Dexterity's impact on critical hits

[Gtype954]

I already told you I am IP banned from KI, and isn't it easier to just say the answer? On KI I saw you say it was over 24% or something but I can't click the link or it will say LOLBANNED.

Couldn't resist...... LOL!

[Shamaya]

Gentlemen,
So, surprise to my own, I might have something interesting to offer this (another necrobump) thread.

I looked at this thread and couldn't help but think how great it would be if crit rate was linear. I looked at some of the ideas and hypothetical plots and formulas that people were coming up with, and naturally it felt as if something was amiss. Either we're depending too much on insufficient data samples, or the formulas we're trying to shape from said data are too complex, or both. Some of us have also been speaking loosely of "tiers" since the Searain data. I've seen some people quote a tier a +40dex over mob agi, and others +20dex. I myself had been using the (0-20dex = placebo, 21-50dex = 1dex=0.5%crit) model for lack of anything better. Until just now something occurred to me that is both as simple and fits the (hints offered by the) data much better.

Prior to seeing Searain's actual LJ, I'd heard lots of talk of "tiers." But when you look at his actual data, you'll see that it really doesn't look terribly tiered. Yet there is a blatant non-linear progression. I always thought that "50" seemed like too convenient a number. Should the same rule apply in the dunes? That would seem absurd from a practical standpoint. I was just messing around with my calculator and noticed that (67 +50) / 67 was startlingly close to 1.75, a very well-rounded number. I couldn't help but wonder if this had something to do with the intended formula. Especially with rampant truncation in ffxi, being slightly off wasn't surprising. 1.75*67 = 117.25. Truncated, that's 117(dex), or exactly +50 per our previous model.

The models we've been coming up with have hinted at an exponential growth. So I tried to go from here and see if something could be shaped from the 1.0agi:dex = 5%CritFloor, 1.75agi:dex = 20%CritCap model. If we attempt a model where crit rate is determined by a function of dex/agi, set the floor at 1.0 for 5% and 1.75 for 20%, and compare it to 2.0 (+100% dex than agi), we can create a theoretical exponential model for crit growth. After some thought and trial-error, I came up with this very simple formula,

Crit Rate = (2 - dex/agi)^-1 * 5%

or

Crit Rate = 5% / (2 - dex/agi)

Extremely simple, yet it gives us the following,
http://img.photobucket.com/albums/v7...CritPlot02.png

There are no actual tiers here. I just marked out the hypothetical tiers that some people came up with for "+20dex" and "+40dex."

Here is a more detailed and interesting look,

http://img.photobucket.com/albums/v7...ritFormula.png

Look at the relationship between the spread of 0->50dex and the crit rates, and compare that to the other data and ideas in this and related threads (and searain's lj). It's surprisingly close to the data. While it doesn't match the data 100%, that's not actually discouraging, since we know that the parses/samples aren't 100% accurate. Relatively though, well, it speaks for itself.

So I'd like to plea from Occam's Razor that we should use this as our current working model for further reference and verification.

Advantages:
*Simple
*Accounts for a broader level range
*Matches our data

Right now I'm interested in two things. I'd like to see if this matches up on a mob with much lower than 67 agi, and I'd like to check if there is any level correction function in play. That would require testing. I myself though am uhh... usually pretty busy with work o.o, though I'd like to.

What think you of this, gentlemen?

[Starr]

That is very interesting indeed, Masamunai's proposal seems far too complicated for FFXI.

[Masamune]

Yes ineed interesting and simple model proposal, the model i posted earlier actually isnot mine: it's just excel who auto extrapolated it XD, i did nothing lol.

[CDF]

Crit rate estimation: who says what is a realistic estimate or not? The estimate is what it is, but at least you can ascribe some measure of uncertainty to it (standard error).

"Fishing for models": If you really wanted to appeal to Occam's razor, piecewise linearity is the simplest explanation.

There are many models that could "match" a specific set of data merely because you're fishing for "100% accuracy" rather than something that actually makes sense to program.

[Nightfyre]

Simple, clean, plausible. I like it. I'm looking into testing Vorpal Blade's base crit rate at the moment, but if there are any suggestions towards testing this simultaneously I'd be happy to contribute data. The simplest way would seem to be testing melee crit rate on a low DEX mob at dDEX < 50 but with DEX/AGI > 1.75 to see if I still cap crit rate. If anybody knows of an ideal test target that fits both tests please let me know.

EDIT: With various -DEX pieces I have I can get well below 50 DEX with minimal DEX set, so I can basically test this on any low-level mob. I'll see about testing this with dDEX >= 50 and something closer to dDEX = 40, which should produce a pretty clear result by the time I have a reasonably large sample for Vorpal Blade.

[Kyreth]

Interesting. Aside from buffing your own DEX, would the appropriate BLM debuff (Frost, in this case) deliver a useful amount of critical hit improvement for melee? It looks like at the current cap (-13 to AGI), Frost could increase your crit rate by a minimum of 1% (assuming attacker DEX = mob AGI) to 9% (if attacker DEX vs defender AGI would get pushed to the cap).

[Masamune]

Just for comparison sake i reported Shamaya's model to image below : looks like might need some minor adjustments ?

[Phraust]

Interesting. Aside from buffing your own DEX, would the appropriate BLM debuff (Frost, in this case) deliver a useful amount of critical hit improvement for melee? It looks like at the current cap (-13 to AGI), Frost could increase your crit rate by a minimum of 1% (assuming attacker DEX = mob AGI) to 9% (if attacker DEX vs defender AGI would get pushed to the cap).

Drk opening fights when they can w/Ab-Agi helps out considerably/noticeably. I think it's -18 Agi to start for EVERYONE in the group that's attacking. Dynamis is a perfect place to use it when you got like ten melee on crap.

[Starr]

This thread needs moar RR vs KJ math using critical hit rate as 40%.

[Nameless]

This thread needs moar RR vs KJ math using critical hit rate as 40%.

The thing is you don't know if the secondary hits follow the same critical hit rate bonus tho. As mentioned in another thread, there is no reason that all hits get such bonus due to the fact that "damage based on tp" ws only effect first hit's ftp.

Also alot of ppl experiencing 300% tp drakesbane or RR don't perform as well as expected could be due to this as well. Perhaps that only the first hit is that high and based on TP.

I personally have no idea how to test that.

[Nightfyre]

SA Raging Rush or Skewer with Blind Pots would be about the best way to go about it.

[Thunder]

Blade: Rin and Ascetic's Fury?

Otherwise raging rush and/or skewer are your best bets.

[Shamaya]

Just for comparison sake i reported Shamaya's model to image below : looks like might need some minor adjustments ?

Hah, that is great, thank you. I wanted to make an image like that myself but didn't wanna take the time to figure it out.

Actually, that image convinces me even more that this formula is either

(1)the correct base formula for critical hits
or
(2)is integrally related and very close to the actual formula

As another person that does game math, I'm sure you feel that it's a huge inconvenience to not have a working formula for crit. And likewise it damages the accuracy of equip/build/etc comparisons people love to make.

The reason I'm so convinced of (1) or (2) is that (counterintuitive?) I did not try to come up with a formula that fit the data. I simply stumbled into a formula that coincidentally matches. I noticed a single coincidence and, on curiosity and a hunch, decided to finish a formula for exponential growth between 5-20% that would make simple sense if I were the programmer. Then I'd see if it was a close match or not. If not, owell, I'd at least tried to kill some boredom (what I thought would happen). But it actually matched.

Further in your graph, Masamune, I find it interesting that the high points for each hypothetical 'tier' come into contact with my curve one after another. Coincidence? =O

We actually can't try to match this data perfectly. Firstly Searain's testing is very good as a base, but while his numbers do an very good job at filling a previous void of information, they don't give us 100% sufficient data. The controls used were only so strong. The mamool parses in particular were done on mixed mobs of varying agi levels (most of which we don't know).

We don't know the exact sample sizes, and surely some or many of them are insufficient. A good anecdotal example is when I went out to robber crabs to test Pahluwahn Body crit. I actually swung at those things (possibly slightly varying levels) for close to two hours. My crit rate was considerably different at 30 minutes (720 hits+) than at an hour (1440+) or an hour and a half (2160+). I'm talking whole 1% differences (ie 19% crit vs 20%) between each half hour. Just arguing from this anecdotal observation, it makes sense to be highly skeptical of Searain's data since he has so many data points, and we could hardly expect him to spend 2+ hours to get a controlled data sample of each of the points of dex in the 1-50 spread.

Further, Nameless's rundown of the data is very rough around the edges, and I'm sure he created it for approximation, not for accurate datum plot points. He also had a tiered model in mind, but I think it is more likely (and simpler to program) that it is not tiered.

TL;DR version
Sooo, what I'm saying is that it is best right now not to come up with a formula that matches the data, but further data that matches the formula. If further data samples at different base agi ranges continue to match, I'd say we have our formula.

[Starr]

The thing is you don't know if the secondary hits follow the same critical hit rate bonus tho. As mentioned in another thread, there is no reason that all hits get such bonus due to the fact that "damage based on tp" ws only effect first hit's ftp.

ok then maybe 40% first hit then 24% for the rest of the hits for now?

[Masamune]

As another person that does game math, I'm sure you feel that it's a huge inconvenience to not have a working formula for crit. And likewise it damages the accuracy of equip/build/etc comparisons people love to make.

Actually, in Excel, computing Searain/Nameless results wasnot "that" inconvenient with just using a data matrix containing said data, coupled with a search() function finding user inputed dDEX.
But yes maybe not having an actual formula might damage the accuracy, but actually the MAIN damaging factor in my opinion is the pDIF formulas, by far.

On topic, i remembered i had test parses @ Gcolis/Lcolis:
on Gcolis war/nin DEX96 : 12,85% (200/1556 #crits/#hits)
on Gcolis war/sam DEX96 ClaymoreGrip : 15,22% (319/2096 #crits/#hits)
Test conditions were std meripo setup with BRDx2, nothing used that could lower coli's AGI or raise my DEX, always meleed/WSd in TP gears, assuming both lvl81&82 Gcoli have SAME agi.
Conclusion from those results is (removing my 4 merits and claymore) :
8.85% with 1.66% error, and 8.22% with 1.54% error @ 95% confidence.
Averaging those gives :
8.535% +- 1.66% (taking highest error value from both samples) for dDEX=96-67
=> dDEX29 : Crit[6.875%;10.195%]

As shown in image, the error makes that point match all proposed models. I'll try to "continue" those parses @ next meripos having same setup (not easy considering prevalence of BRD+COR setups and camp not free or leader prefering mjsp-god i hate this camp for tests-).

I also have solo parses for lvl63,64,65 LesserColibris (~1k #hits each), with no dDEX changes, BUT i have strong doubts regarding their agi values, so far listed as resp. 52,53 and 55... so not posting any conclusion yet (If the agi values are correct, my DEX being 81, results would concern the dDEX points of 26, 28 and 29).

And finally, during the pDIF caps tests before testing RR, deduced the upper crit% cap :
25,77%-4 merits => dDEX~50+ : 21.77% @ 1.11% error = [20.66%;22.88%]
but personnally, i d take that upper cap % with a grain of salt, because during tests i was assuming since i m hitting way too weak lvl mobs, my dDEX should be capped with w/e weapons/gears i would use (never used any crit% items tough). That result still raises the question "Is the upper cap crit% = 20% or 21% ?".

All those results shows at least +- 1% errors that gives relatively "large" room for model fishing.

as a final note, and because i can't bear/don't understand idiot comments like Starr's: I never ever stated at any post RR initial crit% @ 100TP ~ 40%, not even close far from there. Learn to read when i said "so far im @ ~17.7%" doesnot say AT ALL that my tests will continue growing higher and higher, tomorrow can drop again @ 15%ish, i dunno but will certainly NOT keep a constant grow. Also this thread topic is about crit% in general, NOT about RRvsKJ. Hope that will clear some taru mind < <

For Nameless idea regarding secondary hits crit%, i kept track of my 1% tp return hits during tests, but they are very rare (5% occurence since im capped WSaccu on lolmobs) so would have very high error... unless 10 persons help contributing with rigorous tests (so far NOONE helpd). The idea of crit bonus applying only @ 1st hit is interesting tough.

[Nameless]

ok then maybe 40% first hit then 24% for the rest of the hits for now?

Yep, which is going to be alot weaker than all hits 40%.

[Starr]

Yep, which is going to be alot weaker than all hits 40%.

Of course but you're not even right as of yet, so let's see the math with 40% throughout and 40% + 25% extras. I already know RR will win but it's cool.

I would help you Masa but people will try and act like I am fabricating results to make RR look better if they come out high because they all self owned themselves in RR vs KJ.

[Byrthnoth]

Masa's data will answer the 40% on all vs. 40% then 2x 24% question eventually thanks to him keeping track of 1TP return hits. He should be able to tell the difference around the same time that he can distinguish between +10% and +15% Crit rate on the initial hit.

We know that fTP bonuses do not apply past the first hit, but it would be interesting to see if other TP-related bonuses apply past the first hit.

[Nameless]

Nothing against RR or anything tho, I don't even have warrior at 75. But from being a drg and use drakesbane all the time at 300% tp (usually my first ws), I don't get the impression that it does significantly more damage. Could be just luck, you never know tho.