I enjoy theorycrafting and was looking forward to getting started on understanding the fundamentals of Diablo 3, but I've come across a problem.

The intuitive formula for calculating average DPS, which for the time-being excludes attack speed modifiers, additive dmg modifiers and non-attribute multiplicative dmg modifiers

DPS = uva(1 - w) + uvawx = uva(1 + w(x -1))

with

u = Avg Weapon Dmg

v = Attacks Per Second

a = Attribute Modifier (i.e. 1.45 for a DH with 45 Dexterity)

w = Crit Chance (.05 in all the calculations below)

x = Crit Damage Modifier (1.5 in all the calculations below)

Anyways, that formula's pretty basic and intuitive, I really can't imagine that they're using a different formula to calculate the DPS that displays in the character tab.

So, here's where the problems arise. Mind you, all the discrepancies are pretty minor, but as the numbers get larger, and as you start to incorporate other factors such as attack speed, and other dmg modifiers these small discrepancies will become large discrepancies.

Here are 4 examples of the differences in calculated DPS and displayed DPS:

Broad Axe, 6-10 dmg, 1.3 Attacks per Second: Calculated DPS = 15.4570, Displayed DPS = 15.45

Javelin, 5-6 dmg, 1.2 Attacks per Second: Calculated DPS = 10.7010, Displayed DPS = 10.69

Hand Axe, 3-4 dmg, 1.3 Attacks per Second: Calculated DPS 6.7624, Displayed DPS = 6.76

Magic Hand Crossbow, 3-17 dmg, 1.6 Attacks per Second: 23.78, Displayed DPS = 23.77

The differences might not seem like much, but I don't know how to explain them. It isn't a case of the client rounding the values down, because in examples 1, 2 and 4 this doesn't occur. It also isn't a case of the client only displaying to the hundredth and not rounding, because in examples 2 and 4 this doesn't occur.

So, my question is what is happening here?

It's possible that there is a non-discrete, or a discrete non-uniform, probability distribution being used to determine the weapon's damage on each swing/shot, but it would have to be very close to the normal discrete distribution where each value within the range has an equal chance to account for the weapons' displayed DPS values being so close to what you'd expect from this uniform distribution.

It's also possible that the displayed values for the damage ranges for each weapon isn't accurate. If you look at the weapons in the Game Guide, a lot of them have a range of values for the min and max damage values, i.e. http://us.battle.net/d3/en/item/club . It's possible that the min and max values on weapons that drop in game are some number between these ranges and that the game is rounding the number on the tooltips, but all the calculations are done with the non-rounded values. If this is the case, I think we should have an option to show the non-rounded values.

Anyways, I posted this in the Beta feedback section and didn't get any responses. If anyone here has any idea what's causing the discrepancies let me know! This includes calling me a noob and pointing out my mistake, I don't mind this so long as it resolves the problem.

TL;DR: The displayed DPS value in the character info pane is showing values close to, but not exactly what they should be, at least according to what I think the obvious formula is. Looking for input from other people interested in this kinda stuff.

The intuitive formula for calculating average DPS, which for the time-being excludes attack speed modifiers, additive dmg modifiers and non-attribute multiplicative dmg modifiers

DPS = uva(1 - w) + uvawx = uva(1 + w(x -1))

with

u = Avg Weapon Dmg

v = Attacks Per Second

a = Attribute Modifier (i.e. 1.45 for a DH with 45 Dexterity)

w = Crit Chance (.05 in all the calculations below)

x = Crit Damage Modifier (1.5 in all the calculations below)

Anyways, that formula's pretty basic and intuitive, I really can't imagine that they're using a different formula to calculate the DPS that displays in the character tab.

So, here's where the problems arise. Mind you, all the discrepancies are pretty minor, but as the numbers get larger, and as you start to incorporate other factors such as attack speed, and other dmg modifiers these small discrepancies will become large discrepancies.

Here are 4 examples of the differences in calculated DPS and displayed DPS:

Broad Axe, 6-10 dmg, 1.3 Attacks per Second: Calculated DPS = 15.4570, Displayed DPS = 15.45

Javelin, 5-6 dmg, 1.2 Attacks per Second: Calculated DPS = 10.7010, Displayed DPS = 10.69

Hand Axe, 3-4 dmg, 1.3 Attacks per Second: Calculated DPS 6.7624, Displayed DPS = 6.76

Magic Hand Crossbow, 3-17 dmg, 1.6 Attacks per Second: 23.78, Displayed DPS = 23.77

The differences might not seem like much, but I don't know how to explain them. It isn't a case of the client rounding the values down, because in examples 1, 2 and 4 this doesn't occur. It also isn't a case of the client only displaying to the hundredth and not rounding, because in examples 2 and 4 this doesn't occur.

So, my question is what is happening here?

It's possible that there is a non-discrete, or a discrete non-uniform, probability distribution being used to determine the weapon's damage on each swing/shot, but it would have to be very close to the normal discrete distribution where each value within the range has an equal chance to account for the weapons' displayed DPS values being so close to what you'd expect from this uniform distribution.

It's also possible that the displayed values for the damage ranges for each weapon isn't accurate. If you look at the weapons in the Game Guide, a lot of them have a range of values for the min and max damage values, i.e. http://us.battle.net/d3/en/item/club . It's possible that the min and max values on weapons that drop in game are some number between these ranges and that the game is rounding the number on the tooltips, but all the calculations are done with the non-rounded values. If this is the case, I think we should have an option to show the non-rounded values.

Anyways, I posted this in the Beta feedback section and didn't get any responses. If anyone here has any idea what's causing the discrepancies let me know! This includes calling me a noob and pointing out my mistake, I don't mind this so long as it resolves the problem.

TL;DR: The displayed DPS value in the character info pane is showing values close to, but not exactly what they should be, at least according to what I think the obvious formula is. Looking for input from other people interested in this kinda stuff.