Dexterity's impact on critical hits

[Byrthnoth]

Well, the only statistics course I've taken was "Statistics for psychology majors" (mandatory and not substitutable) which cumulated grandly in normal distributions and was mostly involved in social-psych statistic bullshit. Our second test was on the "measures of central tendency" aka Mean, Median, and Mode for chrissakes. That said, I was also a chemistry major so I had to teach myself statistics so I could do lab reports.

Here's the theory as I understand it:
For large n values (like the multi-thousand hits we're working with, but supposedly for n>30) the central limit theorem states that samples of a single population will form a normal distribution. Obviously that distribution has a standard deviation and a true mean (which is the population's mean). So if you take multiple populations with >30 trials (I'm inclined to use ~100), you can assume your samples fall into a normal distribution.
Central limit theorem - Wikipedia, the free encyclopedia

But yeah, I agree that because you split them into crit hits and non-crit hits you can't split that sample up now. If you wanted to test the method, you could split the ones from now until you finish up into chunks and compare it to your overall mean/standard deviation.

[Masamune]

i'll do that for 200TP, i now reached 5% error with 373 WSs for 100TP so fuck it

If yu want a number @ 100TP, contribute, me im going @ 200TP now.

Updated the sheet.

[Retrieving/C.D/Searain]

Hi everyone. I highly doubt I'd be able to make a relevant contribution to the thread at this point in time since I quit a long-ass time ago (it's been over 2 years and I haven't kept up with the game updates either), however there's a few things I'd like to point out (thanks Masamune for PM'ing me and...hey Byrthnoth! Long time no see!):

having several point estimates for a given level of DEX (example 118 ) is better than nothing, but obviously not very efficient. (They could have arose from 2,000 total samples or 20; who the hell knows.)

As I have explained earlier to Masamune via PM each of the Crits % values in the "chart" relies on fairly large sample size: 1500-2000 hits, sometimes even larger than that, case in point being the "115 DEX" parser I've managed to dig up this afternoon from one of my old posts on an italian message board which actually shows a total of about 2400 hits.

Besides the tests were conducted under pretty rigorous conditions: no gear-swapping for weapon skilling purposes, no COR rolls active, no Mighty Strikes, multiple parsers being ran simultaneously by different players to rule out biases in measurement and so forth.

...so yeah, my point is that those numbers (especially the ones which refer to the birds camp since we were exping on the same mobs over and over, as opposed to the inherent variety of the Jade Sepulcher camp) are actually sort of reliable, not perfect by any means but still useful to get a rough estimate of how things work.

Also, little known fact, my tests and the very first BG thread on the matter (the one that got eaten by a forum database rollback which occurred sometimes in 2007) predates the Studio Gobli entry mentioned above by at least a few months.

- - -

Unfortunately, I'm not able to retrieve all of the data at the moment (even though I'm sure it's still hidden somewhere inside my old system hard-disk since I had the habit of keeping pretty much everything "FFXI-science" related for future reference) because I gave away the PC I used to play the game on and the machine now sitting in my dad's lab.

I promised Masamune that whenever I'll go visit my parents (most likely sometimes next week) I'll bring forth a USB pendrive and retrieve as much data as possible though so bear with me.

I apologize for not being of much help but it's been a while, ciao and keep up the good work!


Ninja Edit: I think the LJ entry linked above isn't the "updated" one (it still dates back to 2007/2008 tho and the only difference is a couple more values being added in each table) .

[Byrthnoth]

Hey Searain! Hope things are going well for you! I actually was over in Italy this summer (one of the swarms of tourists) for about 10 days with my girlfriend during a large trip around Europe. We hit a great restaurant in the jewish quarter of old Venice, Osteria Bea Vita. It was awesome, I recommend it if you get the chance.

I can live with +12-22% Crit rate boost on Raging Rush. I was poking around on my computer and found model of Searain's data from the last time I ran it, so I added a few data points and uploaded it:
http://i318.photobucket.com/albums/m.../critgraph.jpg
Dex values of 44 and 45 look odd, and the difference between crit values at 27 is large as well. Measuring lower crit values would be tough, but you can see why I thought that it was essentially linear or piecewise linear. The linear fit is technically better I guess, but the piecewise one has attractive intersects/breaks.

Piecewise linear, the equation would be:
0-9 Dex: Crit hit rate bonus = 0%
10-39 Dex: Crit hit rate bonus ~= (Dex-Agi - 10)/5
40-50 Dex: Crit hit rate bonus ~= (Dex-Agi - 40)*4/5

This is simple and has the right breaks. The low crit rate values need more data. I'd be interested in the sample size for the 111 and 112 data points, because the 40-50 linear fit gets an R^2 of .98 without them and they really haven't fit any model yet. That doesn't necessarily mean they're wrong though.

[Masamune]

if could get an accurate value for Lesser colibri AGI, could add more samples too since they are soloable.

for byrthnoth, yu forgetting something fundamental with searain data :
its data isnot actually single data points but RANGES, you gotta include the error inherent to sample size used for each of those data points, which are actually not one but 2 data points: upper and lower bounds.
Results: since sample are still too low to get data points with a range lesser than 1%, a lot of models can "fits" in obviously.

as example i posted already previous page : http://www.bluegartr.com/forum/3140460-post56.html with 3600+ sample size just for one data point still giving a range of +-1.66% so that gives still lot of room.

[Byrthnoth]

You calculate your standard deviation using a binomial distribution:
Normal distribution - Wikipedia, the free encyclopedia (Control-F for Central Limit Theorem)

That method is largely dependent upon the sample size for reducing the standard deviation. Therefore, if I take numbers with similar values and sample sizes (like the 110 Dex Crit rates for example), they should have similar standard deviations. Averaging those, I should obtain a standard deviation that is smaller than any of the distributions alone. This makes sense, because I've effectively increased the sample size of my measurement by a factor of 5.

So as an example with your data, 1.66% std with n=3000 and an 8.53% average. If you increased n to 6000 without changing the average, you'd decrease the standard deviation by a factor of 2 to 0.83%. So, you could multiply your individual sample sizes by their crit rate, sum them, and divide by the total sample size to get your total population sample size, then use that to calculate a new (lower) standard deviation.
That's not entirely unlike what I'm doing. Because I don't know the sample size but assume it to be large and all about the same, I take the standard deviation of the population averages. It doesn't really work very well with only two population averages though, any more than other statistics work with an n of 2. Again, I'm not sure what's correct here.

Regardless of their standard deviations, my fit is still there and probably simpler than any other solution right now.

[Masamune]

ok pictured my previous post below: As shown Searain data points allow to "build" an upper and lower bounds for half of dDEX values.
BUT and that's what i meant in my previous post, you can see how large the gap is between the 2 boundaries, and i plotted them with assumption all those datas come from samples of exactly 2000 hits.
Can also see a possible error around dDEX=45-47 (guess that's from using a Senjuinrikio? but not specified @ Sea's LJ), and a lil peak @ dDEX=28.
Note some dDEX value presents a lower gap between upper and lower boundaries, because of higher sample size (i also added my crit% @ dDEX=29 on top of searain's)
That pic comes from an excel sheet in attached .zip.

Conclusion so far: nothing can be used as solid reference to allow for a correct model fishing yet. Honestly, Model fishing right now would be like "putting the cart before the horse", as long the gap between those boundaries from parses arenot enough close each other. Solution: instead of posting and exploding our brains on this thread, better get our asses @ Gcolis and get more samples to add @ searain's when he'll get them back from his parents.

Edit: i'll check later what you exposed in your last post Byrtnoth.

[CDF]

Here is an explanation of why it's better to have a single sample proportion along with a measure of its precision, the standard error, than trying to make do with several sample proportions for a given level of DEX (without any standard errors given).

Note: I will refer to the single sample proportion as a "pooled" sample mean to contrast with the splitting of the sample into several sub-samples, which by the way is completely unnecessary to estimate a population mean and ... not good for the following, perhaps hard to follow explanation.

Concerning how to regard sample proportions if you have several sample proportions for a given condition, for example 110 DEX, if you're taking an average of sample proportions at 110 DEX, this is a sample mean of sample means, which still estimates the population mean.

It's possible the sample mean of the sample means could be as efficient as the single, "pooled" sample mean (what should be used) assuming an equal sample size, say "n," associated with the "sub-samples" whose sample means you're averaging. In other words, the actual standard error could be the same in either case.

But even if this is the case, the estimated standard error of the sample mean of the sample means will have more variability than the estimated standard error of the single, "pooled" sample mean. Since it is generally desirable that the estimated standard error is close to the true standard error, you will better satisfy this condition using the "pooled" sample mean.

[frodnonnag]

Here is an explanation of why it's better to have a single sample proportion along with a measure of its precision, the standard error, than trying to make do with several sample proportions for a given level of DEX (without any standard errors given).

Note: I will refer to the single sample proportion as a "pooled" sample mean to contrast with the splitting of the sample into several sub-samples, which by the way is completely unnecessary to estimate a population mean and ... not good for the following, perhaps hard to follow explanation.

Concerning how to regard sample proportions if you have several sample proportions for a given condition, for example 110 DEX, if you're taking an average of sample proportions at 110 DEX, this is a sample mean of sample means, which still estimates the population mean.

It's possible the sample mean of the sample means could be as efficient as the single, "pooled" sample mean (what should be used) assuming an equal sample size, say "n," associated with the "sub-samples" whose sample means you're averaging. In other words, the actual standard error could be the same in either case.

But even if this is the case, the estimated standard error of the sample mean of the sample means will have more variability than the estimated standard error of the single, "pooled" sample mean. Since it is generally desirable that the estimated standard error is close to the true standard error, you will better satisfy this condition using the "pooled" sample mean.

all i got from that is that you used the word "sample" 21 times.

[Byrthnoth]

I understood what he was saying, and it's useful to know. I've always wondered about the different ways to calculate standard deviation/confidence intervals and when to use what. I'm kinda looking forward to taking another statistics course now.

Anyway though, the standard deviation of the 110 Dex point should be fairly low, and 117/118 is considered the cap just as 67 Dex is considered to be the floor. It is hard to fit a nice line to the low crit rate values because the standard deviation of each measurement is so near the slope.

With 10 long parses (x3 DDs so 30 data points) we could probably figure out what the crit formula is.
Focus on dDex values +35-39, +41, and +45-48. - This would tell us whether it's some kind of S-curve or piecewise linear, and probably let us complete the trendline either way. There is a good chance we'd need also some data points at low dDex values to really flesh out the lower end of the curve.

[Masamune]

Thank you CDF and Byrttnoth on your last posts, that's exactly what i meant.

Regarding what cdf wrote, i was thinking about "pooling" directly the different sub-populations each testers would contribute here with their #crits and #totalhits displayed on their parsers, for a declared DEX value used @ Gcoli camp.
Example for a DEX used (with totally imaginary numbers):
PersonX posts 200/2000
PersonY posts 220/2100
PersonZ posts 190/1900

then we can compute with adding each like :
for that dex value, crit%=(200+220+190)/(2000+2100+1900)+-1.96*sqrt((200+220+190)/(2000+2100+1900)*(1-(200+220+190)/(2000+2100+1900))) / sqrt(2000+2100+1900)

right or wrong?

As it concerns me, i already posted results i got for dDEX=29 along ~ 4 meripos with 3652 #totalhits.
i have also a parse on Lessercolibris for dDEX=26,28,29 with 1500ish #hits for each lvl that i can continue anytime, but i dont have their confirmed AGI value.
For making new parses at new DEX values, especially the ones Byrtnoth mentioned, my gear choices are kinda limited to adding KubiraNeck, Warwolfbelt and IotaRing on top of my current war tp setup (i wouldnot tp in HecaHands though) so that makes me available for parsing up to dDEX=96+4+5+3-67=41.

EDIT: after looking closer to the curve i posted above, i noticed already existing data points @ dDEX=34,35 and 42. So regarding which dDEX values we should create a data point, i would say dDEX=38. Along with adding more samples to already existing dDEX=35, 42 and 44.

[Byrthnoth]

I'm honestly not entirely sure how AGI values are calculated. I think the job combination of a monster is deduced from other more easily measurable stats and resistance traits and then the stat equations are used to guess its values.

For instance, level 60-63 Robber crabs are PLD/WAR (I think), so their AGI values would be 43, 43, 44, and 46.

[Masamune]

Allakhazam.com: Final Fantasy XI

Mob stats (STR, AGI, etc) is calculated by summing the function value of monster race, monster main level, and monster subjob level:
monster VIT = fVITRace(Lv, race stat rank) + fVITMJob(Lv, main job stat rank) + fVITSJob(Lv/2, sub job stat rank)

Most monsters is WAR/WAR (main job WAR, sub job WAR) and WAR have rank D VIT

the fVITRace, fVITMJob, fVITSJob use the same formula. The formula is as follow for each stat rank :
A 5+(Lv-1)*0.50
B 4+(Lv-1)*0.45
C 4+(Lv-1)*0.40
D 3+(Lv-1)*0.35
E 3+(Lv-1)*0.30
F 2+(Lv-1)*0.25
G 2+(Lv-1)*0.20


Now, take an example of lv 77 Enkidu.
According to Gobli, Enkidu have rank C VIT (from golem race), and we can easily assume it's WAR/WAR
so :

monster VIT = fVITRace(77, C) + fVITMJob(77, D) + fVITSJob(38, D)
= [4+(Lv-1)*0.40] + 3+(Lv-1)*0.35 + 3+(Lv-1)*0.35
= [4+(77-1)*0.40] + 3+(77-1)*0.35 + 3+(38-1)*0.35
= 34 + 29 + 15 = 78 VIT

and defense can be calculated from this formula :
Defense = [f(Lv,race rank) + 8 + [VIT/2] + Job trait] x Race trait

Rank Lv-1~50 Lv51~
A 6+[(Lv-1)*3.0] 153+[(Lv-50)*5.0]?
B 5+[(Lv-1)*2.9] 147+[(Lv-50)*4.9]?
C 5+[(Lv-1)*2.8] 142+[(Lv-50)*4.8]
D 4+[(Lv-1)*2.7] 136+[(Lv-50)*4.7]?
E 4+[(Lv-1)*2.5] 126+[(Lv-50)*4.5]

So for Lv 77 Enkidu, the Def is :

Defense = [f(Lv,race rank) + Job trait]xRace trait
= 142+[(77-50)*4.8] + 10(Defense bonus) x 1.0
= 142+ 129 + 10 = 281

Total def = 8 + VIT/2 + Def from Def formula
= 8 + 39 + 281 = 328

Method i applied for Colibris' AGI, which are RDM/rdm (check image attached). As you can see i dont get same agi values than found on various sites/forums. So maybe i did an error somewhere i didnot find.

[CDF]

I didn't look at your image, but I'll give lv 81-82 greater colibri a try.

They are putatively RDM/RDM (rank E agility) with rank E agility for mob type.

So, the AGI calculation for for a level 81 colibri would be 27 + 13 + 27 = 67 AGI. It is the same for level 82. Now, looking at your image it looks like you divided colibri level by 2 for the subjob component of AGI, but it seems we are supposed to divide by 2 after computing AGI and then flooring.

Also, I thought Robber Crabs were PLD/PLD (rank G agility) with rank E agility for mob type.

So, the AGI calculation for a level 60 crab would be 13 + 6 + 20 = 39. For levels 61-63, the AGI calculation is 14 + 7 + 21 = 42.

Also, Masamune, I noticed you were discussing your RR crit rate results on Allakhazam. I'm sorry, but the WAR forums are easily the worst on Allakhazam, but I guess you were hoping that even idiots say something non-trivial once in a while.

[CDF]

Regarding what cdf wrote, i was thinking about "pooling" directly the different sub-populations each testers would contribute here with their #crits and #totalhits displayed on their parsers, for a declared DEX value used @ Gcoli camp.
Example for a DEX used (with totally imaginary numbers):
PersonX posts 200/2000
PersonY posts 220/2100
PersonZ posts 190/1900

then we can compute with adding each like :
for that dex value, crit%=(200+220+190)/(2000+2100+1900)+-1.96*sqrt((200+220+190)/(2000+2100+1900)*(1-(200+220+190)/(2000+2100+1900))) / sqrt(2000+2100+1900)

right or wrong?

This is correct ... assuming identical conditions (and obviously random sampling). Because the sample sizes are unequal, the "pooled" estimate would be slightly more efficient (but most optimal) than averaging the three sample proportions .1, .1047619, .1 and taking the estimated standard error of this average (which is just the estimated variance divided by 3).

[Masamune]

For allak war forum, mmm i started to notice... but yea i dont know them at all so gave them a try, based only on Shamaya info THF subforum were great for that kind of test (ie the evisceration one)... But honestly, i m mostly seeking for manpower to help get samples, and that's really not hard at all...

Crabs are indeed PLD/pld found that in a lot of sites/forums.

for my agi calculations, i'll review later, gtg now.

EDIT: allright, thank you CDF, indeed i made an error on when /2 on subjob function, fixed i get indeed correct agi values.

[Masamune]

mmm just made a long merit pt @ Gcolis with 104DEX and nothing that could change mob's agi or my crit rate. Result is really surprising and will disappoint poeple who were model fishing "before the hour" :

dDEX=104-67=37 : 502/3873 #crits/#totalhits = 12.96% so 8.96% removing my 4 merits
=> error = +- 0.900%

Then i reported that point to the graph posted earlier (see image attached) to get a surprise !

As shown, that point disprove any curve between the current data points, leaning more towards a somewhat "tiered" model maybe?

[CDF]

Interesting result.

Did searain give you the sample sizes for each level of DEX he tested? I'm wondering where you got some of those lower and upper bounds for the 95% CIs.

FYI, not that it really matters all that much, but when you're estimating the standard error of your observed critical hit rate, it should be based on the original, observed critical hit rate and not the rate you get taking 4% off.

Suppose your critical hit rate was actually 13% (p = .13) after 4/4 crit hit merits. For a given sample size n and p = .13, the variance is then (.13)(1-.13)/n. But since we know for a fact that 4% of that rate is from merits, then the crit rate before merits is 9%. But that doesn't mean the variance changes merely because you subtracted 4%. You're working with the 13% and not the 9% and the variance depends on the actual p, not the adjusted p.

[Masamune]

Did searain give you the sample sizes for each level of DEX he tested?

Not yet.

..., but when you're estimating the standard error of your observed critical hit rate, it should be based on the original, observed critical hit rate and not the rate you get taking 4% off.
Suppose your critical hit rate was actually 13% (p = .13) after 4/4 crit hit merits. For a given sample size n and p = .13, the variance is then (.13)(1-.13)/n. But since we know for a fact that 4% of that rate is from merits, then the crit rate before merits is 9%. But that doesn't mean the variance changes merely because you subtracted 4%. You're working with the 13% and not the 9% and the variance depends on the actual p, not the adjusted p.

Indeed i calculated the upper/lower bounds using the error calculations based on adjusted p, which gives even closer "gaps" between them, to allow better model fishing later. Is that a mistake to calculate that way ?

Attached the excel sheet with my current data on this topic, so you can see the calculations.

[Byrthnoth]

I can't reason out why SE would have a decreasing crit rate at mid-range Dex values, but I wouldn't put it past them honestly. This makes the values around there all the more interesting.

Have you considered asking the other people you're meritting with what their Dex values are, and to keep their TP gear/food at a constant Dex throughout the party? You could triple your data points/time that way assuming you trust them to do it right.


Edit:
On the plus side, this could explain why "Enhances the rate of critical hits" armors sometimes seem to not be working. It could be that "Enhances the rate of critical hits" does something like dDex+5, which might push it into or just barely through the lower zone.