by JR Cook - 10 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 take another 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

Definitions

From Wikipedia:

“In mathematics, factorization  or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5″

Last week, we took our first look at the damage formula and quickly factored it. If you are wondering why we did that, it is simply to take advantage of the properties of multiplication.

Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the factors. For example 4 * 2 = 2 * 4

Associative Property: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)

Revisiting the Formula:

If you remember correctly, our formula was something like this.

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

How to use it:

Now lets put the properties to good use:

Lets say you are a Monk with 8,000 Dex, 1,600 Average Damage, 50% Crit Chance, 400% Crit Damage, 20% Increased Damage, 1.3 Attacks Per Second, and 1,500% weapon damage on your skill (after Elemental %, and Specific Skill%)

That would be:

Sheet DPS = 8,000%*1,600* (50%*400%+100%) * (20%+100%)* 1.3 = 80* 1,600*3*1.2*1.3 = 599,040

Actual DPS = 599040*1500% = 8,985,600

Ok, so your Monk has almost 9 million DPS when spamming his strongly buffed skill, but what happens if you now increase the Dex to 8,840 by rerolling 3 sockets into your armor and adding some gems.

That would be:

Sheet DPS = 88.40* 1,600*3*1.2*1.3

You could calculate the formula all over again, or you could take advantage of the associative and commutative properties you were taught at school. You can divide 88.40 by 80, the result is 1.105 which means 88.40 = 1.105*80.

If we replace that on the formula and use the associative and commutative property we find out that.

Sheet DPS = 1.105 * (80* 1,600*3*1.2*1.3) = 1.105 *599,040

Actual DPS = 1.105 *(599,040 *1500% )= 1.105  * 8,985,600 = 110,5% * 8,985,600

And just like that we realize that we increased your previous DPS by 10,5%, which is exactly the amount that we increased our Dex, and that’s why we wanted factors on the first place. Because you can now easily estimate how adding a certain stat will affect your total DPS and you can then make the best choice of which property to look for. You could even calculate stat weights which are ever so popular on WoW Theorycrafting.

Choosing the best properties to do battle:

Ok, so what you probably want to know is how to gear your character. So lets look at another character example.

We have a Barbarian, 6000 Str, 25% Crit Chance and  360% Crit Damage (1.9 Crit Factor), 1.1 base attack speed +14% IAS (1.25 Attacks Per Second), 0% Increased Damage,0% Skill Damage, 20% Fire Damage and using Seismic Slam – Shattered Ground(710% weapon damage as Fire.)

Increasing STR:

Lets say we have the chance of increasing 750 STR for a total of 6750 STR. Then we would have 6750/6000 = 1.125, that’s 112.5% or 12.5% increased damage.

Increasing Crit Chance:

What happens if we get an extra 10% Crit Chance for a total of 35% Crit Chance. Putting the values on the formula  (35%*360%+100%)  would take us to 2.26 Crit Factor. Then we would have 2.26/1.9 = 1.19, that’s 119% or 19% increased damage.

Increasing Crit Damage:

How about 100% Crit Damage?  Putting the values on the formula  (25%*460%+100%)  would take us to 2.15 Crit Factor. Then we would have 2.15/1.9 = 1.131, that’s 113,1% or 13,1% increased damage.

Increasing Attack Speed:

With an extra 7% attack speed we would have 21% IAS, over a 1.1 base attack speed that’s 1.33 Attacks Per Second.Then we would have 1.33/1.25 = 1.064, that’s 106.4% or 6.4% increased damage.

Increasing +Skill% and +Elemental%:

If you remember from last week, +Skill% and +Elemental% were used to calculate the Skill WD Factor.

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

If you’ve been paying atention you will realize that those are 3 separate factors and we will take full advantage of that.

If we go from 0% increased Seismic Slam Damage to 15% increased Seismic Slam Damage.  The +Skill subfactor would go from 100% to 115%. The we would have 1.15/1 = 1.15 that’s 115% or 15% increased damage.

If we go from 15% increased Fire Damage to 30% increased Fire Damage.  The +Skill subfactor would go from 115% to 130%. The we would have 1.30/1.15 = 1.13 that’s 113% or 13% increased damage.

Conclusions

As you might have realized it, as you continue to stack the same stat it becomes progressively harder to improve your DPS that way. Getting 100% Fire Damage will double your DPS, but if you want to double it again you’ll need to go all the way to 300%. Since all of the factors we have seen stack obviously multiplicative it is often better to get a bit of each in order to get the best results.

The early numbers show that the can’t miss stats are +Skill, +Elemental and a healthy combination of Crit Chance and Damage. Of course, your mileage might vary with your own level of gear.

That’s it for this week’s edition of Basic Theorycrafting, next week we will take on a more complicated example as we start tackling resource costs and the most basic of skill rotations. Be sure to check it out next Saturday on Diablo.BlizzPro.com

DR23.