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Basic Theorycrafting: The Damage Formula

by - 7 years ago

Hello everyone! My Name is Dannie Ray and I’ll be here every Saturday explaining all things theorycrafting so you can better understand your characters and the game you love, lets hope you haven’t forgotten all the math you’ve learned in school because we will finally have a chance to put it to good use.

Today we are going to look at Damage in Diablo 3, where does it come from? How is it calculated? How can we maximize our damage output? How can I figure out what the best possible build for me is?

All of those questions have one thing in common, and  that is that they are a lot easier to answer once you know how Damage Calculations Work, so lets get into it.


Note: Remember that percentages are actually a division by 100, 500% and plain 5 are the same thing. By the same logic One Hundred Percent equals one

Stats and DPS:

There are many stats that help your DPS in one way or another, we have some that are reflected on the character sheet DPS like: Base Stat, Crit Chance, Crit Damage, Attack Speed and Min-Max Damage. We also have others that don’t, like: Elemental Damage, Specific Skill Damage, Cooldown Reduction, Resource Cost Reduction and more.

Since this is our first rodeo, we will look at a simplified version of the problem. We will analyze our DPS when we are spamming a single skill without worrying about resources and cooldowns. This means that on this article we won’t analyze the value that Cooldown Reduction and Resource Cost reduction bring to the table. (hint: It’s way more than you think)

A later guide will work on how to calculate the damage of your actual skill rotation, but for now lets master the basic Damage Formula.

 The DPS Formula:

At large, the Damage formula is just a multiplication of factors. You have your base weapon damage as a factor, your base stat as a factor, a crit derived factor, a skill weapon damage % factor, a damage to elites %, a damage to all skills factor and a few more. You have to multiply all together to figure out what your damage is going to be.

 

Sheet DPS =  Base Stat Factor * Base Damage Factor * Crit Factor *  Damage Inc. by Skills Factor * Speed Factor.

 

Actual DPS = Sheet DPS * Skill Weapon Damage Factor (*Damage to Elites Factor).

 

You might not understand what all of those factors are so let us take a quick look at each of them.

 

The Base Stat Factor:

Perhaps the easiest one to understand, it’s your DEX, STR or INT depending on your class.

If you are a Monk and have 7000 DEX then your Base Stat Factor is 7000% or just plain 70.

A Crusader with 5430 STR, has a Base Stat Factor of 5430% or plain 54.30.

The same applies to INT classes.

The Weapon Base Damage Factor:

This is your base damage

This is your base damage

This is the Damage your weapon says it does, plus the min-max damage on your jewelry. As you notice from the image above, damage bonus from rubies are automatically factored into the weapon.

Remember that dual wielding hits with only one weapon at the time and alternates between them, for simplicity sake we will asume you are not dual wielding.

 

Base Damage Factor = Weapon Damage + Jewelry Min-Max Damage.

 

The Crit Factor:

You likely know where to find you crit, but I'll leave it here anyway.

You likely know where to find your crit, but I’ll leave it here anyway.

This is how Critical Strikes contribute to your average damage. Imagine you have 50% Crit Chance and 200% Crit Damage. That means half your strikes are doing normal damage and half are doing 3 times its damage.

 

So if your base damage is 100 and you attack twice you should on average get one normal attack for 100 damage and one critical for 300 damage. That’s 400 damage over 2 strikes, or 200 average damage. You are doing double your base damage.

 

To get this factor you must multiply your Crit Chance and your Crit Damage and then add 1 (100%) in other words:

 

Crit Factor = (Crit Chance * Crit Damage) +100%

 

Consider the save values presented above, if you have 50% Crit Chance and 200% Crit Damage, then:

 

50%*200%=100%

 

100%+100% = 200% = 2

 

Your crit factor on this scenario is 2, which means your crit stats are effectively doubling your damage.

 

The Skill Weapon Damage Factor:

D3SkillWeaponDMG

Native Skill Weapon damage, Elemental Damage % and Specific Skill Damage % highlighted.

 

In the Example above, Hammer of the Ancients tells us that it does 640% weapon damage as fire. That value is it’s native Skill Weapon Damage%. This can be increased with the two magic properties highlighted abovie, +Specific Skill Damage% and +Elemental Damage%. Now, none of this is shown on your sheet DPS and it’s often overlooked because of it. In reality most of what makes or breaks a build can be found on this factor.

This is made out of three subfactors:

  1. Native Skill WD Subfactor: What the skill tells you, 640% for the example above
  2. Specific Skill Subfactor: 100%+Specific Skill %, 112% for the example above.
  3. Elemental Damage Subfactor: 100%+Elemental Damage %, 115% for the example above.

Both the Skill Subfactor and The Elemental Damage Subfactor stack additivelly within itself, if I added a 20% Fire Damage Bracers then my elemental damage would be 100% +15%+20% = 135%.

 

Skill Weapon Damage Factor = Native Skill Weapon Damage % * (100% +Specific Skill %) *  (100%+Elemental Damage %)

That’s 824% Weapon Damage for our Example Barbarian, that’s a 8.24 factor.

The Damage Increased by Skills Factor:

D3DmgIncBySkill

Some skills will increase your total damage by a %, Barbarian’s WotB Insanity, Monk’s Combination Strike and many others contribute to this number. In the example above I’m using Fire Ally for a 10% bonus and Unity for another 10% (5% for the Enchantress and 5% for the Fire Ally), you can observe how this stacks additively with itself.

Just like Archon mentioned on an episode of Westmarch Workshop, things tend to stack additively within their own category.

Damage Increased by Skills Factor = 100% + Damage Increased by Skills%

 

The Damage to Elites Factor:

 

This is rather simple and it only applies against elites, my monk has 15% and the factor is calculated like this:

 

Damage to elites factor = 100% + Damage to Elites %

My monk’s Damage to Elites Factor would then be 115% or 1.15.

 

The Attack Speed Factor:

And to close things out we have the attack speed factor. This is the one that changes this from a Damage Formula to a DPS formula. The factor that shows how fast you attack, it’s pretty easy to calculate. It is simply your weapon’s base speed multiplied by your Increased Attack Speed. Once again, things get more complicated with Dual Wielding but we can save that for a later date.

The Attack Speed Factor doesn’t really need to be calculated as your character sheet will tell you what it is exactly, you can find it as “Attacks Per Second”, that number is in fact your Attack Speed Factor.

 

Conclusions:

With all that out of the way, you can finally calculate the actual DPS you do when spamming a single skill. All you have to do is fill out the formulas presented above and multiply all of the factors together.

Now that we know about factors, we can see things more clearly. With a bit of practice you will be able to easily see how changing one of the stats on our gear will affect our total DPS

But this post is already too long so come back to Diablo.BlizzPro.com next week for an all new edition of Basic Theorycrafting where we will go indepth on how changing gear affects our factors and in turn our DPS.

DR23.


Dannie Ray

Reaper of Souls Player and Theorycrafter, former WoW Raider, Finally got my Heroes invitation! On my spare time I might, or might not be working towards a Masters on Computer Science.