Diablo® III

Single/Dual Weapon Equation

i saw a thread about dual wielding and i did some math
here are my calculation - i came up with the following equations
http://img337.imageshack.us/img337/5573/singledualwieldingequat.png

this is how i derived them:

***************************
Variables
DI - Damage Increase
APS- Attacks Per Second
CHC- Critical Hit Chance
CHD- Critical Hit Damage

BADPS- Basic Attack Damage Per Second
D - Damage [d1~d2]
DPS- Damage Per Second
CB- Critical Bonus
DB- Damage Bonus
***************************


for single wielding:

BADPS = [DPS]•[DB]•(CB)
SingleSpellDamage = [D]•[DB]~(add any spell specification)

where
D = [d1+d2]/2 +mod
DPS = D•APS
DB = DI/100+1
CB = [CHC/100]•[CHD/100]+1

mod is ur average bonus damage from items like rings
i.e. ring + 3-4dmg avg is 3.5dmg

------------------------

for dual wielding (* for second weapon):

BADPS* = [DPS]*•[DB]•(CB)
SingleSpellDamage = [D*]•[DB]~(add any spell specification)

where
Dw1 =[d1+d2]/2 (weapon 1)
Dw2 =[d1*+d2*]/2 (weapon 2)
D* =(Dw1+Dw2)/2 +mods (average damage of both weapons combined)
APS*=(APSw1+APSw2)•1.15/2 (average attack speed of both weapons increased by 15%)
DPS*=D*•APS*

***************************
example used:

DI = 32%
CHC = 7.11%
CHD = 100%

Weapon 1 (axe): | Weapon 2 (sword):
APs = 1.3 | APs = 1.4
D(w1) = 11~12 | D(w1) = 10~11

weapon 1:
http://img546.imageshack.us/img546/315/88639140.png

BADPS = [D•APS]•[DI/100+1]•([CHC/100]•[CHD/100]+1) <<<< using weapon 1
BADPS = [14.95]•[1.32]•(1.0711) = 21.137 or 21.37

weapon 2:
http://img815.imageshack.us/img815/7396/81269640.png

BADPS* = [(Dw1+Dw2)/2*•[(APSw1+APSw2)•1.15/2]*]*•[DB]•(CB) <<<<<<< using both weapons
BADPS* = [[11•1.55]*•[1.32]]•(1.0711) = 22.50 • 1.0711 = 24.09

dual wielding img:
http://img577.imageshack.us/img577/6294/2xw.png


note1: if ur offhand is not a weapon(i.e. its a wizard or WD offhand) any bonus damage acts like +mod. YOU DONT GET +15% attack speed increase
note2: spells/skills get attack bonus only from raw damage (attack speed doesnt effect this,unless it specifies) however the faster ur attack speed the faster u cast

so depending on 'u wana cast faster' 'u want hit faster' or 'u wanna smack hard' u choose from the above.
btw those equations are completely useless if u dont understand how to use them :D
plz correct any errors or if i am missing something thanks

Factor points:
1 Precision = 0.0988-0.0989% Critical Hit Chance
1 Attack = 1% Damage Increase


-TitanREW
Edited by TitanREW on 12/26/2011 10:52 AM PST
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dont have Attack, Precision bonuses yet, still trying to see how to add them into constants instead of ID and CB

i am not rly a politician, more like a mathematician... so u can figure out the conclusion...
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12/18/2011 12:10 PMPosted by Noxifer
And quite frankly i find this whole wall of math absolutely redundant to explain the phenomenon as top how one guy has one good weapon and one crap weapon and when he equips them both his DPS goes down...


Imagine you have a hammer and a feather. If you just swing the hammer you'll do damage to your ex-wife's car much faster than if you alternate between swinging the hammer and the feather (even though you can swing 15% faster this way).


"note2: spells/skills get attack bonus only from raw damage (attack speed doesnt effect [sic] this, unless it specifies)"
Isn't casting speed affected by attack speed?
Edited by Woggle on 12/20/2011 3:44 AM PST
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So I am really interested in the math and mechanics behind dual wielding. I know this thread is over a month old but that's not that bad, it's pertinent to what I want to discuss and already has established information.

My question is, are these equations supposed to get what we see as our overall DPS on the character sheet in game?

I can't get the equation to match up with what I'm seeing my DPS as in game for the life of me.

Fine Hand Axe
4-5 Damage
1.30 Attacks Per Second
5.9 DPS
+29% Damage

Inferior Dagger
2-5 Damage
1.39 Attacks Per Second
5.2 DPS
-0.11 Attacks Per Second

These are the weapons, I keep coming up with 7.8462 BADPS but in game it shows my DPS as 7.41 with those weapons equipped.

BADPS* = [(Dw1+Dw2)/2*•[(APSw1+APSw2)•1.15/2]*]*•[DB]•(CB)

BADPS* = (4.5 + 3.5) / 2) * [(1.19 + 1.39) * 1.15 / 2] *1.29 * 1.025 ...becomes....

BADPS = 4(1.4835 * 1.29 * 1.025)

So am I breaking it down wrong somewhere? To be honest I don't fully understand the way you formatted that formula so I worked off of the picture you linked since I understand that better.

Did I do something wrong or does BADPS just not equal in game DPS ?
Edited by D3BETA on 2/3/2012 9:59 PM PST
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