How is listed DPS calculated when dual-wielding weapons?

I was trying out the dual-wielding in Diablo 3, when I noticed really strange. When I equipped my off-hand, which has 0.5 less damage than my main-hand. My overall damage actually went down. So my question is, how does the dual-wielding mechanic work for calculating damage? It seems rather odd that my overall damage should be more with one weapon than with two.

• When you say your overall damage went down, do you mean on your character screen or do you mean based on watching your actual damage? Commented Sep 24, 2011 at 0:46
• @bwarner Both actually. Commented Sep 24, 2011 at 1:04

Dual-wielding does not mean you attack twice as often. There is a slight attack-speed benefit, but this is apparently being offset for you by the lower damage from the offhand weapon.

According to this thread on the forums, the formula for number of attacks per second is

((Main Hand APS*1.15) + (Off-hand APS*1.15))*1/2

Which means that if you had two identical weapons, dual-wielding would give you a 15% attack speed bonus.

The main reason to dual-wield is that you get the bonus attributes from both items. This doesn't mean much early on when attributes aren't very strong, but is a big incentive later on. However, compared to a two-handed weapon that does more DPS, there isn't a clear winner. It will mostly come down to whether you've found better one-handed weapons or two-handed, and what your preference is for faster attack versus stronger attack.

• I have reasons to believe that the average APS is not just a simple average of the two APS numbers. This formula might be a good approximation of the result, but it's quite off when the two APS numbers difer by a lot. See my answer below. Commented Jun 18, 2012 at 12:33
• +1. APS numbers do not differ a lot, so this is the most use-able answer. Commented Sep 18, 2013 at 12:24

According to my own research and experimenting in-game, I have to say that the accepted answer seems wrong. If you read the linked blog in @Midnight Sparkle's answer carefully (And also watch the video), you will see that that the two given answers are contradictory.

If you open the detailed stats panel while dual-wielding, you will see that the attack speed number alternates every time you attack. This is because the damage and speed of your attack is actually calculated independently, depending on which weapon you're going to swing next.

As @Midnight pointed out, if your 1st weapon has an 1.4 attacks/sec and the 2nd weapon has 1.1 attacks/sec, you will swing the 1st, then there will be a 1/1.4 sec delay, then you will swing the 2nd, and there will be a 1/1.1 sec delay. And then the cycle repeats. (I'm going to assume that the attack speed bonus has already been applied to those numbers)

So the actual formula for Average attack per second is:

Average APS = 2 attacks per cycle / Time of cycle

Average APS = 2 attacks per cycle / (Delay of 1st weapon + Delay of 2nd weapon)

And in my example:

Average APS = 2 / (1/1.4 + 1/1.1) = 1.23 attacks/sec

@bwarner says:

Average APS = (1.4 + 1.1)/2 = 1.25 (And I think this is wrong)

Now, you probably think that this is not much of a difference, and there is a certain range where the accepted answer and formula is a good approximation of your average attacks per second. But as the disparity between your two weapons increases, it will be completely off.

Just think about it for a second: If you have a weapon that is extremely slow, say 1, and a weapon that is extremely fast, say 100, the cycle will be dictated by the slower weapon, which creates a 1 second delay after each swing. The delay for the 2nd weapon will be completely negligible, so you will get about 2 attacks per second no matter how fast the 2nd weapon is. This is very far 50.5 attacks per second, given by the accepted formula.

I'm going to go ahead and add the Average DPS. For that we first need to calculate the average Damage per cycle. Lets add two arbitrary numbers for the average Dmg of our two weapons (Average Dmg = (Min Dmg+Max Dmg)/2). 1st = 35 Dmg and 2nd = 55 Dmg.

Average Damage = (Average Dmg 1st weapon + Average Dmg 2nd weapon) / 2 Attacks per cycle

And finally:

Average DPS = Average DMG * Average APS

In our case,

Average DPS = (35+55)/2 * 2/(1/1.4 + 1/1.1) = (35+55)/(1/1.4 + 1/1.1) = 55

• Nice work. I think your math is correct. I do think you should add something at the top about the 15% weapon speed bonus though, since that is the most important detail for most people. If you do that, I think you have the best answer. Commented Jun 18, 2012 at 12:42
• Note that this is the harmonic mean of the APS, which makes sense since harmonic mean comes up a lot with rates. Commented Oct 12, 2015 at 23:22

http://www.osirisguide.com/diablo-3-dual-wield-guide/

When you are dual-wielding weapons, you alternate attacks between them for most attacks. Each weapon retains its own damage and attack speed. For example, if you have a 1.0 attack speed weapon and a 1.5 attack speed weapon, your main-hand weapon will swing first at an attack speed of 1.15 attacks per second (15% bonus from dual wield) and then your next weapon will swing at 1.725 attacks per second.

If we convert these numbers, this means that your main-hand will swing, there will be a .87 second delay (1 second / 1.15 attacks per second) and then your off-hand will attack. Once your off-hand attacks, there will be a .58 second delay before you swing with your main hand again.

Since you alternate attacks when you dual wield weapons, as a general rule of thumb your weapons need to be somewhat close in damage or else you may actually lose damage when you dual wield.

Imagine if you have a 20 DPS club and a 6 DPS club in your mainhand and offhand slot respectively. Even with a 15% attack speed buff, you still have to swing that weak offhand weapon one time for every time you swing your mainhand weapon. This will likely lower your DPS since it is slowing down the number of times you are swinging your much more powerful main-hand weapon.

• So basically the 15% attack speed can mitigate a 15% drop in damage for my lesser weapon. That would mean that if my lesser weapon is only 10% behind my better weapon (damage wise), I would benefit from dual wielding. But not when it is a 20% difference. If I understood you correctly :) Commented May 25, 2012 at 12:09

The other thing to remember when considering this is critical hits. A faster attack speed means more chances to crit, which in turn helps your overall DPS. While this probably isn't calculated within the game's dps system (as many things aren't,) it's very important at higher levels.

To the person asking about whether or not the 15% IAS (increased attack speed) can mitigate a 15% drop in damage, that's a very tricky question.

1. In order for that to be true, the two weapons you are comparing would have to be 100% identical other than damage for that to be true.

2. A faster weapon with a slightly lower dps is most likely going to "win" more often than a slower, stronger weapon due to crit hits.

3. As far as I know, stats on a weapon such as +DEX are NOT figured into dps, because the dps rating is universal across all classes. The stats that ARE figured in (again, afaik,) are +damage and +increased attack speed. That means that, when you're playing a Monk for example, and you see a weapon that is the exact same speed, has 5 dps lower than your current weapon, but also has +60DEX, the game "doesn't know" you're a Monk, so it doesn't factor in the DEX and tells you it has a lower DPS. But, since you're a Monk, that +60DEX is going to increase the damage on BOTH of your swings.

So with all of that said, there is a lot to take into account when comparing weapons. I really hope you understand what I'm trying to explain, but basically you should never simply look at DPS to decide which is better, and keeping your attack speed as high as possible should be one of your top priorities when looking for good weapons / items.

To calculate damage per second (DPS) when dual wielding:

• Find the average damage on each weapon. To do this, average the x-y damage listed on each weapon.

• Multiply each weapon's average damage by APS*1.15, where APS is the weapon's base attack speed (dual wielding gives a bonus of 15% to each weapon, hence the 1.15). This will give you DPS#1 and DPS#2.

• Average these numbers: (DPS#1+DPS#2)/2 = AVGDPS

• Apply your character's modifiers: AVGDPS*(1+MOD)((1-CRIT CHANCE)+(CRIT CHANCE)(1+CRIT MOD)) where MOD is the sum of damage increase by ability and skills (listed in details).

This gives the damage number listed in your character sheet. A key take-away here is that both the APS bonus and base damage of both weapons are taken into account, and it does not matter whether a weapon is in your main-hand or off-hand: the same DPS will be calculated.

Another take-away is that your DPS will only be as good as the DPS of both weapons, as their DPS (with the bonus) is averaged. It will do you no good to equip a poor weapon in your off-hand to get the APS bonus to your main weapon as your overall damage will suffer.

Finally, this insight allows us to calculate the minimum damage a weapon must have to raise the net DPS when dual wielding. If x is the average damage of our main weapon and we wish to add another weapon with average damage y, with APSx and APSy attacks per second, respectively, then y~.74x(APSx/APSy). If both weapons have the same APS (APSx=APSy), then this simplifies to y~.74x, which means the off-hand weapon must average about .74 the main-hand weapon's damage per hit.

Barbarians & Monks primary attacks generate {rage, spirit} Some attacks stun, knockback, or otherwise prevent enemy attacks. Commonly true of close range attacks. In these cases the 15% speed bonus of a twin attack may be worth a reduced DPS. i.e. The "secondary" effect of the attack can be more important than the DPS.

At the opposite extreem if a 2-handed weapon single hit does enough damage to kill all close enemies. Then stun & knockback effects are irrelevant.