Diablo 3: How is Damage Calculated?

There’s a simple formula going around called “SCRAM” that is used to explain how damage is calculated in Diablo 3.

Each letter represents a variable of the formula.

So you start off with S, which is your primary stat.  IE, if you’re a Witch Doctor, Intelligence or if you’re a Barbarian it’s Strength, if you’re a Demon Hunter it’s Dexterity, etc.

* Damage

So let’s use one of my characters as an example to calculate damage.  This is a level 48 Witch Doctor.

S = 965 (intelligence) * 1% (bonus damage per point) + 1 base

So 965 * 1% = 9.65

9.65 + 1 for base =

10.65

S = 10.65

Next we have the variable C.  C is the chance for critical strike plus the magnitude of bonus damage from Crits.  We are going to account for the average amount of damage we gain from Crits.  So we’ll multiply chance to crit against crit bonus damage.

C = 6.5% (crit)

6.5% * 50% (crit hit damage bonus) =

.065 * .5 =

.0325

.0325 + 1 (base)

= 1.0325

C = 1.0325

The next variable is R, which accounts for your weapon speed.  There’s no math required because the character sheet provides R.

R = 1.45 (attacks per second)

Next up we have A, which is the average damage.  We find the average damage by taking all of the + damage items in your inventory, such as amulets etc that might add damage and your weapon damage.  You add minimum damage to minimum and maximum to maximum.  

One of my rings adds 7-14 damage.  My offhand adds 15-25 damage.  My primary weapon is 75-144 damage.

We end up with 7 + 15 + 75 = 97

And 14 + 25 + 144  = 183

183 +97 = 280

252 divided by 2 (for average) = 140

A = 140

Next up we have Variable M, these come from percentage modifiers found in your skills.   On my Witch Doctor I have Pierce the Veil which adds 20% damage.

M = 1 + 20%

M = 1.2

Then we need to put this together.  Damage = SCRAM

S = 10.65

C = 1.0325

R = 1.45

A = 126

M = 1.2

10.65*1.0325*1.45*140*1.2 = 2678

Notice how 2678 is incorrect, I was unable to replicate the error but it has something to do with my gem in my primary weapon.  I believe the tool tip might be displaying incorrect damage.  I ran this formula on my other characters and it came out right, try it and see for yourself.

Keep in mind the attacks per second in the tool tip is rounded up.

My base weapon speed was 1.34 attacks per second.  1.34, keep in mind all things on the weapon including gems and mods are included in the damage and attacks per second when you view your weapon.  So 1.34 * 1.08 (speed enhance from gloves percent plus 1) = 1.4472 instead of the rounded up 1.45.

This brings us to 2673 which would be the correct value if my character wasn’t bugged.

*  Ability Damage

Ability damage is calculated by formula (SAME)

S*A*M*E

Using SAM from above, you take E, which is the percentage modifier applied to your weapon damage by the ability.  So if you have a 25% damage modifier over weapon damage for one of my Witch Doctor abilities I would end up with 10.65 * 140 * 1.2 * 1.25 = 2236 per hit.  If this ability can’t be spammed to beat my current rate of fire, it makes it not worth while using.