Iksar Shaman - Solo Challenges?

[bcbrown]

None of those other calculations use binomial distributions.

Originally Posted by 7thGate [You must be logged in to view images. Log in or Register.]

BCBrown is correct in his analysis.

[DeathsSilkyMist]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

None of those other calculations use binomial distributions.

Yes, they do. Hit/Miss chance is a coin flip, for example. If the mob has 20 swings per fight, you would do a binomial distribution of 20 coin flips to determine damage done to the player.

Again, if you want to do the binomial distributions for all of the variables in the fight, go for it! I am using the normal distribution for simplicity's sake in my examples. You do not get to set one variable to binomial while leaving the rest as normal.

[bcbrown]

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

Yes, they do. Hit/Miss chance is a coin flip, for example. If the mob has 20 swings per fight, you would do a binomial distribution of 20 coin flips to determine damage done to the player.

Hit/miss is bernoulli/binomial, but the damage itself is a multivariate distribution, as there's a separate calculation of actual damage upon a hit. I've been told that this calculation draws from a uniform set of 20 discrete numbers.

Originally Posted by 7thGate [You must be logged in to view images. Log in or Register.]

For DD procs, you can just do a straight average of PPM * damage per proc to get expected damage per minute, because the timing doesn't change it at all. This is because with each success valued the same regardless of sequencing, the mean of a binomial distribution is just the probability of success * number of swings, and the PPM system sets the probability of success such that this always comes out to the number of PPM.

This is not the case with a DOT proc because every proc is not equally valuable, you have to calculate the contribution each branch makes to the average individually and sum them to get the correct average. BCBrown is correct in his analysis. I have no idea why you're just averaging the timing and assuming that's correct when there's a nonlinear impact from the different samples in the distribution.

[DeathsSilkyMist]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

Hit/miss is bernoulli/binomial

There you go!

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

Of course miss rate and proc rate both work the same. They're both a property of an individual swing. Why can't you answer this question? Do you understand the words I am using?

You also agree that Hit/Miss and Proc Rate are the same.

Literally the only difference between the two is the percentage. Hit/Miss is 50%, Proc rate is 10.4% in our example.

I am using a Normal Distribution for damage on all variables. You are trying to change the proc damage to a binomial distribution specifically, while leaving all of the other damages as Normal Distributions.

[bcbrown]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

the damage itself is a multivariate distribution, as there's a separate calculation of actual damage upon a hit. I've been told that this calculation draws from a uniform set of 20 discrete numbers.

[DeathsSilkyMist]

Originally Posted by bcbrown [You must be logged in to view images. Log in or Register.]

I've been told that this calculation draws from a uniform set of 20 discrete numbers.

Indeed! In the case of Ionat:

[44, 54, 64, 74, 84, 94, 104, 115, 125, 135, 145, 155, 165, 176, 186, 196, 206, 216, 226, 237]

In the case of Scourge:

[40, 64, 88, 112, 136, 160, 184, 208, 232, 256, 280, 304, 328, 352, 376, 400, 424, 448, 472, 496, 520, 544]

Both calculations use a percent chance for success, and both calculations use a uniform set of discreet numbers.

[7thGate]

Originally Posted by DeathsSilkyMist [You must be logged in to view images. Log in or Register.]

Indeed! In the case of Ionat:

[44, 54, 64, 74, 84, 94, 104, 115, 125, 135, 145, 155, 165, 176, 186, 196, 206, 216, 226, 237]

In the case of Scourge:

[40, 64, 88, 112, 136, 160, 184, 208, 232, 256, 280, 304, 328, 352, 376, 400, 424, 448, 472, 496, 520, 544]

Both calculations use a percent chance for success, and both calculations use a uniform set of discreet numbers.

Sourge also has 0 as an option, for when you don't proc at all. Ionat's damage does not.

You're also not correctly taking into account the weighting for the probability of landing on each element, which for scourge is computed using the formula BcBrown gave and for Ionat is a complicated, opaque mitigation formula that involves AC being rolled vs. Attack. Your DPS estimate on Ionat also seems to be both ignoring the impact of base attack rate and the impact of AC, but I think that those are errors in opposite directions that are cancelling to a large extent (Ionat probably attacks more than once a second at base, and you've mentioned they hit on the bottom half of the damage interval twice as often as the top).

You could parse either of these to estimate statistical properties of the distributions like average damage done, but its much harder to do with Scourge because its timing depenent, so you're looking at parsing out one specific proc at a location in a fight vs. N attacks over the course of a fight with Ionat. That reduces your sample size considerably leading to greater estimation error and makes it much harder to actually do the parsing code.

We also have the actual formulas for how procs work with Scourge, where the formula is both substantially more complex and substantially less certain for a mitigation roll (its over here https://github.com/EQEmu/Server/blob...ttack.cpp#L913 , but there's damage table and other stuff going on outside this function and to my knowledge noone has done an analysis demonstrating this is unchanged on P99)

Procs though, we know those have a set chance to proc per swing which is set to a % that will lead to an average of 2 procs per minute at max dex. That lets you easily define the binomial distribution for the proc outputs and solve for the various statistical properties like average damage or variance in closed form rather than having to attempt an estimate like you do with attack damage.

[DeathsSilkyMist]

Originally Posted by 7thGate [You must be logged in to view images. Log in or Register.]

Sourge also has 0 as an option, for when you don't proc at all. Ionat's damage does not.

Ionat has a 0 option too. The zero option is not hitting with the weapon swing. Both swinging a weapon and procing a weapon have a hit hance. At 1 PPM you will get 1 proc per minute on average. For Hit/Miss you will hit with half of your swing attempts on average.

BcBrown and yourself continue to be incorrect in the idea that you cannot use a Normal Distribution for DoT procs. I am using infinity for all calculations in my JBB example. You cannot simply change one variable to a finite number of swings to lower the DPS of one variable in a set of Normal Distrubution variables.

If you want to use the precise formulas and binomial distributions for all of the variables, I would love to see it!