The Math Behind DPS - A Discussion and Example

Hello

Lately I've been having a hard time deciding whether an item I am interested in trading for is actually a meaningful upgrade. Sometimes, when you get a new item, you think it'll be awesome, but its actually a DPS downgrade. This can happen because of the complicated mathematics that go on behind the scenes in this very complex but awesome game. I am in the process of making spreadsheets for each of my skills so I can easily alter the numbers to see what the outcome will be and whether that upgrade is really worth a few chaos orbs.

I will be going through these calculations for Whirling Blades and I'd like to hear from you guys if you see any mistakes in my calculations. If we can get a correct example together it could really help those that like to dig into the math and 'order of operations' perse.

So, Here is the 4 link socket item I'm going to be using so you can see all of the numbers.



Here is some given information:

Passive Tree Bonuses
Melee Damage Increase: 0%
Weapon Elemental Damage: 50%
Elemental Damage: 28%
Attack Speed: 0%
Aura buff bonus: 30%

Gear Bonuses
Physical: 10-19
Lightning: 2-41
Attack Speed: 25%

Weapon Stats
Base Physical: 74-193
Attack Speed: 1.38 APS (doesn't matter for WB however)
Lightning Dmg: 1-10

Elemental Auras
Fire: 31-51
Cold: 22% Physical
Lightning: 6-92

And then there is this:


That should be all the useful information we need to start the calculations. Ok, so lets see how this goes. I'll start by calculating all of the different types of damage, in the next post!

Total Physical Damage Min = (Weapon Base Min + Gear Min) * (1+WB Increase+Passive Increase) * (1-(aura cold convert*1.3 + glove cold convert))
= (74+10) * (1+.42+0) * (1-(.22*1.3+.25)) = 54.15
Putting in Max numbers should give a value = 159.6

The next one to calculate will be cold damage. Cold damage conversion numbers will include the .42 physical bonus from WB gem b/c I believe it applies to converted damage

Total Cold Min = (Weapon Base Phys Min + Gear Min) * (1+WB Increase+Passive Increase) * (aura cold convert*1.3 + glove cold convert) * (1 + Weapon Elemental Damage + Elemental Damage)
= (74+10) * 1.42 * .536 * 2.53 = 161.75
Putting in Max numbers should give a value of = 408.23

Fire and Lightning will be easy

Total Fire Min = Aura dmg * 1.3 * (1 + Weapon Elemental Damage + Elemental Damage)
= 31 * 1.3 * 2.53 = 101.96
So, Max = 167.74

Total Lightning Min = (Aura dmg * 1.3 + Gear Lightning Damage + Weap Lightning Damage) * (1 + Weapon Elemental Damage + Elemental Damage)
= (6*1.3 + 1 +2) * 2.53 = 27.32
So, Max = 431.62

That was the hard part. To summarize damage:

Physical: 55-160
Cold: 162 - 408
Fire: 102 - 168
Lightning: 27 - 432

So, lets figure out DPS of Whirling Blades

Attack Speed base for WB: 2.2 Seconds/Attack (I think?)
Attack speed Gear + Gem Bonus = .25 + .39 = .64
Attacks/Second = 1.408 Seconds/Attack

Average Damage = (Sum Min + Sum Max)/2 = 757

DPS = Average Damage/Attack / Seconds/Attack = 537.47

Damage Effectivness of WB is 80%, so 537.47 * .8 = 430 DPS

So, my question is... Is this correct? Are any steps out of order? I hope you guys take a second to look as it may help our understanding and allow us to make more educated decisions. Thanks!