Lots of people are throwing these numbers around. And many of the aforementioned people are decent at math, and get the correct answer. But truly, these large numbers include every logical permutation, including such combinations as: just having 1 skill equipped, having the same skill but with a rune, etc.
In actuality the count of true builds (like what the chat gem on the skill calculator generates) is significantly less, but it's still a large number. So when someone asks you about customization just say there's a large number of builds. If you must use some ridiculous number to convince them, they're probably not worth your time.
Rollback Post to RevisionRollBack
The final test of the Serpent's Form takes place in "The Pit of 12 Vipers." The initiates are not told about the 13th.
I realize there’s a lot of information spread around, I’m hoping to bring some of it to a single post and hopefully get our point across and reassure you that the changes we’re making are for the betterment of character customization options, and ultimately your long-term enjoyment of the game.
So, why did we get rid of skill points?
(Note: this is a supplementary min/max explanation. There are lots of other reasons which have been touched on in the past such as how players approach our game, supporting the idea of builds, observing how players behaved in internal testing, etc. This is just further explanation that I think will resonate with some of you.)
In Diablo III, we really want to improve the combat depth. Part of having combat depth involves having skills that are useful in different situations. In Diablo II players often used a single skill to deal with almost all situations: Blessed Hammer, Frozen Orb and Bone Spirit to name a few. Players invest 20 points into a single skill and use it as much as possible. The only reason a player would swap away from their primary spam skill is due to monster resistances/immunities. If a monster was immune to your primary spam skill, you’d either skip the encounter completely or fall back on a second skill. Neither of these answers provides the player with much combat depth.
To support combat depth, skills need to have different roles. Here is a very simple example:
Magic Missile deals 15 damage to a single enemy
Arcane Orb deals area of effect damage for 10 damage each
With these two skills we’re beginning to develop some combat depth for the player. Use Magic Missile when you’re facing one enemy, use Arcane Orb when you’re facing multiple enemies. But you may also want to use Magic Missile if one enemy is a “high priority target” in a group, and you want it to die quickly. In this simplified example players can still defeat a horde of enemies by casting Magic Missile multiple times, or they could defeat a single large enemy by casting Arcane Orb multiple times, but that wouldn’t be as efficient as a player who uses the right skill for the right situation.
Ok so that basic layout of combat depth out of the way!
With skill point spending your skills get better as you invest points into them. The problem is that this destroys combat depth. If after pumping a bunch of points into Magic Missile it now deals 70 damage to a single enemy, assuming my enemies have any reasonable health, then Magic Missile becomes a better choice than Arcane Orb even in group situations. If after pumping a bunch of points into Arcane Orb it now deals 45 damage, then it deals more damage than Magic Missile to single targets. Now rather than using the right skill for the right situation, I’m using the skill I’ve put all my points into. Skill point spending has eroded away combat depth.
Why did we go from 7 skill choices to 6?
(Note: again, this is a supplementary explanation. We’ve gone over some of the other reasons elsewhere, but this is specifically targeted at those of you here who feel strongly that 7 means there would be more build diversity than 6)
Diablo III emphasizes build customization. We feel that 6 skill choices actually creates more build diversity than 7.
Why? Well for any given set of options, the greatest number of combinations exists when the number of choices you can make is close to half the number of options you have. Some of you may remember a high school math problem like this: There are 12 differently colored marbles in a bag. How many different color combinations can you get by choosing X marbles? Well as it turns out the solution for various values of X are:
1 marble: 12 different color combinations
2 marbles: 66
3 marbles: 220
4 marbles: 495
5 marbles: 792
6 marbles: 924
7 marbles: 792
8 marbles: 495
9 marbles: 220
10 marbles: 66
11 marbles: 12
12 marbles: 1 (there’s only 1 way to choose 12 marbles from the 12 in the bag)
The greatest number of possible combinations happens when you are choosing 6 from a possible 12.
You may be asking what 12 has to do with anything as classes all have over 20 skills available to them...
This is true in theory, but in practice players tend to (and really should) pick up skills to fill different roles so they can be effective. Categories such as single target, area of effect, auto-targeting, debuff, defensive, group buff, escape, crowd control, 2-minute ubers, pet skills, etc. etc. Players generally take at most two (and often one) skill to fill any particular role. For example, the Wizard has Ice Armor, Storm Armor and Energy Armor, but I don’t think anyone is going to take all three (though maybe somebody will take that as a challenge and prove me wrong), most players will choose one Wizard Armor spell (note that this can change dramatically with some rune effects). If we look at each class, depending on how you count, you get anywhere from 8-12 different types of skills. So we err on the high side in our category estimate (12) and that means 6 is a pretty good number to maximize build variety.
It's important to note that we’re not just talking about you and your friend having Wizards with slightly different skills, we’re talking about you and your friend having 6 skills that are different in functionally significant ways.
Closing remark! When we pull math out like this I’m sure somebody will point out that if our only objective was to maximize build combinations we’d have allowed people to also choose 6, 7 or 8 passives rather than just 3. So I’ll counter by saying maximizing build combinations is not our only objective. We also want our system to have aesthetic flavor, to be simple to understand, and to have the passives in particular feel impactful. We have many different goals that we take into account when making any design decision. In the case of active skills, we felt the increase in variety was one of many good reasons to go from 7 to 6.
So how many skill combinations are there now?
Well taking into account 6 active skills, all the rune combinations, and 3 passives we currently expect each class to have roughly 2,285,814,795,264 different build combinations. That’s not taking into account skill types for ‘ideal’ builds, but that’s always been a big part of the fun of experimenting (and longevity for Diablo II) - finding a build that shouldn’t work, and making it.
Lots of people are throwing these numbers around. And many of the aforementioned people are decent at math, and get the correct answer. But truly, these large numbers include every logical permutation, including such combinations as: just having 1 skill equipped, having the same skill but with a rune, etc.
In actuality the count of true builds (like what the chat gem on the skill calculator generates) is significantly less, but it's still a large number. So when someone asks you about customization just say there's a large number of builds. If you must use some ridiculous number to convince them, they're probably not worth your time.
the point of my post was to give people an exact number. therefor they know, and its not a guess. so if someone honestly wants to argue with you, you can give them exact math and number to blow them away
which is why if you read my entire post at the end i mention that there will be significantly less very different builds, also i mean viable builds. the number is still insanely high
Yeah I agree, incredible amount of customisation still, we'll probably never know how many inferno viable builds we'll have per character, whereas with D2 there were about 25 total across all 7 classes.
wait... it seems your numbers are to high according to bash lol the the other poster seem to have more builds than you.. so many different people with different figures... im going to have to trust bashs count on this one tho =P
which is why if you read my entire post at the end i mention that there will be significantly less very different builds, also i mean viable builds. the number is still insanely high
Yeah I agree, incredible amount of customisation still, we'll probably never know how many inferno viable builds we'll have per character, whereas with D2 there were about 25 total across all 7 classes.
ah very very agree! lol. i keep telling people that. because people say "oh well D2 had more possible combo's bla bla" but ANYONE who has played d2 knows theres honestly barley ANY good builds between all of the characters that will actually kill shit. honestly for PVE theres really only like 12 for hell. lol
wait... it seems your numbers are to high according to bash lol
i did this many many times on my calculator and wrote it out and got help from a math major. now I'm not saying bash is stupid or misinformed. just saying I'm sure he didn't spend a long time figuring out the exact number with multiple people. i did. lol
wait... it seems your numbers are to high according to bash lol
i did this many many times on my calculator and wrote it out and got help from a math major. now I'm not saying bash is stupid or misinformed. just saying I'm sure he didn't spend a long time figuring out the exact number with multiple people. i did. lol
im saying I think he would have go the numbers from the devs,... im going to have to trust his math.
But regardless it still a crap load of combinations.
wait... it seems your numbers are to high according to bash lol
i did this many many times on my calculator and wrote it out and got help from a math major. now I'm not saying bash is stupid or misinformed. just saying I'm sure he didn't spend a long time figuring out the exact number with multiple people. i did. lol
im saying I think he would have go the numbers from the devs,... im going to have to trust his math.
But regardless it still a crap load of combinations.
he used marbles and didn't actually show you ANY proof of his exact mathematical equation he used to figure it out. i did. believing him is illogical just because he works for blizzard when he provides no proof to his math. now if bash was some mathematical genius that was famous id say ok. but considering i gave you proof, he didn't. I'm the more logical choice.
edit: there he did correct himself and his number is nearly the exact same number as mine. i just used 15 passives instead of 10, otherwise my number would be identical. so my math is 100% correct. i win. lol
can you link to where he changes it?
The guy who gets close to you, he still links to his, and cant find where he corrects himself.
Just want to see where you said he corrects himself first.
Since the set is non-ordered combinations, you should get (25 choose 6) skills times (15 choose 3) passives = 177,100 x 455 = 80,580,500.
thats not how you times it. use your calculator to do what i showed you and you'll get my number.
You can't just multiply the numbers together. You have to consider the fact that these are combinations. Multiplying them together gives you overlap.
no it doesn't. i edited my last post i sent you with exact numbers. i am making my equation BASED on the fact that you can't use any of the same skill/rune combo's twice. there will be no overlap. and regardless, the number is unfathomably high either way. making it impossible for anyone to say there not unique. the fact that i put 125 THEN 120, because i don't want the same skill/rune to overlap in the equation. otherwise id do 125 x 125 x 125 ect...
You're still just multiplying the entire possible set (25) by 5 each time, which is wrong.
You have to create a combination of the set choice you're interested in: IE there are 25 possible (without replacement) out of 6 choices. That means you get unordered sampling without replacement. i.e. - n Choose k - n being 25, k being 6. Multiply that by the unordered sampling without replacement for passives (15 and 3), then multiply by 30 - (6 skills times 5 rune types). You should get:
updating what I said, The "correction" that you said was the guy I was showing you that calculated it the same way as you (minus the 10 instead of 15) and was wrong o.0; [or else I dont see why he would have linked to what he said in another topic]
updating what I said, The "correction" that you said was the guy I was showing you that calculated it the same way as you (minus the 10 instead of 15) and was wrong o.0; [or else I dont see why he would have linked to what he said in another topic]
ah well. i think once the number of possible combinations per character surpassed 1 million it really didn't matter considering it would be impossible for anyone to try even half of them. oh well haha. :P. still nice to find out its insanely high
updating what I said, The "correction" that you said was the guy I was showing you that calculated it the same way as you (minus the 10 instead of 15) and was wrong o.0; [or else I dont see why he would have linked to what he said in another topic]
ah well. i think once the number of possible combinations per character surpassed 1 million it really didn't matter considering it would be impossible for anyone to try even half of them. oh well haha. :P. still nice to find out its insanely high
yeah I agree 100%, your number or his, the result is the same, its a insane number =P
Since the set is non-ordered combinations, you should get (25 choose 6) skills times (15 choose 3) passives = 177,100 x 455 = 80,580,500.
thats not how you times it. use your calculator to do what i showed you and you'll get my number.
You can't just multiply the numbers together. You have to consider the fact that these are combinations. Multiplying them together gives you overlap.
no it doesn't. i edited my last post i sent you with exact numbers. i am making my equation BASED on the fact that you can't use any of the same skill/rune combo's twice. there will be no overlap. and regardless, the number is unfathomably high either way. making it impossible for anyone to say there not unique. the fact that i put 125 THEN 120, because i don't want the same skill/rune to overlap in the equation. otherwise id do 125 x 125 x 125 ect...
You're still just multiplying the entire possible set (25) by 5 each time, which is wrong.
You have to create a combination of the set choice you're interested in: IE there are 25 possible (without replacement) out of 6 choices. That means you get unordered sampling without replacement. i.e. - n Choose k - n being 25, k being 6. Multiply that by the unordered sampling without replacement for passives (15 and 3), then multiply by 30 - (6 skills times 5 rune types). You should get:
In actuality the count of true builds (like what the chat gem on the skill calculator generates) is significantly less, but it's still a large number. So when someone asks you about customization just say there's a large number of builds. If you must use some ridiculous number to convince them, they're probably not worth your time.
http://www.diablofans.com/blizz-tracker/topic/188792/97-billion-builds-per-class-blizzcon/
Official Blizzard Quote:
I realize there’s a lot of information spread around, I’m hoping to bring some of it to a single post and hopefully get our point across and reassure you that the changes we’re making are for the betterment of character customization options, and ultimately your long-term enjoyment of the game.
So, why did we get rid of skill points?
(Note: this is a supplementary min/max explanation. There are lots of other reasons which have been touched on in the past such as how players approach our game, supporting the idea of builds, observing how players behaved in internal testing, etc. This is just further explanation that I think will resonate with some of you.)
In Diablo III, we really want to improve the combat depth. Part of having combat depth involves having skills that are useful in different situations. In Diablo II players often used a single skill to deal with almost all situations: Blessed Hammer, Frozen Orb and Bone Spirit to name a few. Players invest 20 points into a single skill and use it as much as possible. The only reason a player would swap away from their primary spam skill is due to monster resistances/immunities. If a monster was immune to your primary spam skill, you’d either skip the encounter completely or fall back on a second skill. Neither of these answers provides the player with much combat depth.
To support combat depth, skills need to have different roles. Here is a very simple example:
Magic Missile deals 15 damage to a single enemy
Arcane Orb deals area of effect damage for 10 damage each
With these two skills we’re beginning to develop some combat depth for the player. Use Magic Missile when you’re facing one enemy, use Arcane Orb when you’re facing multiple enemies. But you may also want to use Magic Missile if one enemy is a “high priority target” in a group, and you want it to die quickly. In this simplified example players can still defeat a horde of enemies by casting Magic Missile multiple times, or they could defeat a single large enemy by casting Arcane Orb multiple times, but that wouldn’t be as efficient as a player who uses the right skill for the right situation.
Ok so that basic layout of combat depth out of the way!
With skill point spending your skills get better as you invest points into them. The problem is that this destroys combat depth. If after pumping a bunch of points into Magic Missile it now deals 70 damage to a single enemy, assuming my enemies have any reasonable health, then Magic Missile becomes a better choice than Arcane Orb even in group situations. If after pumping a bunch of points into Arcane Orb it now deals 45 damage, then it deals more damage than Magic Missile to single targets. Now rather than using the right skill for the right situation, I’m using the skill I’ve put all my points into. Skill point spending has eroded away combat depth.
Why did we go from 7 skill choices to 6?
(Note: again, this is a supplementary explanation. We’ve gone over some of the other reasons elsewhere, but this is specifically targeted at those of you here who feel strongly that 7 means there would be more build diversity than 6)
Diablo III emphasizes build customization. We feel that 6 skill choices actually creates more build diversity than 7.
Why? Well for any given set of options, the greatest number of combinations exists when the number of choices you can make is close to half the number of options you have. Some of you may remember a high school math problem like this: There are 12 differently colored marbles in a bag. How many different color combinations can you get by choosing X marbles? Well as it turns out the solution for various values of X are:
1 marble: 12 different color combinations
2 marbles: 66
3 marbles: 220
4 marbles: 495
5 marbles: 792
6 marbles: 924
7 marbles: 792
8 marbles: 495
9 marbles: 220
10 marbles: 66
11 marbles: 12
12 marbles: 1 (there’s only 1 way to choose 12 marbles from the 12 in the bag)
The greatest number of possible combinations happens when you are choosing 6 from a possible 12.
You may be asking what 12 has to do with anything as classes all have over 20 skills available to them...
This is true in theory, but in practice players tend to (and really should) pick up skills to fill different roles so they can be effective. Categories such as single target, area of effect, auto-targeting, debuff, defensive, group buff, escape, crowd control, 2-minute ubers, pet skills, etc. etc. Players generally take at most two (and often one) skill to fill any particular role. For example, the Wizard has Ice Armor, Storm Armor and Energy Armor, but I don’t think anyone is going to take all three (though maybe somebody will take that as a challenge and prove me wrong), most players will choose one Wizard Armor spell (note that this can change dramatically with some rune effects). If we look at each class, depending on how you count, you get anywhere from 8-12 different types of skills. So we err on the high side in our category estimate (12) and that means 6 is a pretty good number to maximize build variety.
It's important to note that we’re not just talking about you and your friend having Wizards with slightly different skills, we’re talking about you and your friend having 6 skills that are different in functionally significant ways.
Closing remark! When we pull math out like this I’m sure somebody will point out that if our only objective was to maximize build combinations we’d have allowed people to also choose 6, 7 or 8 passives rather than just 3. So I’ll counter by saying maximizing build combinations is not our only objective. We also want our system to have aesthetic flavor, to be simple to understand, and to have the passives in particular feel impactful. We have many different goals that we take into account when making any design decision. In the case of active skills, we felt the increase in variety was one of many good reasons to go from 7 to 6.
So how many skill combinations are there now?
Well taking into account 6 active skills, all the rune combinations, and 3 passives we currently expect each class to have roughly 2,285,814,795,264 different build combinations. That’s not taking into account skill types for ‘ideal’ builds, but that’s always been a big part of the fun of experimenting (and longevity for Diablo II) - finding a build that shouldn’t work, and making it.
the point of my post was to give people an exact number. therefor they know, and its not a guess. so if someone honestly wants to argue with you, you can give them exact math and number to blow them away
Yeah I agree, incredible amount of customisation still, we'll probably never know how many inferno viable builds we'll have per character, whereas with D2 there were about 25 total across all 7 classes.
ah very very agree! lol. i keep telling people that. because people say "oh well D2 had more possible combo's bla bla" but ANYONE who has played d2 knows theres honestly barley ANY good builds between all of the characters that will actually kill shit. honestly for PVE theres really only like 12 for hell. lol
i did this many many times on my calculator and wrote it out and got help from a math major. now I'm not saying bash is stupid or misinformed. just saying I'm sure he didn't spend a long time figuring out the exact number with multiple people. i did. lol
But regardless it still a crap load of combinations.
should edit, your method is close to this
http://forums.battle.net/thread.html?topicId=27822632620&sid=3000#0
which bash corrected.
he used marbles and didn't actually show you ANY proof of his exact mathematical equation he used to figure it out. i did. believing him is illogical just because he works for blizzard when he provides no proof to his math. now if bash was some mathematical genius that was famous id say ok. but considering i gave you proof, he didn't. I'm the more logical choice.
edit: there he did correct himself and his number is nearly the exact same number as mine. i just used 15 passives instead of 10, otherwise my number would be identical. so my math is 100% correct. i win. lol
The guy who gets close to you, he still links to his, and cant find where he corrects himself.
Just want to see where you said he corrects himself first.
You have to create a combination of the set choice you're interested in: IE there are 25 possible (without replacement) out of 6 choices. That means you get unordered sampling without replacement. i.e. - n Choose k - n being 25, k being 6. Multiply that by the unordered sampling without replacement for passives (15 and 3), then multiply by 30 - (6 skills times 5 rune types). You should get:
(25 choose 6) * (15 choose 3) * 30 = 593,775*455*30 = 8,105,028,750 possible combos.
(my previous try did not take into account runestones), but you should just have to multiply by 5 for each skill (30).
I'm looking at this powerpoint from Stanford.
I'd like to see Blizzard's math on that number.
Edit: there's also this very concise (and very reliable) source: Wolfram Alpha
ah well. i think once the number of possible combinations per character surpassed 1 million it really didn't matter considering it would be impossible for anyone to try even half of them. oh well haha. :P. still nice to find out its insanely high
Skill combos = (25 choose 6) = 177,100
Passive combos = (15 choose 3) = 455
Rune combos = 5^6 = 15,625
Total (multiply those) = 1,259,070,312,500 for each class
Of course, right now each class does not have 25 actives and 15 passives.
Real numbers here: http://www.diablofans.com/topic/27956-number-of-different-builds/