Diablo® III

Weapon Study

87 Orc Warrior
Posts: 421
I've been wondering about which weapon to use whenever I pick up some weapons. I've wondered so much, that I feel I have to do some research and testing about the weapon calculations. So I did.

I am not going into too much detail (hopefully). I will list out some seemingly facts. For people who don't want to read, jump to the end.

Let me clarify a term first - weapon damage
Weapon damage is a vague term, there's maximum damage, minimum damage and there's bonus damage added to them. what the game uses (to calculate the weapon DPS and other) is the average base damage plus average bonus damage. for example

Reckless Sickle of the Angels
Magic Mighty Weapon
14.9 Damage Per Second
8-15 Damage
1.30 Attacks Per Second
. +1-3 Holy Damage
. + 3 Maximum Fury (Barbarian Only)

Now how do we read it? What is the weapon damage? The weapon damage of this weapon is (8+15)/2=11.5. Do note that the 1-3 holy damage is purposely ignored, because the displayed 8-15 damage already includes that. (check any same type of magic weapon, subtract the white damage by the bonus damage, you will get the same base damage, thus the white damage listed already includes the bonus damage)

After knowing the weapon damage, the dps is easy to get: weapon damage x APS = DPS.
Thus in our sickle's example, 11.5*1.3=14.95 (round down to 14.9, the game seems round down damage/dps all the time)

This is a typical weapon with bonus damage, easy to understand. Now what if the weapon has IAS stat on it? well it's also easy, the IAS is already included in the white APS number. for example:

Grand Initiation
Rare Mace
13.1 Damage Per Second
8-13 Damage
1.25 Attacks Per Second
. +2-3 Lighting Damage
. Increase Attack Speed by 4%
. Each Hit Adds +2 Life
. Monster Kills Grant +4 Experience.

In this example, we notice the weapon attack per second is 1.25, while a white mace's APS should be 1.2. with 4% increase, 1.2 x 1.04=1.248 (round up this time to 1.25. I really don't know how blizzard does the rounding) which gives us exactly the listed APS

My level 10 barbarian, with 60 str (which is a 60% damage increase), 10% crit chance and 100% crit bonus (which is a 10% damage increase on top of everything), passive skills included, in her bare hands, does 4.40 damage per second. This is the number listed on my character screen what does this mean? That means her hands' damage per second x 1.6[str] x 1.1[crit] x (1+dual wield bonus [which is 0 here]) = 4.40

That translates into a 2.5 dps with her bare hands before the multipliers. Which I suppose is 2-3 or 1-4 damage with a 1 attack per second speed. Now substitute the 2.5 hand dps with any weapon dps, you will have the formula for any single weapon (either 1h or 2h). When dual wielding, just do this equation twice for both weapons, where the DW bonus is 15%; add them up and divide by 2.

Now let's move onto weapon choices. Say if I have a good 1 hander, under what condition should I switch to DW and score a dps gain? same question for switching to 2handers.

Before we going into these two questions, I have to let you know that weapon damage and weapon speed doesn't really matter by themselves, DPS is the only thing that matters, because almost all the skills in this game (up to level 13 at least) is on real swing timer, rather than on cool down. If a skill is on cool down, it then favors slower weapon of the same dps, but since the skills we have aren't cool down based, we only need to look at DPS.

That said, knowing the equations and the fact that we only care about dps, I have the following conclusions:
1. use dw only if the second weapon's listed dps is more than 74% of the first one. 74% is the breakeven point. That means if a second weapon's dps is weaker than 74% of the first weapon, it'll in fact make your dps output less to dw (better weapon's dps x 0.74, compare to the worse weapon).
2. Comparing a 2hander with dw, use 2hander only if it's listed dps is more than 115% of the 2 1handers' average dps (add up the 2 1handers' dps, divide by 2, then times 1.15, compare that to the 2hander).
3. Because any dps related stats on weapon are already calculated into the listed dps, dw doesn't benefit your dps stats-wise. stats like mf, exp bonus, life leach etc don't really contribute to your overall dps. (Life leach on one weapon actually contributes to both weapon hits when dw.)

All in all, when deciding what weapon to use, just check the damage number on character screen. it's an absolutely accurate reference unlike damage numbers Diablo 2, thanks to the game design.

Ps. Please point out any mistakes I made, if you see any. Thanks for reading.
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87 Orc Warrior
Posts: 421
Just to add something about quivers

quivers I've seen all have 10% IAS, which of course contributes to the main hand range weapon. So it's a main hand range weapon x 1.1 compare to 2 weapons' average x 1.15, in the case of 2 demon hunters.
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100 Tauren Druid
Posts: 4,963

Use 2hander only if it's listed dps is more than 115%

This conclusion hasn't included how a 15% multiplicative bonus factors off_weapon damage sources.

if a majority of damage is created off_weapon lowering APS can net a final loss

Weapon tooltip dps should be used only to quickly compare weapons, such as 2h vs another 2h.. or a 1h vs another 1h
...but when comparing single wield with dual wielding you certainly want to use the sum of all gear, e.g. equip them and check the final DPS listing on your character
Edited by Korba on 3/12/2012 11:30 AM PDT
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87 Orc Warrior
Posts: 421
Honestly, I don't understand what exactly you are saying, but...

Well my conclusion is sufficient in most cases (up to level 13 at least), with the exception of having primary stats on the weapon(s), that is str, dex, int for corresponding classes. Without primary stats, my conclusions should be correct.

edit: grammar
Edited by Tauntface on 3/12/2012 6:15 PM PDT
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You did not take into account +damage items (rings/amulets) or + attack speed item (gloves).

Lets say you have a single 2-4 damage amulet equiped.

You have two one handers with 2 attacks per second and 4-6dmg. (10DPS ea, so 11.5 dps with DW bonus)
Your dps with the amulet will be 16dps for 1 1hader or 18.4 dps dual wielding these weapons.

Now lets compare that to a two hander with 1.15 aps and 8-12 damage (11.5dps, same as DWing the two one handers if amulet is not considered)
Dps with the amulet will be 14.95, significantly less than that of two one handers, even though the items themselves had equal dps.
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100 Tauren Druid
Posts: 4,963
Off_weapon damage sources are treated as if they are part of the weapon. Imagine the following, 2-4 ring, 1-2 ring & 2-4 amulet with the following options for weapons

scenario A)
a Fuscina 'off the eel' (1-2 lighting) creates a 11-16 damage @ 1.2 speed = 16.20 DPS

scenario B)
a shiv with 4-11 damage @ 1.5 = 11.25 DPS

scenario C)
dual wielding scenario B's 4-11 with 11.25 DPS each, but your final APS is = 1.72

((11+16)*.5 + (5+10)*.5 ) * 1.2 = 25.2
((4+11)*.5 + (5+10)*.5 ) * 1.5 = 22.5
((4+11)*.5 + (5+10)*.5 ) * 1.72 = 25.8

scenario C is highest because speed bonuses multiply the additional source of damage from rings/amulet greater than what the Fuscinas DPS with its slow speed

edit (changed scenario A to an actual 2-hand weapon)

so it's fine to use weapon tooltip to compare weapons that are used the same, 2h vs 2 hand.. 1 hand vs 1 hand. but not 2h vs dual wield 1 hand, for that you should check the final damage on equip
Edited by Korba on 3/12/2012 10:50 PM PDT
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87 Orc Warrior
Posts: 421
guys, i have to admit i haven't take into account the rings and amulets, that's my fault. However, that's because I haven't seen them yet in beta. I started palying since patch 14.

Anyway, a fixed damage increase on non-weapon pieces will for sure favor faster APS weapon(s), no doubt about that.
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