# Basic Theorycrafting: The Damage Formula

by JR Cook - 9 years ago show comments

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 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:**

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:**

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:

**Native Skill WD Subfactor:**What the skill tells you, 640% for the example above**Specific Skill Subfactor:**100%+Specific Skill %, 112% for the example above.**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:**

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.

Great first look into calculating DPS. Looking forward to you continuing this. I think people are finally coming around to +elemental% (and +skill% as a result) as powerful affixes, but there is definitely room for education on cooldown and resource reduction. It’s funny how much the character sheet serves to mislead people in gearing/enchanting choices now more than ever.

I don’t think it misleads people at all. Its a tool like anything else. People are at fault for being lazy and relying on a can opener to fix their diet.

Dannie Ray this forum is terrible and wont let me reply directly.

It’s not harder at all. All you do is calculate the uptime for a spell when dealing with CDR and with CR all you do is calculate the spamability over time. Very simple stuff.

You understimate the disdain that the average player has for math related activities. It is pretty simple if you know what you are doing, it is not hard to know what you are doing but yet most people are kinda clueless about it. Consider yourself on the top 10%.

Very nice guide, really helped me a lot 🙂 Thanks.

I’m preparing a very interactive sheet on Excel based on your formulas. Will share it with you once complete maybe it could be helpful to some people

I have a quick question maybe you can help me out, where does the (x-y) Fire Damage property on a weapon fall in this equation? Does it affect weapon damage? Or is this already calculated in the tooltip ?

But yet and still, 1 final step I’m looking for is missing, all of these steps tell me how to figure out, my sheet damage, and my true Skill damage with Elemental factors and things of that nature, but what factors do I put together to get the expected damage per button press?

With your example of HotA, reaching a factor of 8.24, what do I multiply that against to see what damage numbers would pop up on my screen?

So, I was working on a spreadsheet to theorycraft for the new sets coming out next patch. But I wanted to get my formulas right before I did so I would be working with accurate (or close to it) information.

I was wondering if you could explain exactly how min-max weapon damage factored into the sheet dps calculation (as seen in your in-game profile) because my spreadsheet dps is still 8k below my in-game profile dps (789,276 spreadsheet vs 797,870 in-game).

I got the weapon dps cell by writing the formula as an average of min and max strikes then multiplying the average by the weapon attacks per second until it matched the weapon’s tooltip dps, then calculated the average weapon damage by dividing the weapon dps by the attack speed.

There is specific mention to min-max jewelry damage in the article. reread the article

Since this post is a year old, D3 patch 2.3 has been released.

Does the calculation still valid for patch 2.3 ?

I have the same question than Omar Sultan.

Everyone is talking about damage for weapons or skill.

But you can find amulets for example that give you 70-140 damages bonus.

How do you calculate that ??? :-S

what I’m curious about shouldn’t have changed in any patches thus far. I’m wondering if your weapon damage that skills calculate their damage from are your weapons base damage or DpS?

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How does Aura of Death work?

and does locus swarm spreading count as hits or are hits only when you hit the key and nothing that auto attacks/spreads

does soul smasher proc area damage?

and what is area damage?

Would Skill Damage properties as part of a legendary orange text fall in as part of damage increased by skills factor, or as increases additive or multiplicative to the base % of the original skill, Such as Blade of Prophecy for crusaders increasing Condemn by 800%. Would that be +600-800% to it’s initial (~1160%) skill, as Initial skill (~1160% * (600-800%)), or *800% in the skills increased by section of calculation