Strange weapon damage distribution

[Draner]

Hello everyone, this is my first post on this forum so before I introduce my point, I would like to thank everyone who has been contributing. There is some really advanced material on this board, like guys using Taylor series to solve Hungering arrow problems!

I wanted to test in an empirical way how the damage dealt by spells is being created in Diablo III. So I took my barb and killed 200 ravenous deads with HotA and got the following distribution (see "damage distribution" enclosed picture).

I got an average damage of 68.14. Since I have 94 str and HotA does 200% of weapon damage, I calculated 68.14/((1+94%)*200%) and I found 17.56 as the average base weapon damage. Since I have a 14-21 sword, that is to say a 17.5 average base weapon damage, I can safely say that the formula:
spell damage = base weapon damage*spell damage%*(1+bonus damage from attribute%)
is true. Here 68.14=17.5*200%*(1+94%).

But I have 2 issues that need your help:
- First, as you can see, the chart is not flat. Does somebody have an explanation for this? I expected each value to be as likely to happen.
- Second, I deducted the base weapon damage that was randomly selected between 14 and 21 to form those spell damage and plot the distribution (see the "base weapon damage distribution). It is not an integer (that is to say 14, 15, 16...). It may be obvious for you but it was not for me :), but the strange point is that this random value seems never to be close to the extremums of the range (14 and 21).
It does not look like it is caused by an armor effect because the minimum base weapon damage is 14.7 and it does not go above 20.4... the effects seems to play in opposite ways at each side of the 14-21 range. Is my formula somehow wrong? A non-linearity of the formula could explain this result.

I hope this is clear enough for you ! If it is not, do not hesitate to ask for precisions.

Thanks for your help,

Draner

[Eagle]

- First, as you can see, the chart is not flat. Does somebody have an explanation for this? I expected each value to be as likely to happen.

Insufficient data. Increase the sample size by a lot. You can't draw much in the way of conclusions about the distribution you have there.

[isak viking]

it looks great, i dont see the problem

[HardRock]

First, as you can see, the chart is not flat. Does somebody have an explanation for this? I expected each value to be as likely to happen.

Like Eagle said, you need more data. You would need an infinitely large sample to see a perfectly flat distribution.


Second, I deducted the base weapon damage that was randomly selected between 14 and 21 to form those spell damage and plot the distribution (see the "base weapon damage distribution). It is not an integer (that is to say 14, 15, 16...).

Damage is calculated as a floating point number internally and then displayed as an integer.


but the strange point is that this random value seems never to be close to the extremums of the range (14 and 21).

Again, this is most likely because of insufficient data. Another possible cause could be how D3 rounds off decimals. For example, a displayed integer DPS of 14 could be 14.9 or 14.1.


It does not look like it is caused by an armor effect

I'm not sure if enemies have armor or not. If they do, you can't ignore it. Damage resistance from armor is reduced to insignificant amounts when you're much higher level than your target, but it never becomes zero as far as I know (except when armor is zero of course). It can easily reduce your damage by a few tenths.

[NeoLearner]

For some reason I thought the problem was that the distribution was not Guassian. Seems like I've been working in the real world for too long :)

Did we in fact expect a "flat" distribution? For some reason I was expecting some approximation of a normal or a triangle distribution or something. Was it always like that?