Sunday, May 20, 2012

How Many Diablo III Builds Are There?

In Diablo III you can have a an ability mapped to both of your mouse buttons and to the 1-4 keys on your keyboard. By default each skill in the game can only be placed on a particular button. For example, my Zombie Dogs have to be bound to the 1 key. This means that under the default settings you can't have some skills on your bar at the same time because they would have to be bound to the same key.

There is, however, an option called elective mode that removes this restriction and allows you to put whatever skills you want on whichever key/button you want. This has led me to wonder how many different builds you can get out of each particular mode. So to look at this, I will use my witch doctor, Tauzex, as an example. The number of skills I use in this post will come from him. Other classes have different numbers of skills, so these numbers will vary from class to class.

Some background on what goes into a build
  • You have 6 active skills and 3 passive skills at max level
  • Each active skill can have 1 of 5 runes attached to it. 
  • I will assume that you'd never want to use a skill unruned
  • In both modes at max level, you can pick any 3 of your passive skills with  no restrictions.
I will not be considering a build with the same skills but on different buttons as being a different build. 

For my witch doctor, the number of skills that I can attach to each key in standard mode is
  • 1 key: 4
  • 2 key: 3
  • 3 key: 4
  • 4 key: 3
  • Left Click: 4
  • Right Click: 4
  • Passive Skills: 15
In general, the number of builds in either mode is the number of choices you have for your active skills times the number of choices you have for your passive skills (since your active skill choices and your passive skill choices are independent of each other). In both modes, the number of passive skills that you can select is the same
The middle section is read as "15 choose 3" and is explained in the footnote*
To count the number of active skill choices, I will first count how many choices of skills you have and then factor in the different rune choices for those builds. If you have a selection of 6 skills and each of those skill has 5 runes, the number of ways that you can rune a particular set of skill is 
So now we just have to count the number of skill choices each mode has.

Active Skill Choices in Standard Mode
To figure out the number of builds in standard mode, I just have to multiply the number of choices I have for each skill slot. This comes out to
choices for your active skills. In whole, this brings active mode to 
builds for your character. That's over 16 billion distinct builds.

Active Skill Choices in Elective Mode
In elective mode, you aren't restricted by abilities needing to be placed in certain positions. So as a witch doctor I would just need to select 6 active skills out of my 22 total active skills. The number of choices in elective mode is 
choices for your active skills. In whole, this brings elective mode to 
builds for your character. That's over 530 billion distinct builds. This can be done for the other classes as well, which gives us the following table.

ClassGuided ModeElective Mode
Demon Hunter21,840,000,000717,670,078,125
Witch Doctor16,380,000,000520,451,796,900

We shouldn't forget our followers! They play an important role in single-player gameplay. So how many choices do we have for our follower builds. Well, there are 3 followers, and each one requires that you make 4 choices that each have 2 options. 

So that multiplies the number of distinct was to outfit your character by 48. Of course, since you don't have a follower in multiplayer mode, this doesn't apply there.

Wow, that's a ton of different builds for your characters, and elective mode has so many more builds. In fact, elective mode over 32 times as many builds as standard mode does. I don't believe I have to tell you that that's an impressive number of choices!

* As I said above, that particular notation is read as " choose ." In mathematics it's known as a combination (as opposed to a permutation) and is calculated as follows.