## An analysis: Number of builds for each class.

• Quote from youwillneverknow

we get it, D3 is more customizable than D2. Anyone who says different is retarded
Quit making these "analyzing the number of builds" topics. This is like the 5th one Ive seen

• Quote from Drsniper

Barbarian

# of active skills = n = 22
# of passive skills = p = 16

Therefore S = 22C6 x 5^6 x 16C3 = 652,863,750,000. (652 billion+)

Pfft.... Only 652 billion? Pathetic

I think you are doing it wrong here, if you want to choose any 3 passive skills from a set of 16 where the order does not matter, then the no. of ways this can be done is 16C3 = 16!/(3!13!). Your calculation 16!/13! also includes the order so you are overcounting.

Check this simple example. Let there be 5 passive skills and you can choose only 2, then by your calculation no. of ways of choosing 2 passives is 5!/3! = 20. However that is not true. The no. of ways of picking 2 passive skills from 5 where the order does not matter is 5!/(3!2!) = 10. If you number the 5 passive skills by 1, 2, 3, 4, 5. Then here are all the possible 10 choices of 2.

1, 2
1, 3
1, 4
1, 5
2, 3
2, 4
2, 5
3, 4
3, 5
4, 5
http://diablo3barb.wordpress.com/barbarian-calculator/

My D3 blog
http://diablo3barb.wordpress.com/
• Quote from TheBigL

Quote from Drsniper

Barbarian

# of active skills = n = 22
# of passive skills = p = 16

Therefore S = 22C6 x 5^6 x 16C3 = 652,863,750,000. (652 billion+)

Pfft.... Only 652 billion? Pathetic

yah I know....D2 had like 5...

Wait! Lower is better right?!? Ya know like golf....
"Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him God?"

Epicurus
• Quote from Drsniper

I think you are doing it wrong here...

Pointing out that his math was wrong, but conclusion correct is SOOO page 2, get with the times ^^!
Winter is coming...
• D3 has so much more customization than D2.  It's not even funny the two are league's apart.

There isn't necessarily gonna be a whirlwind build or whatever because you get to have 6 skills.

You may have a build that has 1 skill that is the most important, but it will likely require other skills and certain passives, affixes and gems to really make it work.

It's not going to be as easy to label specific builds because there are so many options and that is a good thing.

I could play a demon hunter and you play a demon hunter and we both have the exact same skill, but each chose different runes and passives and our 2 builds could be vastly different.

Here's an example:

Build A

http://us.battle.net...YXSV!YcU!aZZacY

Build B

http://us.battle.net...YXSV!XeT!cYbcZZ

Both builds use the exact same skills, but have different runes and different passives.  Both would play quite abit differently.

If you completely changed even 1 skill between the 2 builds you could massively change them.

This is real customization.

Not oh hey, whirlwind, alright.Figured I'd add that build A would me much more defensive and focusing on not getting touched and build B would be more about all around damage.
• i wouldnt count the no rune in calculations, theres always a rune that improves the basic skill without modfying the basic effect, and its pointless going without a rune when you have all unlocked
• runes arent really a customization!

Ray of Frost

Cost: 20 Arcane PowerProject a beam of frozen ice that blasts 215% weapon damage as Cold to the first enemy it hits, slowing the target's movement by 30% for 3 seconds.

+ Numb rune

Increase the amount the target's movement is slowed to 60% for 3 seconds.

___________________________________________________________________________________________________________________________

Arcane Orb

Cost: 35 Arcane PowerHurl an orb of pure energy that explodes when it hits, dealing 175% weapon damage as Arcane to all enemies within 10 yards.

+ Obliteration rune

Increase the damage of the explosion to deal 228% weapon damage as Arcane.

____________________________________________________________________________________________________________________________

see what i did here? that are the same skills only with more slow or more significant damge. you cant count them as a different skill. thats annoying. you also dont count in wow the different glyphs as skills...

yes you know im right!
• Quote from Klusterboy

runes arent really a customization!

Ray of Frost

Cost: 20 Arcane PowerProject a beam of frozen ice that blasts 215% weapon damage as Cold to the first enemy it hits, slowing the target's movement by 30% for 3 seconds.

+ Numb rune

Increase the amount the target's movement is slowed to 60% for 3 seconds.

___________________________________________________________________________________________________________________________

Arcane Orb

Cost: 35 Arcane PowerHurl an orb of pure energy that explodes when it hits, dealing 175% weapon damage as Arcane to all enemies within 10 yards.

+ Obliteration rune

Increase the damage of the explosion to deal 228% weapon damage as Arcane.

____________________________________________________________________________________________________________________________

see what i did here? that are the same skills only with more slow or more significant damge. you cant count them as a different skill. thats annoying. you also dont count in wow the different glyphs as skills...

yes you know im right!

And that's why we dont count unruned skills, since there are these runes, that just improve the base effect.

Hey Everyone,

UPDATE: Thanks to Drsniper, a simple math error has been pointed out and the math is updated. I verified this math with an engineer today and is 100% accurate. We'll all have to wait and see how applicable it is!

*** This post and it's calculations holds true ONLY if you play NON-elective mode or default skill mode ***

*** The math below represents the lowest amount of skill combinations because in the initial calculation, I do not consider rune variations *** (however I did calculate that too)

I'd like to provide clarity on skill combinations (viable or not) comparing diablo 2 to diablo 3 when playing in non-elective mode. What we need to consider is that, in the case of the d3 barbarian who has 22 active skills, is that they are divided up into level sets. So, again in non-elective play, first time around you have to pick 1 of 3 and then on the next set you have to pick 1 of 4 and so on. In total, assuming your character level is maxed out, you have to pick 6 active skills. In another words, you can’t pick “bash” on your right mouse button skills or assign it to your number pads in non-elective mode. Once you pick one in that set, the others are locked out. So in the case of the barbarian there is exactly 22 active skills and then you get to pick 3 out of 16 passive skills where order does not matter. The problem and formula for it is as follows:

If you have to choose 1 item from six different categories, and then 3 out of

16 separate items, how many combinations are there?

Set 1 Choose 1 of 3
Set 2 Choose 1 of 4
Set 3 Choose 1 of 4
Set 4 Choose 1 of 4
Set 5 Choose 1 of 4
Set 6 Choose 1 of 3

Set 7 Choose 1 of 16
Set 8 Choose 1 of 15
Set 9 Choose 1 of 14

[(3x4x4x4x4x3)(16!/3!13!)] = 1,290,240 total combinations for the barbarian and non-elective (default) mode.

Now what’s great about this is that the way the “sets” are set up makes a vast majority of these combinations could be viable… of course depending on the gear. Now others will take this farther to say the 5 rune variations (or 6 rune effects if you choose to use “no rune”…which is pointless) greatly magnifies the variations. Here are the results of that effect:

[(15x20x20x20x20x15)(16!/3!13!)] = 20,160,000,000

That is for each of the 1,290,240 combinations, there is 15,625 different ways to play. Now that's a lot of variation... and that's one class of character.

Its hard to say how many of those are going to viable, but the way the Blizzard has these skills separated and setup, it seems initially like an intelligent system in place to naturally have these 6 options work well together along with the 3 passive skills. Now we’ll have to see how uber the gear is setup, but we can assume Blizzard created gear to enhance player builds and options.

Now on Diablo 2

Now if we look at Diablo 2 and focus on the Paladin. The benefit of diablo 2 is that we know pretty much everything there is to know. It’s widely accepted that the Paladin has generally the largest amount of viable builds… somewhere around 10. Looking at www.diabloii.net under the strategy guide section, you can good a good list of effective builds. The Paladin has 10, the Barb has 9, the Necro 5, the Amazon 5, and the Sorceress has about 5. Now I know people will call foul here so for the sake of argument, lets double that number. Lets just say that the number of viable- hell difficulty Paladins is 20. Still not satisfied, how about 50 builds for the Paladin? Keep in mind that there are 30 skills total with no variation to them. Plus most, if not all builds, require that at least 3 skills are maxed, taking 60 points with about 12 points in pre requisites (in which you don’t have a choice there) out of the total available of 110. Most builds level up at least 1 or 2 of a level 30 skills and very few players use lower level skills as a primary attacker (Go Skeletons!) but instead for synergies. I haven’t seen too many hell driven fire-bolt sorceresses out there! The best skills are generally at the latter parts of the skill tree. In diablo 3, spell damages are based on the weapons and therefore its like having all level 30 skills, just unlocking at different increments, and are all viable based on the items you’re carrying. Diablo 2 has the illusion of choice in which over 99% of them are “wrong” choices. I mean you could put 4 points in every skill you have and you won’t make it far into nightmare, or even beat normal I’m not sure (experiment anyone?). The reality is, each class only has a handful of viable skills that work in hell. That was the flaw with diablo 2 and is simply the truth. Because of the nature of stat point allocations and skill point allocations, its near impossible for me to figure out the best formula to figure out total combinations.

Conclusion

But let me conclude that its not the number of combinations (in which diablo 3 still has more) but the viability and playability of those combinations. Blizzard has definitely without a doubt, succeeded in marking each class have at least 22 viable skills that can be used in any difficulty level. Why? Because it’s based mostly on your items stats. Now multiply that by rune effects and passive skills and all the sudden the truth is pretty evident… is that you can have 100 players playing and creating characters on battlenet and every single one of them will do something completely different. You still don't believe the math!! Well let me tell you this... if only .0005% of the Barbarian’s D3 skill combinations are viable, we still have 645 combinations that are worth experimenting with. Because there are no “bad” spells or “wrong” choices. The players that will be rewarded will be the ones that can masterfully apply their skills in the right situations and play for the long haul to acquire the equipment that supports their build. Now the difference here is that no one is “locked” in a build because anyone can switch to another build by simply clicking onto different skills. However on the flip side of things, by the time we get to hell difficulty in Diablo 3, our gear, more than anything will define our build. But that’s a different story. Hope this clarifies what Blizzard is saying.
• Yrrolock made the succinct reply on the math side, allow my to make the same point in a demonstrative fashion.

Point:
Quote from Klusterboy

Ray of Frost

Cost: 20 Arcane PowerProject a beam of frozen ice that blasts 215% weapon damage as Cold to the first enemy it hits, slowing the target's movement by 30% for 3 seconds.

+ Numb rune

Increase the amount the target's movement is slowed to 60% for 3 seconds.

___________________________________________________________________________________________________________________________

Arcane Orb

Cost: 35 Arcane PowerHurl an orb of pure energy that explodes when it hits, dealing 175% weapon damage as Arcane to all enemies within 10 yards.

+ Obliteration rune

Increase the damage of the explosion to deal 228% weapon damage as Arcane.

Counter point
A)
Numb: Increase Slow (Change: Defensive tool)
Snow Blast: Progressive Damage increase (Change: offensive channel)
Cold Blood: 0 AP cost (Change(minor): Primary attack)
Sleet Storm: local AoE (Change(major): skill retool)
Black Ice: DoT on ground (Change: Offensive utility)
result 1 Drastically different skill; 2 significantly different skills; 2 fundamentally similar skills

Obliteration: Damage increase(Change(minor):Offensive tool)
Arcane Orbit: charge based persistant local AoE (Change(major): Skill retool)
Arcane Nova: Instant local AoE (Change(major): Skill retool')
Tap the Source: mana reduction (Change(minor): offensive tool)
Celestial Orb: Penetration(Change: AoE redistribution)-->closest thing to Frozen orb in D3?
Result: 2 Drastically different skills; 1 significantly different skill; 2 fundamentally similar skills (depending on your view on Celestial Orb which I mapped as significantly different)

On topic: The math pages are really interesting, how could you include the fact that not all skills can be mapped to the LMB? this removes the possibility of some builds in classes with more than 5 such skills (Barb:8 DH:6 Monk:10(again hit hardest!) Doc:5 Wiz:7) or is that just dumped into 'about 70% of these builds will be trash but who cares because that still leaves more than 10 billion builds' idea?

Edit the sunglasses was supposed to be B and ) but I won't change it cause it made me giggle.
If that made sense to you, Bravo! I think I even confused myself...
• yeah... I already did a small post on page 1 on how to calculate for non-elective mode.
• Quote from Raptorbonz42

Yrrolock made the succinct reply on the math side, allow my to make the same point in a demonstrative fashion.

Point:
Quote from Klusterboy

Ray of Frost

Cost: 20 Arcane PowerProject a beam of frozen ice that blasts 215% weapon damage as Cold to the first enemy it hits, slowing the target's movement by 30% for 3 seconds.

+ Numb rune

Increase the amount the target's movement is slowed to 60% for 3 seconds.

___________________________________________________________________________________________________________________________

Arcane Orb

Cost: 35 Arcane PowerHurl an orb of pure energy that explodes when it hits, dealing 175% weapon damage as Arcane to all enemies within 10 yards.

+ Obliteration rune

Increase the damage of the explosion to deal 228% weapon damage as Arcane.

Counter point
A)
Numb: Increase Slow (Change: Defensive tool)
Snow Blast: Progressive Damage increase (Change: offensive channel)
Cold Blood: 0 AP cost (Change(minor): Primary attack)
Sleet Storm: local AoE (Change(major): skill retool)
Black Ice: DoT on ground (Change: Offensive utility)
result 1 Drastically different skill; 2 significantly different skills; 2 fundamentally similar skills

Obliteration: Damage increase(Change(minor):Offensive tool)
Arcane Orbit: charge based persistant local AoE (Change(major): Skill retool)
Arcane Nova: Instant local AoE (Change(major): Skill retool')
Tap the Source: mana reduction (Change(minor): offensive tool)
Celestial Orb: Penetration(Change: AoE redistribution)-->closest thing to Frozen orb in D3?
Result: 2 Drastically different skills; 1 significantly different skill; 2 fundamentally similar skills (depending on your view on Celestial Orb which I mapped as significantly different)

On topic: The math pages are really interesting, how could you include the fact that not all skills can be mapped to the LMB? this removes the possibility of some builds in classes with more than 5 such skills (Barb:8 DH:6 Monk:10(again hit hardest!) Doc:5 Wiz:7) or is that just dumped into 'about 70% of these builds will be trash but who cares because that still leaves more than 10 billion builds' idea?

Edit the sunglasses was supposed to be B and ) but I won't change it cause it made me giggle.

lmao I saw the sunglasses and was like 'yea yea I know, way to go, showoff'
^ YouTube.Com/IceBleuGaming ! It's a thing! Check it oooout!
• Quote from Ayr

yeah... I already did a small post on page 1 on how to calculate for non-elective mode.

Those skills can't be applied to the LMB even in elective mode...like Mantras or Sentry.
If that made sense to you, Bravo! I think I even confused myself...
• Quote from Klusterboy

runes arent really a customization!

Ray of Frost

Cost: 20 Arcane PowerProject a beam of frozen ice that blasts 215% weapon damage as Cold to the first enemy it hits, slowing the target's movement by 30% for 3 seconds.

+ Numb rune

Increase the amount the target's movement is slowed to 60% for 3 seconds.

___________________________________________________________________________________________________________________________

Arcane Orb

Cost: 35 Arcane PowerHurl an orb of pure energy that explodes when it hits, dealing 175% weapon damage as Arcane to all enemies within 10 yards.

+ Obliteration rune

Increase the damage of the explosion to deal 228% weapon damage as Arcane.

____________________________________________________________________________________________________________________________

see what i did here? that are the same skills only with more slow or more significant damge. you cant count them as a different skill. thats annoying. you also dont count in wow the different glyphs as skills...

yes you know im right!

But let me guess, a 134-144 damage fireball is a different skill than a 145-155 damage fireball?
• Quote from Raptorbonz42

Quote from Ayr

yeah... I already did a small post on page 1 on how to calculate for non-elective mode.

Those skills can't be applied to the LMB even in elective mode...like Mantras or Sentry.

That's only an issue for combinations where all 6 of the active skills cannot be mapped to LMB. Since order doesn't matter, just map something else to LMB. Might be awkard to play with, but there's nothing stopping you from completely remapping your keybinds either.
• Quote from Burzghash

Quote from Klusterboy

runes arent really a customization!

Ray of Frost

Cost: 20 Arcane PowerProject a beam of frozen ice that blasts 215% weapon damage as Cold to the first enemy it hits, slowing the target's movement by 30% for 3 seconds.

+ Numb rune

Increase the amount the target's movement is slowed to 60% for 3 seconds.

___________________________________________________________________________________________________________________________

Arcane Orb

Cost: 35 Arcane PowerHurl an orb of pure energy that explodes when it hits, dealing 175% weapon damage as Arcane to all enemies within 10 yards.

+ Obliteration rune

Increase the damage of the explosion to deal 228% weapon damage as Arcane.

____________________________________________________________________________________________________________________________

see what i did here? that are the same skills only with more slow or more significant damge. you cant count them as a different skill. thats annoying. you also dont count in wow the different glyphs as skills...

yes you know im right!

But let me guess, a 134-144 damage fireball is a different skill than a 145-155 damage fireball?

It is because I made a choice to upgrade that skill. In D3 what choice do I make? I am a jack of all trades, I can do everything to the absolute best. That to me is boring, that does not create connection, does not tell my character apart at all.

It is because I made a choice to upgrade that skill. In D3 what choice do I make? I am a jack of all trades, I can do everything to the absolute best. That to me is boring, that does not create connection, does not tell my character apart at all.

You make the choice of what abilities you want to use for that run through. With the valor buff, you're actually encouraged to stick with one build for that one run through. Just because Blizzard doesn't force you to stick with a choice, doesn't mean you cannot force yourself. Self~control is too hard? Cannot enjoy the game without Blizzard holding your hand?...

ecutruin +9000
• Quote from ecutruin

It is because I made a choice to upgrade that skill. In D3 what choice do I make? I am a jack of all trades, I can do everything to the absolute best. That to me is boring, that does not create connection, does not tell my character apart at all.

You make the choice of what abilities you want to use for that run through. With the valor buff, you're actually encouraged to stick with one build for that one run through. Just because Blizzard doesn't force you to stick with a choice, doesn't mean you cannot force yourself. Self~control is too hard? Cannot enjoy the game without Blizzard holding your hand?...

Oh no, I can. However...why should I? They seem to enjoy holding everyone elses hand, why not mine too?