Dexterity's impact on critical hits

[Masamune]

wow that's fast cdf o.O

Have an event right now, gotta stop, i'm now @ 1301/13006=10.00% @ +-0.516% error.

(5.02% on ExtraAttacks BrutalEar btw XD)

Next will be dDEX=10 this night, lets see tomorrow...

[ringthree]

Note: i got intimidated with my CrimCuisses, which confirms the DRG job.

Actually, that just confirmed the Dragon Killer job trait, it doesn't confirm the DRG job itself.

[willriker]

Slight Derail.

:O time to go cap my weapon skill levels on goldfish while i sleep! and without any 3rd party tool. LMAO too awesome. They are like fortifications now. Can skill up at 0 risk if you can find a 1 dmg weapon and get your STR low enough.

I swear you guys are like the space program. You go to check one thing out, but many more, accidental, discoveries are made in the process.

[Byrthnoth]

You can't skill up with hits for 0 damage. They nerfed that a while back. People used to skill up their weapons on sleeping monsters that way.

dDex of 8 = 10% Crit rate now? (-9% from Merits/Base = 1%)


PS. Has anyone ever confirmed the 5% crit rate base?

[Masamune]

dDex of 8 = 10% Crit rate now? (-9% from Merits/Base = 1%)

Yes, but Pchan plans to verify if the jump actually occurs earlier @ dDEX=7.

PS. Has anyone ever confirmed the 5% crit rate base?

That's what CDF is doing atm.

For info, Sham intends to deal with the region dDEX=[39;48], considering the super high-end large choice of gears he has at his disposal XD (while having lolmithra str /joking <3 mithras :Q___ )

So that let us still a lot of points from dDEX=10 to 38.

I'm launching dDEX=10 this night.

[Byrthnoth]

Sweet. Why are we convinced that it isn't linear and uses whole % numbers now?
It seems likely to me that it could go up by increments of ~0.4% or even 0.1% if it's floored.

We know that Critical Hit rate max is 100% due to Mighty Strikes. It's likely that they're working in a x/256 or x/1024 system, so their units are likely something like: 100/256 = ~.4% 100/1024 = ~.1%

[Deadgye]

This is making me want to reactivate my account again, lol. I have the lolstr and gear to hit almost all the ranges for ddex 0-50 while still having a fstr of -1, but I never got around to doing it before school started up again. Oh well, even if I don't it's still my amazingly awesome and lazy testing method we're using. :3

[Masamune]

Yea all credits to you Deadgye for putting that method up after all this time ^^

Why are we convinced that it isn't linear and uses whole % numbers now?

Because so far we had only a few points in range dDEX=[15;40] from which we extrapolated a "fitting" regression line, which were pointing almost exactly @ point [dDEX=5;crit=9%].
So i tested with Deadgye method @ dDEX=6, got ~9%, then Pchan and me got 10% @ dDEX=8 => the lower bound from error makes the linear regression line "out of bound" => disprove ANY linear model. (can check image a few posts above)

[pchan]

i'm now @ 1301/13006=10.00% @ +-0.516% error.

I'm at

dDEX=8 : 1252/12445=10.06% +/- 0.53%

which puts our total masamune+pchan at

dDEX=8 : 2553/25451=10.03% +/- 0.37%

Looks good.

[CDF]

I'm still letting it run mainly to show that both melee hit rate and crit rate take only integer values, which would be evidence of flooring (like SE ever uses ceiling).

In hindsight it shouldn't have been surprising that SE truncates crit rate through flooring, like many other calculations, so strictly speaking, +1 accuracy is probably +1% hit rate or nothing.

[Byrthnoth]

In hindsight it shouldn't have been surprising that SE truncates crit rate through flooring, like many other calculations, so strictly speaking, +1 accuracy is probably +1% hit rate or nothing.

This would be very very interesting. Are your Hit rate numbers coming out to integers as well?

[CDF]

Actually, I forgot I used two different weapons, so I can't draw any conclusion about hit rate although I could compare the observed hit rate with that from direct calculation based on what we think we know about hit rate calculation. From now on, I will use two daggers...

As for crit rate given (DEX - AGI) = +3, this is easy.

Data:

1445/16200 => 8.92% crit rate (observed)

A 95% CI for the real crit rate is (8.49%, 9.37%) The estimated margin of error is 0.439%.

So, how confident can I be as far as distinguishing 9% from 9.375%?

For the sake of statistical argument, if I put forward 9% as the straw man (null hypothesis) to knock down in favor of my "continuous" linear model, what would be the probability that I would knock it down (reject the null) if 9.375% (the expected crit rate under the continuous model) were the real crit rate?

From the normal approximation, given n = 16,200, the probability is only about 0.44. Of course, if 9% were the real crit rate, the probability of "failing to reject" is 0.05.

But this isn't the only sample to consider. So far, the data as a whole point to integer values of crit rate.

[Shamaya]

http://img.photobucket.com/albums/v7...Rate39dDex.png
~8hours,lvl70fish,dDex39

so crit point at 40 is unharmed, and the tiered model continues to look strong
i'll try to continue this when possible int eh 41-50 region

Can you guys help a poor soul to finally figure out how to find confidence, made easy? It can't be that complicated but every time it comes up I go glance at wiki, and am left helpless and confused. I wanna get it down once and for all ><

edit: curious as well, what did your hit-rate% come out to, CDF?

[CDF]

Calculator: confidence interval for binomial proportions

Right now I have 4580/4915 = .932 for observed hit rate with daggers. Direct calculation gives the following total accuracy:

skill before 200: 200
skill after 200: 27
DEX contribution: 45
accuracy equipment: 23
level difference: 20
total = 315

Predicted hit rate: (315 - 280)/2 + 75 = 92.5%

[Masamune]

For Shamaya @ dDEX39, 2139/16454=13.00% @ 0.51% error, <=> crit%=[12.49%;13.41%]

EDIT: after plugging in my curve Sham's point [dDEX39;crit%=13%] actually "harms" a tier just before point [dDEX40;~14%]. Which means Shamya actually found a "jump" earlier than thought to be @ 40, but actually might starts @ 39 ! Good job Sham.

[pchan]

dDEX=7 : 1528/15002=10.19% +/- 0.48%

The first jump is occuring at dDEX=7 then since masamune found 9.13% +/- 0.5% for dDEX=6

[Byrthnoth]

Wow though, guess it really puts "stacking Dex" in perspective. These tests would probably make me not use a Dex build on anything whose Dex I didn't know for sure. There's a range of 39 Dex over which you gain 4% Critical Hit rate . . .

Hmm.... Looks like the probable trend is something like:
dDex 0-39 : Scales between +1 and +4% Critical Hit rate in some kind of floored equation.
dDex 40-50 : 1% Critical Hit rate per Dex.

Yaaaay! The data is yaaaaaay~!

[Masamune]

so far im getting an approximative model matching a few averages, but staying within errors bounds with:

@ dDEX=[0;40], Crit%=floor(dDEX/7 + 5)% + 4%
@ dDEX=[40;50], Crit%=floor(dDEX - 6*5)% + 4% (very approximative cuze goes out of bounds @ dDEX>47, only matching 39,40,41,42 and 43)

for info, i tried those models ONLY to get a rough idea where jumps could be, approximately. those are in no way definitive (unless super luck lol)

[CDF]

Based on the observed jump from dDEX = 6 to dDEX = 7, dividing dDEX by 8 and flooring doesn't quite work. So like Byrthnoth suggested maybe there's division by 256, 512, or 1024 with flooring. But we know that additional DEX at the low end sucks anyway.

I decided to check DEX - AGI = 91 - 67 = 24 and see if there was a jump from 22 to 23, which would be predicted by floor( DEX/8 ).

dDEX = 24:

Level 72 (?) Ul'hpemde

Yeah, question mark. I wasn't paying attention and I got killed by a few crit hits while the mouth was open. However, we could infer the level from the observed hit rte.

Crit rate, point estimate: 1583/12834 = 12.33%
Crit rate, interval estimate (95% CI): (11.77%, 12.92%) (M.E. roughly 0.57% from the normal approximation)

Hit rate, point estimate: 12834/14636 = 87.69%
Hit rate, interval estimate (95% CI): (87.14%, 88.21%) (M.E. roughly 0.53% from the normal approximation)

Predicted accuracy (direct calculation) from...
From skill <= 200: 200
From skill > 200: 27
From DEX: 45 (floored)
From equipment: 23
From level difference: 12
Total: 307

Predicted hit rate (%): floor[(307 - 280)/2] + 75 = 88% (so it appears to be level 72)

These were the results for dDEX = 23:

Level 71 (?) Ul'hpemde. I was in a hurry so I didn't get to kill this.

Crit rate, point estimate: 518/4580 = 11.31%
Crit rate, interval estimate (95% CI): (10.41%, 12.27%) (M.E. roughly 0.92% from the normal approximation)

Hit rate, point estimate: 4580/4915 = 93.18%
Hit rate, interval estimate (95% CI): (92.44%, 93.87%) (M.E. roughly 0.70% from the normal approximation)

Predicted accuracy (direct calculation): 311

Predicted hit rate (%): (311 - 275)/2 + 75 = 93% (so it appears to be level 71)

What's the estimate of difference between crit rate at dDEX = 22 and at dDEX = 23?

You can see from above that the relevant 95% CIs overlap, so the difference is not statistically significant. A test for two proportions gives a 95% CI of (-0.07%, 2.12%).

Conclusion: the jump from dDEX = 22 to dDEX = 23 is statistically borderline, and I didn't really show that hit rate takes only integer values, only that the observed hit rates are consistent with those from the usual calculations.

[Byrthnoth]

Sorry to has stupid moment, but I was trying to do the math to show the odds that our population averages are the same (for dDex 3 and 6 for instance).
For large samples with different means and two different sample sizes, we use:
t = (Pop Average 1 - Pop Average 2) / SQRT[ STD1^2/n1 + STD2^2/n2 ]
with:
STD = SQRT[Pop Average*(1-Pop Average)*n]
It feels wrong to mix proportions (the population averages) and the standard deviation (raw number of hits). I'm rationalizing it by saying that the STD^2/n is how the formula converts it to a ratio though.

It seems likely that there could be another jump (10 to 11%) in the neighborhood of dDex=14 to dDex=15.