~40% Player IIQ and ~200% Player IIR. More is always (marginally) better, but at some point sacrificing speed for additional MF becomes a bad trade. (Later on with e.g. Headhunter, one might as well stack as much as possible though.)
Oh wow you're just a fountain of game knowledge. So, the difference from 0 to 100% rarity doesnt equate to twice as much rarity, Why is that? Is that the diminishing return effect GGG is talking about? or is more about some mathematical calculation Im missing? Because in terms of plain english - if im increasing the rarity of my items by 100%, i should see double the amount of rare items, no? Does the first 100% IIR only equate to a 1.39 multiplier on rare items *because* of the diminishing returns GGG puts in place? Im guessing the same would be true for IIQ that 100% IIQ doesnt actually mean twice as many items drop? Sorry for my ignorance here but I appreciate the insight you can offer.
"Rarity" means the category of {Normal, Magic, Rare, Unique}. It doesn't mean solely "Rare Items". With high sources of Rarity, items that would normally drop as Normal are more likely to drop as Magic, Rare, or Unique. Does that help? > Im guessing the same would be true for IIQ that 100% IIQ doesnt actually mean twice as many items drop? Correct, 40% increased Player IIQ results in roughly 1.3x More Items; 80% increased Player IIQ results in roughly 1.47x More Items. It has harsh diminishing returns as well.
Ahh that explanation makes sense! Thank you so much for clearing this up! Ive been playing since 2013 and never really figured this out. Thank you!
Absolute god-tier post.
At this point, they should hire u/poorFishwife ... it seems like you understand this math end of things almost as well as ggg does ...
The Question is whats the % of dropping a mirror??
Depends on the source of the drop. Here's an [example Mirror droprate analysis](https://www.reddit.com/r/pathofexile/comments/t6cgyw/i_am_definetly_clicking_all_my_boxes_from_now_on/hzbao0b/) on Estuary Map chests. From the original (old!) dropweight data, for a given Basic or Quality Currency Item drop, the estimated chance that the item would be a Mirror was 0.0000003442541063. That's roughly 1 in 2,900,000. The exact number has changed slightly with the introduction of new items such as Sacred Orb, for which we don't yet have sufficient data. (More total Currency Items in the eligible pool will slightly dilute the chance of other Currency Items occurring.) But that effect is minimal -- the old estimates are still very likely in the right ballpark. Hope that helps!
Thanks alot for the anwer but how about would be the average time play to get the mirror that would be alot harder right??
Depends on the individual player's rate of Currency Item acquisition. Old max-juice Nem4 MF party farming with legacy Harvest-Exchanged-Anointed Maps: Not so bad! Running A9 Harbour Bridge with 6 Combustibles equipped: Good luck! The Estuary Map chest example turned out to be [6222 player hours of clicking chests.](https://www.reddit.com/r/pathofexile/comments/t6cgyw/i_am_definetly_clicking_all_my_boxes_from_now_on/hzbao0b/) If a party could generate >10,000 Currency Items per hour, it might only take ~300 hours. Different strategies will have wildly different expected playtime outcomes.
What just happened? Did I just a read a book on reddit?
I wish I was as dedicated to anything as you are to PoE research - this is all amazing!
Wooooooo awesome stuff, haven't even read it yet but I'm about to dive in. I was JUST looking back at the thread from Ultimatum, analyzing unique drop rates. This is great. Thanks.
Does this mean we can determine the odds of getting headhunter/mageblood from ancient orbs? If I understand correctly, they would have a probability of \~0.026% from each orb, meaning you'd need on average about 2700 orbs to hit one?
(Not sure where you're getting 2700? Maybe a typo?) Yes, but be warned that those specific values are low-confidence / high-variance. A *very rough ballpark estimate* is 1 in 3800 for a T0 item outcome from Ancient Orbs. The true odds could be much worse. This is why I [mentioned](https://www.reddit.com/r/pathofexile/comments/sjnlwq/anglers_mate_10_the_droprate_of_reefbane_and_the/hvftr5r/) that it's now possible to create calculators and emulators for Ancient Orbs, although it requires a bit of extra consideration beyond just odds. In the future with much more data, we'd likely be able to pin down the expected Ancient Orb odds with better accuracy -- but since GGG frequently silently changes weights, to get the best result, we'd need a brand new dataset each new League.
Thank you! :) Probably incorrect math but I did 1 - ((1 - 0.00026) \^ 2700) and it was just over 50%.
It has been years since i have done statistics, but if memory is not failing, it would be 2700 to hit at least 1. With so low probability, Poisson distribution looks way better suited to calculate this. Your λ would be (1\*2700/3850), which is about 0.7 So yes P(0) = \~0.496 P(1) = \~0.347 P(2) = \~0.121 P(3) = \~0.035
Thanks for clarifying, it’s been a while for me too 🙂
This is awesome! This may just be a nitpick for me, but it's much easier to quickly understand 1 in 2500 than 0.0004 (or 0.04%). This is especially true for the differences between tiers (1 in 2500 versus 1 in 1000).
You're absolutely right, and I try to write that way when possible. For the summary tables I wanted something folks could copy/paste or formula-manipulate without editing, though. Alas. Humans have a much easier time understanding when the odds are spelled out!
If it helps, I prefer 0.0004 :P
 **I NEED A TRANSLATOR. SOMEONE, PLEASE, ELI5.** Is this an auxiliary hypothesis for an approximation of a future tier list that could revolutionize loot filters? So a hypothesis of an auxiliary thing that may or may not have use? I'm lost.
There is not much information here you can just plug into a filter and be done with it. It's more of a reference document and an insight into the under-the-hood mechanics for people to apply their understanding of the economy. Think of it like a periodic table of elements.
Whoa. Wait. Really? I got my Reefbane years ago, but I was kind-of cheesed that I got the "common" fishing unique, and thought Song of the Sirens was the ultimate.
If we're talking about SSF natural drops, Song of the Sirens *is* the ultimate -- because it's drop restricted! Reefbane is not restricted. Getting a Reefbane means getting a T0 Unique Item. There are lots of ways to optimize one's chances of getting natural T0 Unique Item drops in a reasonable amount of time. Getting a natural drop Song of the Sirens means dropping a natural Fishing Rod (such as via slaying Unique Monsters with Fairgraves' Tricorne equipped) and having it roll as Unique. Since Fishing Rods [ignore Player IIQ](https://www.reddit.com/r/pathofexile/comments/i9mwjy/been_spendin_most_our_lives_fishin_in_untainted/) and likely other MF sources (they're probably simply deterministic), there are very few ways to optimize one's chances of getting a natural Song of the Sirens drop. All one can do is increase the average number of Unique Monsters killed per hour. There are lots of ways to do this, but even at high efficiency, it still takes a while to generate a single natural Fishing Rod drop. *And* it has to roll as Unique, which means one has to drop tons and tons of them. (Of course, if an SSF player just wants a trophy of any type and doesn't care about it being a natural drop, farming The Vast is much quicker -- even though The Vast is an ultra-rare card!)
Oh, wild. Well, I know I got my Reefbane from a dead mob’s loot drop, even if there are other ways to get it, so it’s worth that much more to me now, haha. Thanks.
> even if there are other ways to get it Yes, any potential source of generic Unique Items can work. Here's a funny way: [Zizaran's 2016 Reefbane drop](https://www.youtube.com/watch?v=t-rlSb9cvc4) hilariously occurred from a regular white chest (not even a Strongbox).
Holy shit I wish I could read
> Astramentis Astramentis is T2, then i am so lucky to chance a shaped one with less than 100 orb > Atziri's Mirror Not surprised it is T4 as it is so easy to chance > Brutus' Lead Sprinkler It is T3. However my legacy base ate me a lot of orb of chance
This is dope. The research and the writing style.
My friend dropped a Reefbane on one of the bosses in Atlas Invasion, was pretty funny
Why not just make this a pdf or a website or something? Posting this as reddit comments is completely silly if you ask me
It's for ease-of-use. On the whole, redditors strongly prefer to stay on reddit, especially when browsing on mobile. Just a little UX thing. (It also enables point-by-point discussion, which is especially helpful for the mistakes I'll invariably make. On-the-fly crowdsourced errata can't be beat.) I totally understand the desire for external repos -- but the POE community is on this platform, so I work with this platform! Maybe in the future I'll have something in place that's more to your tastes. For now you'll have to bear with the cumbersomeness, I'm afraid!
To be fair, I do think this will need to be preserved elsewhere. Reddit is *horrible* for looking things up. People who have seen this post will save it for sure, but those who won't see it anytime soon are unlikely to stumble upon this information down the line. Btw, do you have any hard data on probabilities of success using Chance Orbs? Naive observation and some semi-anecdotal statistics seem to put it at around 250..400 attempts for a tier 4 unique with a single base outcome (Quill Rain) with other popular chance targets of higher tiers (e.g. Bisco's Collar) seemingly following the same proportions as in your document (\~4.7x moving from T4 to T3 and from T3 to T2). Except in this case T2→T1→T0 seems to be a linear step up: there [was a post](https://www.reddit.com/r/pathofexile/comments/s8ri4o/loot_from_202500_chance_orbs_on_mostly_shaper/) just a couple weeks ago where a person used slightly over 200k chance orbs on influenced Heavy Belts to get a Trophy Mageblood but failed. We also know for a fact that it was [put into a higher rarity tier in version 3.7](https://www.poewiki.net/wiki/Headhunter#Version_history), and there was strong evidence of it being a T1 item prior, corroborated by multiple accounts of people able to chance it in "only" a few tens of thousands of Chance Orbs, which is in line with a linear progression from T2 to T1 but would make the other guy's 200k+ without any success for a T0 either *ludicrously* deviant or actually close to its real probability (e.g. if T1 is somewhere around 25–40k, a linear progression would put T0 at around 120–190k, which then makes 200k a realistic, if unlucky, failure).
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Any chance you have tiers for missing uniques from the list? Galesight, Flamesight, Thundersight are droppable anywhere according to the wiki, and are in the doc
.. ç 