# Is “+attack speed” more beneficial to fast weapons?

I've read through various existing "attack speed" related questions - notably this one and this one and this one. However, I can't seem to find the answer I'm looking for. I have two similar DPS weapons, but one has a significantly higher attack speed. I know that the attack speed is factored into the DPS stat of the weapon, but I'm curious whether one of those weapons will benefit more from increased attack speed from other items and abilities.

For example, given a 1000 DPS dagger and a 1000 DPS axe, will the dagger (faster) benefit more from increased attack speed (from gloves, Frenzy, etc)? Or will the two weapons benefit equally?

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The 1000 DPS already factors the attack speed into it; the dagger, since it attacks faster, will have much lower base damage than the axe. Theoretically, the faster the weapon, the more it will benefit from attack speed bonuses. – Frank Sep 18 '12 at 1:17
DPS is `(damage-per-attack)*(attacks-per-second)`. If you increase either of them by a percentage, DPS goes up by that percentage. It's as simple as that. – BlueRaja - Danny Pflughoeft Sep 18 '12 at 4:29

Because attack speed is based on attacks per second and additive, a bonus to attack speed will affect fast and slow weapons equally.

Some basic maths can be used to demonstrate this.

Consider the following:

• A very slow weapon that hits very hard ("Weapon A")
• A very fast weapon that hits very weakly ("Weapon B")
• +100% attack speed halves the attack interval (that is to say, you get twice as many attacks per second as you did before).
``````                         Damage     Attacks       Damage
Dealt     per Second    per Second

Weapon A                  100 HP  *   .5    =   50 DPS
Weapon A +100% atk speed  100 HP  *    1    =  100 DPS

Weapon B                    1 HP  *   50    =   50 DPS
Weapon B +100% atk speed    1 HP  *   100   =  100 DPS
``````

As you can see, each weapon benefits equally from the attack speed boost, regardless of the starting attack interval.

This works for any value of attack speed, because it stacks *additively. To wit, +20% attack speed plus +50% attack speed = +70% attack speed. The above example holds true for any value of attack speed; as long as your math is right, you'll get the same increase to DPS independent of your starting attacks per second).

There's some argument to be made back and forth about the benefits of attack speed for things other than your "Auto-Attack" damage, but they'll still have the same relative comparison after the attack speed has been applied.

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Worth noting if IAS is in absolute term (read: Echoing Fury), it's more beneficial to slow weapons. – NS.X. Sep 18 '12 at 5:45
Just as well, away from damage, faster attack speeds means more procs for LoH and other on-hit modifiers. – Vael Victus Sep 18 '12 at 12:09
@ravendreamer Thanks for the maths. I felt there must be a simple explanation, but it eluded me. Great answer. – EBongo Sep 18 '12 at 13:57
+1 for comedic value – Mike Sep 20 '12 at 14:07
Chantodos also has the +APS attribute I believe. – RedDeckWins Oct 7 '12 at 12:46