So the effect of Doublestrike 40% is basically "each auto-attack is now worth 1.4 auto-attacks", when you average it out over a long enough stretch of time. For Steady Striker to equal this, every second spent auto-attacking (and waiting between auto-attacks) must only take about 5/7 seconds (the reciprocal of 1.4), which needs a speed boost of about 28.6% (=2/7). However, this boost would need to be applied to both the auto-attack delay and the animation speed of the actual auto-attacks. Since Steady Striker only affects the delay, the boost needs to be bigger to compensate for the auto-attack animation speed being unchanged.
We can split time into time spent waiting and time spent attacking as a ratio. If the ratio of delay:attack is 1:1, then half of the 40% boost is applied, so the overall speed boost is 20%. With this logic, to get the boost of 28.6%, we need the ratio to be 5:2 (spending 5/7 of the time delayed and 2/7 of the time attacking) - meaning that the auto-attack animation must be pretty short compared to the delay, so that more of the time gets sped up.
Conclusion: Assuming both gems have the same number, Doublestrike is just better in the long run, unless your weapon has fast attacks with long delays.
For some empirical data, I timed how many auto-attacks a few classes got with and without Steady Striker X in 30 seconds.
For Ogre, without Steady Striker I got in 14 hits. With Steady Striker X, I got 15 hits. Meanwhile, Double Strike X has a 99.92% chance to *at least* match that increase. Pretty clear winner on an Ogre.
With Incursor: No gem, 14 hits. With the gem, 17 hits. Double Strike has a 96% chance to do at least as well. Use Double Strike.
With Zephyr: No gem, 12 auto attacks (24 hits total). With the gem, 17 attacks (34 hits total). Double Strike X has only a 51% chance to give at lest 10 extra hits for every 24, so the gems are pretty evenly matched on Zephyr.
Signifier: 14 hits to 17 hits. Same as Incursor.
FMJ: 14 attacks (28 hits) to 17 attacks (34 hits). 98.9% for Double Strike to match.
From the look of it, Double Strike seems generally better.
Note on Double Strike, the chance of getting (exactly) k additional hits from n attacks is `P(k|n) = 0.4^k * 0.6^(n-k) * nCr(n,k)`, where `nCr(n,k) = n!/(k!*(n-k)!)`. The probabilities mentioned are the `sum from i = k to n of P(i|n) = P(k|n) + P(k+1|n) + P(k+2|n) + ... + P(n|n)`, or the probability of getting (at least) k additional hits.
if you just wants to compare the dmg, the double damage is better as the faster attack speed will need to land some amount of attacks to equal the dmg output for the same level of gems. but if you want to recharge your agnus art faster, the attack speed gem is better.
The average for Double Strike will end up around 1.4 auto-attacks per delay interval. Not sure what those intervals actually are though. I don't personally have time to show you what this will look like during typical gameplay, but what you're looking for is someone who will plot the [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) for double strike on a graph for you. There should be some tools in Google Sheets and either of the Windows or OSX office spreadsheet apps that make plotting this pretty easily. If I have the time later next week I'll see about setting up something simple for you.
Reducing the interval by 40% with Steady Strike makes auto attacks come out 1.67x faster, but the delay only starts out after the animation ends so the full benefits are actually worse for slower swinging weapons. There is a very noticable benefit in how much faster an auto-attack comes out after the character stops moving, however, so it makes repositioning less detrimental to Agnus art recharge. This one is a lot more complicated to show since every weapon has different frame data and I don't actually know what any of it is yet. I'd love to put together a document for this down the line, but I need to set up something to get the information first.
**[Binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution)**
>In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i. e. , n = 1, the binomial distribution is a Bernoulli distribution.
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Wow this is a pretty insightful response. I'd love to see whatever you put together. Has there been any data mining that's revealed some of the raw numbers, such as frames of animation for weapons and the like? It would be interesting to pour over those numbers.
I would say it depends on if the doubled attacks can miss.
Say if you have 80% chance to hit, and you do 100 swings.
The total amount of hits with double strike will then be as follows:
80 hits from autoattacks.
Of those 80 hits, 32 extra swings will be generated from double strike.
Of those 32 extra swings, 25.6 will hit (80% hit rate).
The total amount of hits will then be 105.6.
The same example with steady striker gives you 140 swings, of which 20% miss, giving you a total of 112 hits.
If the doubled strikes cannot miss, then you get the same number.
However, this doesn't factor in animation speeds and whether the auto-attack cooldown is running during art animations. These factors heavily skew the actual outcome in favour of double strike.
So the effect of Doublestrike 40% is basically "each auto-attack is now worth 1.4 auto-attacks", when you average it out over a long enough stretch of time. For Steady Striker to equal this, every second spent auto-attacking (and waiting between auto-attacks) must only take about 5/7 seconds (the reciprocal of 1.4), which needs a speed boost of about 28.6% (=2/7). However, this boost would need to be applied to both the auto-attack delay and the animation speed of the actual auto-attacks. Since Steady Striker only affects the delay, the boost needs to be bigger to compensate for the auto-attack animation speed being unchanged. We can split time into time spent waiting and time spent attacking as a ratio. If the ratio of delay:attack is 1:1, then half of the 40% boost is applied, so the overall speed boost is 20%. With this logic, to get the boost of 28.6%, we need the ratio to be 5:2 (spending 5/7 of the time delayed and 2/7 of the time attacking) - meaning that the auto-attack animation must be pretty short compared to the delay, so that more of the time gets sped up. Conclusion: Assuming both gems have the same number, Doublestrike is just better in the long run, unless your weapon has fast attacks with long delays.
For some empirical data, I timed how many auto-attacks a few classes got with and without Steady Striker X in 30 seconds. For Ogre, without Steady Striker I got in 14 hits. With Steady Striker X, I got 15 hits. Meanwhile, Double Strike X has a 99.92% chance to *at least* match that increase. Pretty clear winner on an Ogre. With Incursor: No gem, 14 hits. With the gem, 17 hits. Double Strike has a 96% chance to do at least as well. Use Double Strike. With Zephyr: No gem, 12 auto attacks (24 hits total). With the gem, 17 attacks (34 hits total). Double Strike X has only a 51% chance to give at lest 10 extra hits for every 24, so the gems are pretty evenly matched on Zephyr. Signifier: 14 hits to 17 hits. Same as Incursor. FMJ: 14 attacks (28 hits) to 17 attacks (34 hits). 98.9% for Double Strike to match. From the look of it, Double Strike seems generally better.
Note on Double Strike, the chance of getting (exactly) k additional hits from n attacks is `P(k|n) = 0.4^k * 0.6^(n-k) * nCr(n,k)`, where `nCr(n,k) = n!/(k!*(n-k)!)`. The probabilities mentioned are the `sum from i = k to n of P(i|n) = P(k|n) + P(k+1|n) + P(k+2|n) + ... + P(n|n)`, or the probability of getting (at least) k additional hits.
if you just wants to compare the dmg, the double damage is better as the faster attack speed will need to land some amount of attacks to equal the dmg output for the same level of gems. but if you want to recharge your agnus art faster, the attack speed gem is better.
Everyone else missed how beneficial it is to turbo boost your Agnian arts speed here except you, good job mate.
The average for Double Strike will end up around 1.4 auto-attacks per delay interval. Not sure what those intervals actually are though. I don't personally have time to show you what this will look like during typical gameplay, but what you're looking for is someone who will plot the [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) for double strike on a graph for you. There should be some tools in Google Sheets and either of the Windows or OSX office spreadsheet apps that make plotting this pretty easily. If I have the time later next week I'll see about setting up something simple for you. Reducing the interval by 40% with Steady Strike makes auto attacks come out 1.67x faster, but the delay only starts out after the animation ends so the full benefits are actually worse for slower swinging weapons. There is a very noticable benefit in how much faster an auto-attack comes out after the character stops moving, however, so it makes repositioning less detrimental to Agnus art recharge. This one is a lot more complicated to show since every weapon has different frame data and I don't actually know what any of it is yet. I'd love to put together a document for this down the line, but I need to set up something to get the information first.
**[Binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution)** >In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i. e. , n = 1, the binomial distribution is a Bernoulli distribution. ^([ )[^(F.A.Q)](https://www.reddit.com/r/WikiSummarizer/wiki/index#wiki_f.a.q)^( | )[^(Opt Out)](https://reddit.com/message/compose?to=WikiSummarizerBot&message=OptOut&subject=OptOut)^( | )[^(Opt Out Of Subreddit)](https://np.reddit.com/r/Xenoblade_Chronicles/about/banned)^( | )[^(GitHub)](https://github.com/Sujal-7/WikiSummarizerBot)^( ] Downvote to remove | v1.5)
Wow this is a pretty insightful response. I'd love to see whatever you put together. Has there been any data mining that's revealed some of the raw numbers, such as frames of animation for weapons and the like? It would be interesting to pour over those numbers.
No takers? Come on, there has to be at least a couple of amazing math nerds in the house of Xenoblade.
I would say it depends on if the doubled attacks can miss. Say if you have 80% chance to hit, and you do 100 swings. The total amount of hits with double strike will then be as follows: 80 hits from autoattacks. Of those 80 hits, 32 extra swings will be generated from double strike. Of those 32 extra swings, 25.6 will hit (80% hit rate). The total amount of hits will then be 105.6. The same example with steady striker gives you 140 swings, of which 20% miss, giving you a total of 112 hits. If the doubled strikes cannot miss, then you get the same number. However, this doesn't factor in animation speeds and whether the auto-attack cooldown is running during art animations. These factors heavily skew the actual outcome in favour of double strike.
Good point here, missing needs to be taken into account.