defense, attack, damage

I didn't know where to put this so I put it here as it's battle related. I did a bunch of test on the test server to express the distribution of melee hits between min damage and max damage, assuming they are given.

Let r=(your attack)/(mob's defense) [not bothering with level correction]

First case 0.75< r <1.25

Call a and b min and maximum damage, DMG your total weapon damage (incl fstr for those that know what it is). If you know what the 5% "randomizer" is those are values before accounting for this randomizer. The law of the random damage generated by the game is

d=((1-U)*V1+U*DMG)*(1+e)

e= unfiorm between 0 and 0.05; this is the so-called randomizer.
DMG= your weapon damage
U= a bernouilli variable which parameter is unknow so far, taking 2 values, 0 or 1
V1=uniform on [a,b]

In other words
IF U=0 THEN d=DMG*(1+e) ELSE d=V1*(1+e) END IF;
is a simple code that give this random variable.

Notes : this is obtained through data. When fighting EM sandsweepers in aby-altepa, if your def is in the correct range then there is a fixed interval of values (it's the same interval regarless of your attack) that have high frequencies, and they are always DMG->DMG+5%. For instance I was on pup and had 104 total damage including fstr, then I would find that the values 104,105,106,107,108,109 happen nearly 30-50% of the time.

This implies the following form for the distribution of the random damage 'd'

http://i189.photobucket.com/albums/z...104_ATT429.jpg

The average damage is therefore

d*=(1-q)*1.025*(b+a)/2+q*DMG*1.025 where q is parameter of the Bernouilli U

The proportion of numbers lying is the interval [DMG,DMG*1.05] seems constant equal to about 35% and doesn't seem to vary much with attack values. This proportion is , with the above model,

q+(1-q)*ln(1.05)*DMG/(b-a) .

Can provide data if needed.


second case 0.75> r > 0.5
In this case of DMG is equal to b we still have:
d=((1-U)*V1+U*(DMG)*(1+e)

The frequency spike happens at the upper bound of the damage range (b=DMG so the actual maximum observed is DMG*1.05).


second case case r>1.5
In this case DMG is still outside of [a,b] (DMG<=a) there are not high frequency values, so it's natural assumption that the roll U is equal to 1. It means that the parameter of the bernouilli U is likely zero when ratio>=1.25

exemple

http://i189.photobucket.com/albums/z...nterstance.jpg
(only the shape of the graph is relevant)

How to find a mob's damage
Easy. Get hit a a couple of times with a non retarded def and examines is the lowest value of the frequency spikes. Exemples, the chigoes in caedaerva mire have about 70 damage as "weapon"

**asuming mob's pdif works the same**

How to find a mob's VIT
Check what is the minimum frequency spike you are getting and reverse the fstr formula.

Edited the previous post as the behavior is changing for 1.25<r<1.5 and 0.5<r<0.75

second case case r>1.5
Same as above, d=(1+e)*V1

So it's roughly uniform

third case 1.5>r>1.25
In this case the equation still holds
d=((1-U)*V1+U*DMG)*(1+e)
because in this case the true min pdif equals weapon DMG, therefore the distribution has a spike at its lower bound
However the frequency is decreasing if r grows towards 1.5 at which point there is no more spike (assuming therefore that the parameter of the bernouilli is equal to 0 at 1.5 pdif)

What remains is to examine the variation of the parameter of U with r. i'm suspecting that this parameter p is 0 for r>1.5 and r<0.5 which is basically when the weapon DMG doesn't appear in the hits values, making the formula still hold. However monster vs player seem to indicate that at very low pdif a frequency spike appear at the lower bound of the damage values so something else could happen at this point (flooring).

Sorry... I didn't see where you define a and b, as well as p. Mind elaborating those points?
The model offered seems plausible to generate the spiking behavior.

I'm not interested in findind a,b. For this look at the threads on BG. Knowing a and b, aka the min and max pdif values (more or less 5%) isn't going to help you modelize damage.

P is the parameter of the berouilli it is unknown what exactly it is dependant from, though likely a function of ratio. It is 0 at 1.5 pdif and decreasing between 1.25 and 1.5. I need larger samples per data point to estimate it correctly. p is responsible for the "spike" around the DMG value +0~5%.

Which Samples do you need at which cRatio ? i made a large number of parses which may help you ?

I have questions about your reasoning:
- what tells you the primary pdif (before the 5% randomizer is applied) follows a Bernouilli-type law ? (and not a uniform or gaussian law for example)
- what tells you the "thresholds" are 0.5 0.75 ? (and not 0.43 or 0.71?). 1.25 and 1.5 were already known so np.
- can you post your "data" somewhere please ? (because sansweepers using berserk can screw things)

The primary pdif is not a Bernouilly and honestly I don't trust SE for generating anything but uniform laws. The primary pdif is

(1-U)V1+U*DMG, V1 uniform on [a,b] and U a bernouilli. Why ? because It's not a bell curve basically and outisde of the spike the frequencies look about the same. Also all the spikes happen between DMg and DMG*1.05 whatever you do so it's not gaussian. The reason the frequencies of the spike are not equal is because of flooring, which makes certain values less or more likely.

Also I posted this comparison on the wiki :

http://images3.wikia.nocookie.net/__.../Pdif_r094.jpg

All the data between 0.75 and 1.25 follow the same trend except for the position of spike due to a & b changing.

Under <0.75 is only assumption on my part since data is had to get, the lowest I have is 0.59 pdif. For me it's clear that the limits are determined by ratio values at which min pdif=1 (assuming 1.5) and maxpdif=1 (assuming 0.5 since it's before randomizer).

data under 0.75 pdif, everything is done on PUP without any AF3 or close to naked THF
(format : melee hit value : frequency, H2Hskill_strvalue_attvalue_damagevalue on H2Hwpn)
H2H300_STR94_att273_D0:= [[9,11],[10,15],[11,9],[12,13],[13,17],[14,21],[15,21],[16,18],[17,20],[18,25],[19,15],[20,10],[21,22],[22, 8 ],[23,28],[24,15],[25,13],[26,20],[27,20],[28,24],[29,19],[30,18],[31,24],[32,19],[33,14],[34,25],[35,19],[36,12],[37,35],[38,30]]:
H2H300_STR134_att288_D0:=[[17,1],[18,8],[19,3],[20,4],[21,5],[22,7],[23,7],[24,5],[25,7],[26,5],[27,4],[28,9],[29,7],[30,4],[31,12],[32,5],[33,10],[34,11],[35,6],[36,7],[37,4],[38,7],[39,2],[40,11],[41,5],[42,7],[43,10],[44,26],[45,15],[46,19]]:

data 0.75<r<1.25 pdif,
H2H404_ATT350_STR91_D0:=[[20, 7], [21, 17], [22, 36], [23, 39], [24, 36], [25, 35], [26, 35], [27, 34], [28, 41], [29, 40], [30, 36], [31, 48], [32, 32], [33, 37], [34, 44], [35, 33], [36, 33], [37, 42], [38, 50], [39, 33], [40, 38], [41, 28], [42, 47], [43, 36], [44, 33], [45, 37], [46, 39], [47, 211], [48, 186], [49, 187]]
H2H404_ATT360_STR116_D39:=[[45,6],[46,2],[47,7],[48,3],[49,6],[50,3],[51,2],[52,6],[53,9],[54,2],[55,6],[56,1],[57,2],[58,4],[59,2],[60,2],[61,3],[62,3],[63,2],[64,4],[65,2],[66,3],[67,2],[68,7],[69,4],[70,4],[71,7],[72,3],[73,3],[74,5],[75,6],[76,3],[77,3],[78,2],[79,4],[80,5],[81,5],[82,4],[83,2],[84,6],[85,2],[86,5],[87,5],[88,4],[89,3],[90,4],[91,19],[92,19],[93,27],[94,21],[95,19],[96,2],[97,2]]
H2H427_ATT399_STR176_D42:=[[59, 2], [60, 5], [61, 4], [62, 3], [63, 14], [64, 6], [65, 5], [66, 9], [67, 5], [68, 6], [69, 4], [70, 9], [71, 4], [72, 4], [73, 6], [74, 7], [75, 4], [76, 5], [77, 4], [78, 12], [79, 4], [80, 3], [81, 5], [82, 4], [83, 5], [84, 5], [85, 9], [86, 9], [87, 9], [88, 4], [89, 8], [90, 7], [91, 6], [92, 8], [93, 6], [94, 10], [95, 9], [96, 15], [97, 5], [98, 7], [99, 3], [100, 8], [101, 3], [102, 10], [103, 6], [104, 45], [105, 46], [106, 44], [107, 37], [108, 29], [109, 43], [110, 8], [111, 12], [112, 10], [113, 13], [114, 7], [115, 6], [116, 4], [117, 8], [118, 5], [119, 6], [120, 9], [121, 7], [122, 0], [123, 2]]
H2H427_ATT429_STR176_D42:=[[67,3],[68,6],[69,6],[70,13],[71,9],[72,7],[73,9],[74,10],[75,14],[76,16],[77,5],[78,4],[79,7],[80,4],[81,12],[82,8],[83,8],[84,12],[85,6],[86,7],[87,7],[88,8],[89,12],[90,8],[91,10],[92,9],[93,7],[94,7],[95,7],[96,9],[97,16],[98,8],[99,15],[100,8],[101,12],[102,13],[103,4],[104,56],[105,48],[106,46],[107,54],[108,61],[109,52],[110,10],[111,7],[112,8],[113,7],[114,7],[115,10],[116,10],[117,12],[118,11],[119,9],[120,4],[121,10],[122,9],[123,10],[124,9],[125,3],[126,6],[127,5],[128,5],[129,3]]:
H2H404_ATT467_STR91_D0:=[[34,9],[35,28],[36,38],[37,29],[38,40],[39,31],[40,37],[41,22],[42,41],[43,33],[44,42],[45,41],[46,32],[47,205],[48,190],[49,158],[50,35],[51,30],[52,33],[53,28],[54,26],[55,34],[56,30],[57,31],[58,26],[59,37],[60,33],[61,29],[62,16],[63,13],[64,9]]:
H2H427_ATT572_STR176_D42:=[[104, 88], [105, 88], [106, 108], [107, 104], [108, 110], [109, 113], [110, 19], [111, 20], [112, 20], [113, 26], [114, 7], [115, 25], [116, 18], [117, 26], [118, 9], [119, 20], [120, 15], [121, 13], [122, 13], [123, 20], [124, 17], [125, 16], [126, 24], [127, 24], [128, 16], [129, 28], [130, 13], [131, 16], [132, 17], [133, 16], [134, 21], [135, 15], [136, 17], [137, 33], [138, 30], [139, 22], [140, 19], [141, 11], [142, 12], [143, 15], [144, 15], [145, 17], [146, 20], [147, 21], [148, 27], [149, 33], [150, 23], [151, 9], [152, 26], [153, 22], [154, 17], [155, 19], [156, 24], [157, 19], [158, 13], [159, 13], [160, 28], [161, 18], [162, 17], [163, 20], [164, 12], [165, 22], [166, 10], [167, 5], [168, 7], [171, 5]]:

data above r=1.5
H2H427_ATT715_STR176_D42:=[[112,2],[113,1],[114,7],[115,9],[116,8],[117,6],[118,7],[119,17],[120,8],[121,14],[122,9],[123,9],[124,5],[125,6],[126,8],[127,5],[128,9],[129,6],[130,9],[131,8],[132,9],[133,17],[134,11],[135,5],[136,4],[137,6],[138,11],[139,12],[140,9],[141,4],[142,6],[143,11],[144,11],[145,7],[146,6],[147,4],[148,8],[149,11],[150,10],[151,6],[152,4],[153,12],[154,7],[155,9 ],[156,13],[157,5],[158,7],[159,10],[160,9],[161,8],[162,11],[163,8],[164,6],[165,4],[166,4],[167,12],[168,9],[169,7],[170,6],[171,8],[172,13],[173,8],[174,9],[175,11],[176,8],[177,11],[178,5],[179,13],[180,7],[181,16],[182,9],[183,7],[184,6],[185,3],[186,5],[187,8],[188,15],[189,8],[190,7],[191,10],[192,11],[193,4],[194,8],[195,8],[196,5],[197,11],[198,9],[199,10],[200,15],[201,8],[202,9],[203,3],[204,6],[205,4],[206,5],[207,3],[208,2]]:
Got other data for high pdif but it's monter vs player.

Nice !

Thanks for the explanations and data (where are crits?).

What are SandSweeper's Defense and VIT ? How you filtered out hits landed during their Berserk ?

Did you get a look at tests done @ Mathy BG forum ? some data might help ? You didnot answer my 1st question: which test do you need (at which cRatio) ?

EM sandsweepers have 457 def idk about their vit but it should be easy to get from the data itself. The first data set for H2H=300skill, no weapon, 94 str gibes you a base damage of 37. As 0.11*300+3=36, you are @ +1 fstr. Now the data H2H404_ATT350_STR91_D0 gives 47 damage, while 404*0.11+3=47 so that's +0 fstr. Thy have between 101 and 104 VIT I guess ? The exact value doesn't matter as your total damage can be read on the graphs.

Berserk is not a problem, you just move to the next mob.

I would need data between 0.5 and 0.75 to confirm the variations of the paramater 'q', namely that it is zero @ r=0.5 (vanishing spike). I have good approximations @ r=0.75, 1, 1.25, 1.5.

Also in order to maximize the data I removed all crit atma/merit/dex w/e so their data is too small. I could do that later to examine how a crit is obtained.

For crits in abyssea, i parse with 50% critrate using atmas GnarledHorn and DarkDepths, yielding 40% together on top of your own ~10% base critrate. So a parse of 3k hits should have about same sample size for normal or crit damage.

Regarding generation of a crit, it's easy:
On the formula, particularly the term V1, instead of using a simple RAND(0;1), you add another term to it:
+ IF(RAND(0;1)<=CritRate%;1.x;0) ,where x=the gap between crit mins and normal maxs.

Regarding thresholds below r<~0.8, we still trying to figure out if it occurs at 0.8 0.75 or 0.7, but not easy to discern because of the secondary randomizer... Same problem around r~0.5 or 0.45?

I forgot also to mention something fundamental about the way to consider this frequency modeling:
The frequency spike(s) is a "signature", ie i think is something original SE devs actually didNOT want. That means those spikes are INDIRECTLY generated from a formula "format" non determinist, ie can NOT model something like "30% of the time, when 0.75<=r<=1.25 we have pDIFa=1, and normal randomized shape otherwise"... and that's what you wrote basically :s
This particular signature also "transfers" to crits at low cRatios, when pDIFa=1 belongs to crit damage.