Fatality Belt Latent Testing

[Raelia]

Heres my theory in a bite sized chunk: Calculation of damage effectively didn't change at all, Ratio now caps instead of cRatio and theres a 5% randomizer tacked on the end. I've tested the upper-end 2-handed numbers on the wiki and looked over most of your data, and they look right with the 0-5% secondary modifier.

Its all about Occam's Razor, which I offhand to Hanlon's.

As for the trapezoidal distribution: Spot on, though I think even with a biased second multiplier (1.00-1.05) its still symmetrical because either end remains a 5% spread. 1 +0.6/-0.6 is still equal to .4 +1.2/-0 or 1.6 +0/-1.2.

What Masa is encountering is a German Tank Problem. You have a ton of data, but you can't be sure if you've seen where it starts and ends. This is the problem with trying to test until the world explodes; in the end its still a guess. Thats why I proposed abstracter methods and even founded a working model, with a second randomization, after observations of the spread of capped crits.

If we can approximate damage calculation just as well with Damage * pDIF * 1.00~1.05, what is the problem with applying it as long as there is no glaring error that can't be attributed to the confoundment of testing on variable mob levels and stats? Example: Masa pointed out an error between his testing and my model, I pointed out a gain in fSTR, Masa thinks I said his STR changed and screams bloody murder that it didn't, I actually implicated that the lv63 colibri has lower VIT than cited on the wiki, it was never his error, not to mention fSTR is still only estimated except at cap. I actually witnessed this discrepancy personally while checking numbers on the very same birds.

I'm not sure of your nationality Masa and thus if you've heard this phrase or not, but its very applicable: Work Smarter, Not Harder.

Beat numbers together all day, or look at the bigger picture and a surprisingly simple explanation?

Direct consequence: exact DMGmin and DMGmax functions (same for crits) are still unknown, just have a very rough highly approximated idea...

Maximums are easy. People have been throwing max-pDIF numbers around for a long time, and 2.77 and 3.15 are the favorites.

Crit pDIFa caps at 3.0, this was actually never changed, instead a secondary randomizer was applied to make damage fluctuate (and confound the hell out of analysts):

3.0 pDIFa * 1.05 = 3.15 pDIFb

Max pDIF used to be 1.2 * cRatio.

Ratio was changed to being capped, at 2.2, instead of cRatio. Presume zero level correction for now.

2.2 * 1.2 = 2.64

Apply secondard randomizer, maximum 1.05:

2.64 pDIFa * 1.05 = 2.772 pDIFb

Sound familiar? Nothing changed except for a capping method and an extra, random, final multiplier.

Occam's Razor: The Simplest explanation is usually the correct one.

You keep coming at this with the thinking that one of us is wrong, which is completely the wrong attitude to have. You need to chill out and give it a shot. Your data fits my model with but a few exceptions, one of which I already cleared by virtue of incorrect source data (why would a lv63 and a lv64 Lesser Colibri have the same VIT value anyway?). Nothing you've posted is incorrect or invalidated. You open hostility seems to betray that you perceive I'm calling you a liar or something. This began when I pointed out an error that wasn't yours, and suddenly you had this righteous mission to deny and destroy everything I might bring to bear about damage calculation no matter how viable.

I ask that you step back, check your bias and grudge at the door, and take a harder look at this simpler method. It even surprised me how little SE had to change to turn what people thought of damage calculation upside-down, though in reality it hardly changed at all.

[Masamune]

Raellia i'm totally agreed with what you wrote, and i even started the same way !

Problem is when confronting this simple theory to the rest of damage distributions i got: like 80% gets more and more damage discrepancy as Ratio decreases... That alone definitely shows there is more than just a fSTR jump for a particular level of tested mob (which would be seeable through curves with saw shaped, which isnot the case)

2nd problem is pointing at a wrong VIT value may sound logical at 1st glance between decreasing lvls of mobs, but then that would put in question the whole method of determining said VIT value (fSTR=-1 + dmg1 weapon) which leads again to another possible conclusion that fSTR function maybe badly determined ? I didnot make tests yet for fSTR, so i don't know and kept an assumed constant fSTR.
Same problem applies to the mob_defense values used: where are the tests proving that /checks with player attack values are :
Scenario a) Currently used: LowDef message -> your Attack-1=25%*def, HighDef message -> Your attack+1 = Def
Scenario b) (LowDef Attack - HighDef Attack)/2 = Mob_Def ?
Scenario c) other ratio between LowDef attack and HighDef Attack ?
So there again i assumed they correct.

And last problem is nothing tells me that the measured extremes dmg values i got are the actual extremes ones :s ... except maybe sample size of 1k+hits/test.

For info, Motenten also had a look at my distributions, and came up at a much more complicated model with like 2-3 of intermediate multipliers to almost reach all extremums dmg values of any of my distributions.

So under all those asumptions and observations, yes it's tempting to just use "a guess" like you well explained with German Tank problem, but isnot my goal honestly. Indeed, that's exactly what japanese did with approximating currently used equations coefs, and now you with this additional post-randomizer of 5%.
So why would i bother doing all those tests ? to actually avoid those approximations leading to wtf results like Ringthree 1st pointed out at his blog (showing a clear dmg difference). Lastly, the averages calculations are also as much important if not more than extremes values : the observed enhanced frequencies in some distributions definitely fuck up any "simple" linear average calculations.

Personnaly, i wish i had something to backup initial asumptions we are all using, ie the VIT and Def methods. Without backup data, all we doing is assuming and so i "screamed bloody murder" that just pointing a possible fSTR jump (due to one of mob level VIT maybe wrong) isNOT an actual data proof ! Personnaly i can't go lower than STR60 @ 75, and don't have any non75 job above lvl65, so how to prove those VIT values* ?.

*Edit: with another method than working backward from lvl81/82 Gcoli stats, which give VIT52 52 55 for resp lvl63 64 65 Lcolis.

EDIT2: forgot to mention something else also: if that [1;1.05] post-randomizer exists, then corrected dmg distributions (DMGmeasured/1.05) would show missing values. Sadly, almost all tests show that each single dmg value within the range is generated, except the tests with dagger (probably because of the 1.25 piercing bonus) which shows missing dmg values ending with "4" or "9". So maybe your post-randomizer would apply ONLY at end dmg values ? (which sound highly impractical in terms of implementation, compared to a direct formula)

[CDF]

There is a subtle difference between a sum of uniform random variables and a (very special case of the...) product of uniform random variables. The probability densities basically will look trapezoidal for the most part (for the product, the "linear" increasing and decreasing regions vary logarithmically). However, the density of the product will look less symmetrical where the density of the sum is symmetrical.

[Masamune]

Ok good to know, just i'm more concerned by the basis, ie what Raellia pointed: maybe wrong VIT values for lvl 63 and/or lvl64 test mobs.

While searching for methods for determining vit, i remember reading Nagamaki using the Mode of its distributions, ie the famous "spike" observable for Ratio below 1.5.
Problems are :
1. that spike usually doesnot apply to 1 dmg value but 2-3 values, within a range corresponding to 1.0<=pDIF<=1.05.
2. After did recently a distribution with Attack=241, DMG1 weapon and STR=85, only on Lcoli lvl65, i get a clear spike for only the dmg value "9" (other values get much lower frequencies). So if i use that value like this :
ModeDMG=(WeapDMG+fSTR)*pDIF, with pDIF=1 since my attack = LcoliLVL65_Def
...leads to :
fSTR=ModeDMG-WeapDMG
((STR-VIT)+4)/4=9-1=8
85-VIT=8*4-4=28
VIT = 57 for Lesser Colibri level65

Such difference with the common value of 55 would means basically that Gcolis VIT is wrong too ?
Another explanation would be the whole fSTR approximation being wrong, which explain a lot why never managed to get matching models...

[Raelia]

I was under the impression that Gobli's mob data was more of a table lookup based on mob, job, and level, not some crazy derived equation. Nobody has 'tested' the Mamool Ja Stabler's VIT value, but it was estimated from being a beastman, BST job, lv81-83, but from the wiki:

Level 81: Defense 336, Evasion 334, VIT 77, AGI 69
Level 82: Defense 341, Evasion 339, VIT 77, AGI 69
Level 83: Defense 346, Evasion 344, VIT 77, AGI 69

Why do they have all the same stats? Something should change over three levels.

Studio Gobli does note the Aht Urghan mobs are very complicated.

They call out D VIT and F AGI for BST. and most other times mobs have racial ranks of 'C'. Subjob is usually the same as main job (PCs don't get that benefit).

Subjob correction doesn't kick in til level 30 but I'm not sure of the scaling. I'll use 0.5 just for kicks.

Race + Main Job Rank + Subjob rank * Subjob Rank Correction
C + D + D*0.5

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

Level 81:
33 + 29 + 7 = 69 VIT

Level 83:
34 + 29 + 7 = 70 VIT

The subjob correction may need to be picked at by someone who speaks Japanese marginally better than I can (not a kanji reader). I believe the implication is that it scales up from 0.0 starting at level 30 or SJ level 30 (main 60), but I think it bears significance towards something:

Lesser Colibri, E rank VIT, RDM/RDM (E):

Lv 63
19 + 19 + 4 = 42 VIT
Lv 64
19 + 19 + 5 = 43 VIT
Lv 65
20 + 20 + 5 = 45 VIT

I know these numbers are likely incorrect, they seem much too low, but it shows well enough that VIT should change across all three levels. Notice the drop in VIT from Subjob at 63/31, perhaps the error made was in simply spreading the subjob value across all three levels after calculating once.

Edit: I think I'm missing base stats somewhere, else they'd be completely zero at level 1.

[Masamune]

Check "mob Data" tab in my excel tool in my sig, calculations showed for Gcolis 81/82 and for Lcoli63/64/65 VIT/AGI and Def/Eva.
(with source links)
Posted also on various mob's Discussion page the calculations for their stats (see for example Colibris and Ul'Hpemdes).

I may get some confirmation of Lcoli vit from direct fSTR-1 method from Pchan/CDF/Shamaya (when they can)

[pchan]

Target are level 65 LC

@ 42 str you hit for 1
@ 41 str you hit and crit for 0

This means str 41 is dstr=-14. So 55 VIT

[Raelia]

Its the level 63 we're interested in.

[CDF]

Level 65 (verified by EXP points)
41 STR: hit for 0
42 STR: hit for 1

Level 63 (verified by check)
38 STR: hit for 0
39 STR: hit for 1

Level 64 (verified by check)
38 STR: hit for 0
39 STR: hit for 1

Now, I don't know how the game handles fSTR when it is not an integer (assuming the model is correct). For example, if level 63/64 lesser colibris have 52 VIT, then fSTR = -3/4, rounded to 0?

Methods section:

NIN75/SMN01 tarutaru (54 STR)

Trainee burin
War shinobi gi: -2
Steppe stone: -5
Snow ring: -2
Cursed soup: -7
other items to add str +1
Swift belt to modify attack for /check (H2H skill 200)

[Masamune]

Thank you both Pchan and cdf.

regarding :

Now, I don't know how the game handles fSTR when it is not an integer (assuming the model is correct). For example, if level 63/64 lesser colibris have 52 VIT, then fSTR = -3/4, rounded to 0?

Imo i think the game just do the calculations without any truncations until the end (just before displaying on log) where it applies a truncation to integer. Just my opinion, but it gives us some margin to play with data, as long the final number obtained, despite its decimals, matches the observed one.

For Raelia: apply same methods (fSTR-1 and stats formulas) on Colibris lvl71-73, you'll find also all 3 levels gets same VIT value (and same AGI value too btw).

So in the end, if there were a prob with determining VIT methods, then would have to reconsider the whole system of VIT and Def :/
So just for convenience, i think better to leave it as it is and try to get a DMG formula with those VIT/def values.
Personnally, there are so much possibilities of dmg formulas to test i think there should be at least one somewhere that gives exact same values as observed ones.
Only thing i'm sticking at is the format :
DMG = Randomizer(s) x f(Ratio) x g(WeaponDMG + (STR-VIT))

... for example:
DMG = FLOOR( ( RAND1[R1min;R1max] + RAND2[R2min;R2max] ) * (a*Ratio+b) * (c*WD + d*(STR-VIT)+e) )
solve with data available for (R1min,R2max,a,b,c,d,e). Personnally, i fail with Excel Solver and multiple datas... but should make it work one day lol.

[Raelia]

Now, I don't know how the game handles fSTR when it is not an integer (assuming the model is correct). For example, if level 63/64 lesser colibris have 52 VIT, then fSTR = -3/4, rounded to 0?

The game likes to floor lots of stuff before final damage. Take a look at WSC mods for level 75, let's say 63 STR on a 50% mod:

You take .50 * 63 for 31.5, floor that, multiply by ~.83 for lv75 correction, and floor it again. It gives only 25 WSC, not 26 if it wasn't floored. Theres a more specific example I could give, where you can identify both floorings because the WSC is reduced by two, one for each, but I can't recall it at the moment.

If fSTR is being floored in much the same manner (after calculation, but before final damage multiplication) then indeed the "-1 fSTR" method only gives the maximum VIT the mob can have. The lv63 LC can have as low as 49 VIT and still provide that result, and definitely be providing an extra fSTR at high values.

[Masamune]

The game likes to floor lots of stuff before final damage. Take a look at WSC mods for level 75

It's not the game, it's the little genius(es) that modelized the whole system that decided that multiple floorings is needed to obtained "accurate" numbers in the end. Big difference.
Even worse, your WSC example i think has been modelized most probably from .... base dmg formula we are trying to "fix". Same for all the rest of formulas...
That's why i think we should focus on that dmg formula and base stats VIT DEF, while completely forgeting what comes after (ie WS formulas, crits dmg, JA dmg, range dmg, bluphysmagic dmg, pets dmg etc...).

[Raelia]

I think you're trying too hard to rewrite everything.

The damage formula set didn't change that much with the first and second 2-hander updates. We still have working functions for getting our base damage, even with those wacky WSC calculations (which never fail actually).

In a fit of rage over people giving advice like 'pump cRatio to overcome level correction' and other crap that no longer worked (level correction was still apparent), I sought to figure out what SE changed and found it. I knew they wouldn't have done a fundamental rewrite of the whole damage system (and especially still end up with mostly the same numbers).

Damage calculations from scratch already as close as possible, and then two piddly things changed and it seems the confidence was lost.

1. Ratio is now capped, 2.0 for 1-handers 2.2 for 2-handers (cRatio is no longer capped, this was to make level correction always have an effect on final damage)
2. A final randomized multiplier, ranging between 1.00 and 1.05 was added after damage calculation.

I can say these things with utter confidence, because with their application (or rather, divide them out) all of the old stuff still, for the most part, fits. Particularly, everything for Ratio>10/6 fits perfectly. I could definitely understand if SE boosted pDIF for Ratios between 5/6 and 10/6 to help one-handers at the same time.

I don't understand your complete lack of confidence in current knowledge of damage calculation save for a muckup with fSTR calculation and some mid-level-Ratio quirkyness that I already attributed to a plausible 1.25x multiplier instead of 1.2x for pDIFmax. If anything, with my additions of cap changes and the secondary randomized multipler, you would have a hard time disproving it all save for discrepancies with the pDIF tables.

A suggestion: If you're not sure about the new pDIF tables, use these additions and rewrite those first. Incorporate the secondary randomizer/multiplier (divide your averages by 1.025 or maximums by 1.05) and you should get even digits (1.2, 1.25, etc).

I would rather a discrepancy with the system lead to reasonable modification than scrapping the whole thing entirely. Especially if it works perfectly most of the time (Ratio > 1.66~)

It's not the game, it's the little genius(es) that modelized the whole system that decided that multiple floorings is needed to obtained "accurate" numbers in the end. Big difference.

Except thats how SE coded lots of the game. You can see them flooring lots of things, best example: TP-per-hit is floored to one decimal after Store TP is applied. Its a pattern to follow and when it works... well you just go right ahead and make an umpteen-bazillion-polynomial-brainfuck equation to replace current WSC math and see which one gets used.

[Masamune]

I think you're trying too hard to rewrite everything.

Did you at least wonder yourself once why am i going this way, apparently against common and easiest sense ?

The damage formula set didn't change that much with the first and second 2-hander updates. We still have working functions for getting our base damage, even with those wacky WSC calculations (which never fail actually).

How can you say they never fail ? It's those WS numbers on contrary that showed us at the very 1st place there were something wrong with numbers, which led us to the very basis of the system, ie the dmg formula, fSTR and possibly Mob_VIT/def.

In a fit of rage over people giving advice like 'pump cRatio to overcome level correction' and other crap that no longer worked (level correction was still apparent), I sought to figure out what SE changed and found it.

Levelcorrection stuff comes AFTER base dmg formula, so there again suffice a small quirk into the base formula to be amplified after by additional mods, like Level correction or WSC.

I knew they wouldn't have done a fundamental rewrite of the whole damage system (and especially still end up with mostly the same numbers).

i'm noticing you using a lot the terms "mostly" "almost" "close" etc... which are used in a context of approximations and usually with % to quantify the relative uncertainty. Such mentality would apply on a real world phenomenon due to high constraints and costs. Here this is a lolinformaticgame with infinite possibilities to test, so why not aim to obtain an exact model ?

Damage calculations from scratch already as close as possible, and then two piddly things changed and it seems the confidence was lost.

Exactly.

1. Ratio is now capped, 2.0 for 1-handers 2.2 for 2-handers (cRatio is no longer capped, this was to make level correction always have an effect on final damage)

I didnot look at that yet, since it comes AFTER the basis.

2. A final randomized multiplier, ranging between 1.00 and 1.05 was added after damage calculation.
I can say these things with utter confidence, because with their application (or rather, divide them out) all of the old stuff still, for the most part, fits. Particularly, everything for Ratio>10/6 fits perfectly.

I don't understand your complete lack of confidence in current knowledge of damage calculation save for a muckup with fSTR calculation and some mid-level-Ratio quirkyness that I already attributed to a plausible 1.25x multiplier instead of 1.2x for pDIFmax. If anything, with my additions of cap changes and the secondary randomized multipler, you would have a hard time disproving it all save for discrepancies with the pDIF tables.

Hard time disproving? was actually pretty easy: i simply divided ALL my max values by 1.05. They "almost" match with 1-2 dmg discrepancies when starting from the caps... then those discrepancies regularly increases as you test for lower Ratios... until they become something like +10dmg difference... i don't call that a "perfect fits".
It seems i already told you someday ago that current multipliers CAN'T be constant (if using current model), all the tests shows that. Also you have the guts to tell me to look at the bigger picture while apparently you failed to notice those multipliers not only are not the same for pDIFmin and pDIFmax, but also LOWER than 1.2.
And finally, sure it can makes you have utter confidence if you stop your theory @ Ratio=10/6 without considering closely what's happening below, sure that's calling "looking at the bigger picture" ....
If could solve these general observations, yes it would raise a bit my self-confidence. For now, i call BS for anything not matching this.

A suggestion: If you're not sure about the new pDIF tables, use these additions and rewrite those first. Incorporate the secondary randomizer/multiplier (divide your averages by 1.025 or maximums by 1.05) and you should get even digits (1.2, 1.25, etc).

Like i said earlier, i started like you last year, but i didnot kept the excel sheet since numbers were going wrong that way... tough you tempt me to redo it just to make you realize how gross such approximation is, and maybe make us work together ?

I would rather a discrepancy with the system lead to reasonable modification than scrapping the whole thing entirely. Especially if it works perfectly most of the time (Ratio > 1.66~)

I wished too lol, sadly it doesnot work most of the time (i don't call just the portion Ratio>1.66 "most of the time")

Except thats how SE coded lots of the game. You can see them flooring lots of things, best example: TP-per-hit is floored to one decimal after Store TP is applied. Its a pattern to follow and when it works...

mmm personnally the tp example shows only one single flooring: the one for displaying, nothing else, and it works without any intermediate floorings, direct calculation. Well so far i didnot notice any single quirk when using non-floored decimals until the integer display... That TPmodel is exactly what i call a perfect model yielding exact same numbers as observed ones. Kudos to the genius that found it. Why not aim for same with DMG formulas ?
and again, i'll repeat one last time: SE never ever disclosed any info as critical as those formulas, those comes from dudes like you and me. Big difference making me say "i don't know" instead you saying "i'm utterly sure SE coded this and that like that.". Consequence of this difference of points of view: you stopped with this approximated solution which isnot one (and even yields enhanced errors at lower ratios), while me still trying to understand how those japanese even tested their fSTR shit while making abstraction of Ratio and WeaponDMG (especially when they didnot have Colibris or KParser 5 years ago).

So yea when no find an exact model PERFECTLY fitting data, then you tends to an harder way. This is last time i'll explain how and why i arrived to this point.

[Raelia]

I've reached a conclusion: Masa is a mathematical masochist.

Have fun reinventing the wheel.