Dexterity's impact on critical hits

[WraithLakshmi]

I think it's time this was better researched. I'm going to do some testing to find the actual equations for crit hit%.

Knowns:

• The low cap on crit% is 5%, and the high cap is 20%
• The high cap is reached at 50 more dex than the enemy's agi
• The curve is either some form of exponential, or there is a different equation for dDEX 40-50
• merits and crit weapons can break the caps.

To start off, I researched at what value of dDEX the low cap could be found. I did 1000 melee swings on level 65 lesser colibri with exactly 65 dex. I have 4/4 crit merits and I was single wielding a senju, and my number of critical hits was exactly 150, giving a crit% of 15% exactly. This means that when dDEX = 0, you are low capped on crit% rate.

My theory is that the low cap is at dDEX = 0, so when you have equal to or less dexterity than the enemy's agility, your base crit rate will be 5%. I also theorize that the equations from 0 < dDEX <= 40 and 40 < dDEX <= 50 are linear and that there are different slopes in those two integrals.

What I would like to find, and would welcome help on, is what the slopes of the dex/crit graph are in those two integrals. I'm hoping this is nice and linear, but if it turns out to be exponential it will be a bit more difficult :'-(

[Hogie]

Nice testing so far. I think the next step would be to try 1000 more swings with as much neutral gear as possible and trying to get 100 DEX total. Use senju again since the first test was done with this, and see what the difference from 65 -> 100 dex is. You could even add say 20 more dex to make it a easier equation and do the swings with a total of 85 DEX and go from there.

[ringthree]

Originally Posted by WraithLakshmi

I think it's time this was better researched. I'm going to do some testing to find the actual equations for crit hit%.

Knowns:

• The low cap on crit% is 5%, and the high cap is 20%
• The high cap is reached at 50 more dex than the enemy's agi
• The curve is either some form of exponential, or there is a different equation for dDEX 40-50
• merits and crit weapons can break the caps.

To start off, I researched at what value of dDEX the low cap could be found. I did 1000 melee swings on level 65 lesser colibri with exactly 65 dex. I have 4/4 crit merits and I was single wielding a senju, and my number of critical hits was exactly 150, giving a crit% of 15% exactly. This means that when dDEX = 0, you are low capped on crit% rate.

My theory is that the low cap is at dDEX = 0, so when you have equal to or less dexterity than the enemy's agility, your base crit rate will be 5%. I also theorize that the equations from 0 < dDEX <= 40 and 40 < dDEX <= 50 are linear and that there are different slopes in those two integrals.

What I would like to find, and would welcome help on, is what the slopes of the dex/crit graph are in those two integrals. I'm hoping this is nice and linear, but if it turns out to be exponential it will be a bit more difficult :'-(

As a clarification, just because you had 1000 swings and had 150 crits does not mean that you always have a 15% crit chance. The probably is likely, but not guaranteed.

That said, I think you are heading in the right direction for the formula. Also, I disagree with the previous poster. I think it would be better to set a base line without any crit hit bonus if possible.

[Zsky]

Originally Posted by WraithLakshmi

Knowns:

• The low cap on crit% is 5%, and the high cap is 20%
• The high cap is reached at 50 more dex than the enemy's agi
• The curve is either some form of exponential, or there is a different equation for dDEX 40-50
• merits and crit weapons can break the caps.

Thanks for this, I've always wondered how DEX and crit% rate was calculated.

With that said, does COR's rogue roll (crit rate up) break caps as well? Or simply adds to the crit rate calculated from your DEX over mob's AGI ?

[Nameless]

I think somewhere in alla there was a test on someone's LJ. Allakhazam.com: Final Fantasy XI: Monk is the original thread, and seaseaseaseasea - DEX/Critical hits relation data. is the LJ data. I read it and got a pretty good understanding of the test result. This is just the conclusion that I get from the test data:

Base Crit. 5%
Merit 4%

Dex over mob agi - 0~20 = 1%
Dex over mob agi - 21~25 = 2%
Dex over mob agi - 26~30 = 3%
Dex over mob agi - 31~35 = 4%
Dex over mob agi - 36~37 = 5%
Dex over mob agi - 38~39 = 6%
Dex over mob agi - 40~41 = 7%
Dex over mob agi - 42~43 = 8%
Dex over mob agi - 44 = 9%
Dex over mob agi - 45 = 10%
Dex over mob agi - 46 = 11%
Dex over mob agi - 47 = 12%
Dex over mob agi - 48 = 13%
Dex over mob agi - 49 = 14%
Dex over mob agi - 50 = 15%

In other words, it works indeed like a tier, except that the tier itself changes when dex over mob agi increases. It seems like 0-20 = 1%, anything over 20, it is 1% every 5 dex until 35, then it is 1% every 2 dex until 43, then anything over 43 is 1% every 1 dex til you cap.

This theory works in both set of datas that you see from the links. The actual number might not be accurate, but you can get a sense of how it works. That's why if you can't stack a huge amount of dex, don't bother. And most likely on HNM, your dex build will be ineffective.

[WraithLakshmi]

Originally Posted by Nameless

Dex over mob agi - 0~20 = 1%
Dex over mob agi - 21~25 = 2%
Dex over mob agi - 26~30 = 3%
Dex over mob agi - 31~35 = 4%
Dex over mob agi - 36~37 = 5%
Dex over mob agi - 38~39 = 6%
Dex over mob agi - 40~41 = 7%
Dex over mob agi - 42~43 = 8%
Dex over mob agi - 44 = 9%
Dex over mob agi - 45 = 10%
Dex over mob agi - 46 = 11%
Dex over mob agi - 47 = 12%
Dex over mob agi - 48 = 13%
Dex over mob agi - 49 = 14%
Dex over mob agi - 50 = 15%

This is the kind of data I'd like to find, using this we could extrapolate some sort of equation. I don't think that list is very accurate, though, since we know that at dDEX >= 50 your crit will cap at 20%, not 15%.

Originally Posted by Zsky

With that said, does COR's rogue roll (crit rate up) break caps as well? Or simply adds to the crit rate calculated from your DEX over mob's AGI ?

Rogue's roll does break the cap, similar to how merits and crit weapons work. Basically, you have your base critical chance, calculated by dDEX, which caps at 20%. Merits, crit+ from weapons, and Rogue's roll are added on top of that, and are, as far as we know, uncapped.

This means that the maximum critical chance you could attain would be 48% not including gear, with dDEX at 50, 4 merits, and an 11 rogue's roll with either a thf in party or a cor with relic hat. Would make for some crazy DPS if you add destroyers on top of that =P

[Nameless]

15% + your base of 5% is 20%

[Nameless]

Also, my mistake, it should look like this:

Base Crit. 5%
Merit 4%

Dex over mob agi - 0~10 = 0%
Dex over mob agi - 11~20 = 1%
Dex over mob agi - 21~25 = 2%
Dex over mob agi - 26~30 = 3%
Dex over mob agi - 31~35 = 4%
Dex over mob agi - 36~37 = 5%
Dex over mob agi - 38~39 = 6%
Dex over mob agi - 40~41 = 7%
Dex over mob agi - 42~43 = 8%
Dex over mob agi - 44 = 9%
Dex over mob agi - 45 = 10%
Dex over mob agi - 46 = 11%
Dex over mob agi - 47 = 12%
Dex over mob agi - 48 = 13%
Dex over mob agi - 49 = 14%
Dex over mob agi - 50 = 15%

it seems like you don't get the first % without having 10 dex over mob's agi. Found that mistake after reviewing my older data.

[WraithLakshmi]

Ahh, ok, that makes sense then.

I just ran a parse of 1000 melee hits with dDEX = 50 on lesser colibri. I was a bit surprised because my crit% came out lower than expected, 23.76%. With 4 merits and duel wielding a senju and unji, it theoretically should have been 27%. I'm going to attempt another set and see if I get similar results.

Edit: Just ran another 1000 hits and parsed crit rate of 28.21% this time, so all's right in the world, lol. Just goes to show how much variance you can get in a data set of n=1000.

[Marootsoobutsu]

Correct me if I'm wrong here, but don't weapon crit +s only work on the specific weapon?

In that case, Senju would only really provide about a 3% total crit+ modifier, since Unji doesn't have one. So it looks like you're marginally over the expected 23% critical hit rate, probably a result of killing colibri on a Senju critical.

[WraithLakshmi]

Originally Posted by Marootsoobutsu

Correct me if I'm wrong here, but don't weapon crit +s only work on the specific weapon?

In that case, Senju would only really provide about a 3% total crit+ modifier, since Unji doesn't have one. So it looks like you're marginally over the expected 23% critical hit rate, probably a result of killing colibri on a Senju critical.

I have 4/4 crit merits

[Starr]

Originally Posted by Nameless

%

Dex over mob agi - 0~10 = 0%
Dex over mob agi - 11~20 = 1%
Dex over mob agi - 21~25 = 2%
Dex over mob agi - 26~30 = 3%
Dex over mob agi - 31~35 = 4%
Dex over mob agi - 36~37 = 5%
Dex over mob agi - 38~39 = 6%
Dex over mob agi - 40~41 = 7%
Dex over mob agi - 42~43 = 8%
Dex over mob agi - 44 = 9%
Dex over mob agi - 45 = 10%
Dex over mob agi - 46 = 11%
Dex over mob agi - 47 = 12%
Dex over mob agi - 48 = 13%
Dex over mob agi - 49 = 14%
Dex over mob agi - 50 = 15%

Graph form please

[Tulun]

So.. if that's right.. if you can't reach that 36 and above (capping at 50) stacking dex really isn't doing jack for you?

[WraithLakshmi]

Originally Posted by Tulun

So.. if that's right.. if you can't reach that 36 and above (capping at 50) stacking dex really isn't doing jack for you?

Yeah, that's about right. There appears to be an inflection point at dDEX = 40 where adding more dex causes very large gains, but unless you can get that much it's not worth gearing for, no.

[Shinryuu]

[Shinryuu]

I'm lazy, if you don't know which axis means what you're dumb and retarded.

[Ferien]

Originally Posted by WraithLakshmi

Yeah, that's about right. There appears to be an inflection point at dDEX = 40 where adding more dex causes very large gains, but unless you can get that much it's not worth gearing for, no.

It also sucks complete ass for Elvaan.

[Shinryuu]

My MNK has around 80 base DEX, if I get hachiryu kote I could cap the DEX-AGI thing on Colibri. Shame my WAR is better there.

[Cream Soda]

Should only be better as war if you don't have enough acc to support not using madrigal tbh, unless you're somedecked out adabeurk ect war.

[Shinryuu]

My WAR has a little less than 85% accuracy while using a polearm, so if there's a madrigal or hunter's I switch to that; and I'm one of those crazy people that likes to fulltime hasso, something MNK isn't able to do. I don't have an adaberk, but I don't have a black belt either. I'll give MNK merits a try after I get hachiryu kote, I guess. It's been a while.

[Cream Soda]

With the gear in my avatar, swap out merman's for minuet, I do 85% on lv 82 birds, higher on lv 81 birds. Throw in focus and I'll usually parse 88-92% at a colibri pt as mnk.

[Shinryuu]

Well you're going to have more accuracy than me; I gain ACC on neck (PCC) and my DEX (80), while you have 7 more on head, 7 more on feet, 2 more on ammo, 1 more on body, presumably 4 more on rings... I need to finally get the 25 piece for usukane somen, I've had the 35 piece for a bit. I use noritsune kote, by the way. Attack hands are overrated.

I don't remember parsing as low as ~80% or less without ACC songs on birds, though. Do you have 8 H2H? As I've said before I'll go merit on MNK sometime soon again. I became too infatuated with WAR.

[Cream Soda]

Yes, I have 8/8 h2h and while focus is up, I swap to turban and Bkote. If by some reason we have madrigal for other DDs, I'll use rajas as well. And yes, x2 toreador's.

[Chenzhen]

Don't know if you're still interested in more data but I just did two sets of 500 swings on Greater Colibri which according to wiki has 67 AGI. This puts me at 53 more DEX than the Colibri.

This was on SAM, which is the reason it's a small sample.

Other mods:
Crit merits +4%
Claymore grip +3%

First sample:
19.60% critrate

Second sample:
18.28% critrate

I know from earlier tests (sadly all gone now with numerous disk formats) that adding more DEX (not much) will put me around 25-28%. The addition of certain items I've found it hard to live without have forced me away from the max DEX-setup, but recently we've seen items added that I could use to boost DEX again, like Cuchulain's mantle and Hachiryu kote. Just need to grind a bit to attain them.

[Loziel]

Could people perhaps do these tests without the use of critical weapons and grips so we can get a cleaner set of data. unji and senj are not good to test this with based on how each hands crit is independant of the other weapon

[Agana]

I'd like to see some dex testing on drakesbane, vs. str testing :3

[urat]

Did some quick stat plot / regressions, if the difference between your dex and mobs agi is only variables that influence crit rate (not including crit rate armor/weapons cause those are added in after)

Then the exponential regression appears to be:

Crit rate= o.339 x 1.077 ^ (your dex-enemy agi capping at 0)

then add in gear.

I'll take a look at other forms of regression to see if any other forms fit better, but this one is almost dead on.

[Masamune]

Sorry for necrobumping, but i'm wondering a few points:

1. How did you guys differentiate your Crits numbers from Normal ones since that update which changed all pDIFs ? asking that because my recent tests (posted here @ BG) on pDIFs under capped conditions showed dmg numbers totally wrong with pDIFs listed @ wiki (at the exception of 3.15 cap which most poeple figured), resulting maybe in wrong differentation between Normal Highs and Lowest Crits, in tests involving crits or pDIFs?

2. Does any -rigorous-test exist regarding crit% @ 100/200/300TP for RagingRush and Drakesbane ? I've started one for RR over there @ KI WAR forum, but need help with more sample to lessen the error%... but for Drakesbane, i can't test since i dont have drg75.

3. What do you think of this regression @ image joined ? In blue, the brute data posted in this thread, red the model from Urat, and black the one i'm proposing (Polynomial regression @ 4th degree).

[ringthree]

Fuck, I contributed to bumping an old thread. But at least the new information is interesting.

[Nightfyre]

Your regression fits the data very well, much better than urat's at low and high dDEX. You already knew that though. Unfortunately, the sample size that would be required to disprove one of the proposed equations is huge.

Not to be an asshole and present something we essentially can't prove either way, but we also have to consider this from a programming standpoint. You've got some very small decimals attached to those variables, is it not possible and potentially even probable that they wrote a floored equation (hell, they floor everything else) or an if-else string that provides the stepped data we already have? It's possible they mapped out a rough range of intended data points and then found an equation that fit the data just as we have, but I suspect they took the easy way out.