In the 2010 BlizzCon, it was revealed that there was 96 886 969 344 different builds in the game.
This number was derived from the number of different active skill combinations (7 skill slots and 24 skills per class): 24*23*22*21*20*19*18/(2*3*4*5*6*7) = 346 104
The number that is left when this id divided form the original number is 279936
This number is the number of different rune combinations per skill. At the time there were 7 skill slots, so that's 7 skills.
That number is X to the 7th power X=6
This means that 6 Runestones were planed.
Now this number is very different:
--------------------------
There are:
24 skills/class
20 passives/class
5 runestones
8 different qualities of runestones
The math:
24*23*22*21*20*19
6*5*4*3*2
number of active skill combinations
5 * 8 + 1
number of different combinations of runes per skill + unruned (if no runes were put into it)
5 different runes * 8 qualities of those runes + unruned
41*41*41*41*41*41 (41^6)
number of different combinations of runes per 6 skills
20*19*18
3*2
number of passive skill combinations
Totaling at: 728 853 334 680 665 040
----------------------------
Recalculated version for less passives:
There are:
24 skills/class
15 passives/class
5 runestones
8 different qualities of runestones
Build combinations: 956 893 437 500 (0,00330/00 of total combinations)
Total combinations: 290 901 988 841 844 380
-------------------
Barbarian
Active Skills: 22
Passive Skills: 15
Number of builds: 530 451 796 875
Number of skill combinations: 94 476 058 707 571 778
Demon Hunter
Active Skills: 23
Passive Skills: 13
Number of builds: 451 106 906 250
Number of skill combinations: 83 836 328 480 574 640
Monk
Active Skills: 21
Passive Skills: 13
Number of builds: 242 492 250 000
Number of skill combinations: 45 118 631 019 401 728
Witch Doctor
Active Skills: 22
Passive Skills: 12
Number of builds: 256 482 187 500
Number of skill combinations: 49 042 259 641 604 104
Wizard
Active Skills: 25
Passive Skills: 12
Number of builds: 608 781 250 000
Number of skill combinations: 116 233 880 268 736 912
-------------------
It has been taken in account that a build consists of a full Tier 7 Runestone in each of the skills and that all 6 active and 3 passive skills have been selected.
In depth math:
Na - Number of active skills (of class)
Np - Number of passive skills (of class)
[Na!/((Na-6)!*6!)] //*Number of combinations of active skills
[5^6] //*Number of Runestone combinations
[Np!/((Np-3)!*3!)] //*Number of combinations of passive skills
While a skill combination can consist of any Tier or no Runestone in each of the skills and that any number of active and passive skills have been selected.
Na - Number of active skills (of class)
Np - Number of passive skills (of class)
36 - Number of Runestone combinations (5*7+1)
8 different qualities of runestones
...
5 * 8 + 1
number of different combinations of runes per skill + unruned (if no runes were put into it)
5 different runes * 8 qualities of those runes + unruned
I think this should be omitted from the equation because we're talking about "builds". Runestone levels only give more of the same thing, and effectively everyone is going to want to upgrade them. I would be considered to have the same "build" as the next person with identical skills and runestone types, even if my runestones were different qualities.
How did you arrive at this number? Each class has a different number of known passive skills (for example the Wizard has 15). It's all quite speculative at the moment, but let's assume ~20 passive skills per class:
Ap = 24 (Active Skill pool)
As = 6 (Active Skill slots)
r = 5 (Rune types)
Pp = 20 (Passive Skill pool)
Ps = 3 (Passive Skill slots)
[Ap! / As! / (Ap - As)!] * r^As * [Pp! / Ps! / (Pp - Ps)!]
[24! / 6! / (24 - 6)!] * 5^6 * [20! / 3! / (20 - 3)!]
134,596 * 15,625 * 1,140
2,103,062,500 * 1,140 (the first number is Active builds the 2nd is Passive builds)
2,397,491,250,000 possible builds per character
Due to the speculative basis of the passive skills, I will have to remove the number from our wiki. I'll leave a reference to your thread for readers who are interested in precising the numbers.
8 different qualities of runestones
...
5 * 8 + 1
number of different combinations of runes per skill + unruned (if no runes were put into it)
5 different runes * 8 qualities of those runes + unruned
I think this should be omitted from the equation because we're talking about "builds". Runestone levels only give more of the same thing, and effectively everyone is going to want to upgrade them. I would be considered to have the same "build" as the next person with identical skills and runestone types, even if my runestones were different qualities.
Quote from "DiabloWiki" »
With the number of skills and passives, Runestones, Runestone qualities
When I saw that qualities were considered as a par of a build, i had to calculate the new number, because there is a great difference between 15 625 and 4 096 000 000. If hadn't been stated "Runestone qualities", I wouldn't have had a problem with that.
How did you arrive at this number? Each class has a different number of known passive skills (for example the Wizard has 15). It's all quite speculative at the moment, but let's assume ~20 passive skills per class:
That seems to be the general opinion and the equation you provided in the following quote also uses 20 as the number of passives.
24 skills to choose from.
5 runes.
As far as we can tell, you arn't going to want to use a skill without a rune (ther are runes that simply do flat damage increase for example).
You are only going to use the best runes available to you. Saying the exact same build but with one skill that has a lower level rune is a different build is silly.
6 Skill slots.
Assume 20 traits.
3 trait slots.
24 skills to choose from.
5 runes.
As far as we can tell, you arn't going to want to use a skill without a rune (ther are runes that simply do flat damage increase for example).
You are only going to use the best runes available to you. Saying the exact same build but with one skill that has a lower level rune is a different build is silly.
6 Skill slots.
Assume 20 traits.
3 trait slots.
10.3 quadrillion possible builds not including items, per class?
Assuming 15 traits it's
4,133,779,650,000,000 (or 4.1 quadrillion possible builds not including items, per class).
My math might be off (let me know), but I would expect this to be a more likely number.
You counted in different positions of skills in the bar as a different build. What you should have done is divide the number by 6! for Active Skills, and 3! for Passive Skills.
If you had done that you would have gotten about 2.400.000.000.000
I do not really see more than one build per class at the moment due to being easy to switch to any skill (as seen on the recent F&F beta streaming videos). Yes runes will make an impact on the skills but the skill is still going to be close to the core skill.
If it is still easy to change skills when the final version is out then I will call the entire class the build and hope that you do have to use all the skills in different parts of the game to warrant the easy swap.
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I do not really see more than one build per class at the moment due to being easy to switch to any skill (as seen on the recent F&F beta streaming videos). Yes runes will make an impact on the skills but the skill is still going to be close to the core skill.
I agree, the ability to change out skill selections has pretty much ended "builds" as we know them. You can have fun generating some monstrous number of combination possibilities anytime you have multiple variables that relate in a factorial sense. However, you could do the same thing for sandwich possibilities at Subway. It's easy to generate a system with quadrillions of combinations, it only becomes interesting to consider this number when you are forced to pick only ONE.
The difference is that in D2 we had to pick a sandwich and eat it, whereas in D3 we get a sandwich and then sit there and swap out toppings all day. I personally like to eat my sandwich, and think that being able to change skill selections is a horrible idea. For me, much of the end game involved specialty builds. I would build an mf character for a specific area, or try a non-traditional build that I felt may have some potential. These pursuits represented an investment of time, and a sense of finality when skill selections were made. Putting forth the effort to create these builds was rewarding because you would have specialty type characters that others did not have. I would have a Buffing barb, WW barb, Frenzy barb, Singing barb, Goldfind barb, etc, etc. With the current system we will just build one barb that can instantly morph into whatever we want at the time. That sucks!
Let's not forget how runes will affect the skill system in D3. Sure people might wanna change skills all the time, but once they've figured out an optimal build for their playstyle, and start putting high-rank runes (by the end of Normal, beginning of Nightmare) to boost those "prefered" skills, I don't think people will be constantly swapping skills
Maybe runes are what will make people really "commit" to a skillset, specially if removing them is expensive/costly (costly in the sense that the Rune drops a rank or resets its "random affixes", for instance).
I do not really see more than one build per class at the moment due to being easy to switch to any skill (as seen on the recent F&F beta streaming videos). Yes runes will make an impact on the skills but the skill is still going to be close to the core skill.
I agree, the ability to change out skill selections has pretty much ended "builds" as we know them. You can have fun generating some monstrous number of combination possibilities anytime you have multiple variables that relate in a factorial sense. However, you could do the same thing for sandwich possibilities at Subway. It's easy to generate a system with quadrillions of combinations, it only becomes interesting to consider this number when you are forced to pick only ONE.
The difference is that in D2 we had to pick a sandwich and eat it, whereas in D3 we get a sandwich and then sit there and swap out toppings all day. I personally like to eat my sandwich, and think that being able to change skill selections is a horrible idea. For me, much of the end game involved specialty builds. I would build an mf character for a specific area, or try a non-traditional build that I felt may have some potential. These pursuits represented an investment of time, and a sense of finality when skill selections were made. Putting forth the effort to create these builds was rewarding because you would have specialty type characters that others did not have. I would have a Buffing barb, WW barb, Frenzy barb, Singing barb, Goldfind barb, etc, etc. With the current system we will just build one barb that can instantly morph into whatever we want at the time. That sucks!
If you had written this comment a few days ago, I would agree 100% with you on that. But if you take that Runestones bind to skills rather then not bind at all, you would risk loosing a powerful runed skill by changing the "build" you currently have. Although, I am a fan of the old system, I wouldn't be so fast to judge the new (now). I'd like to try it out and see how it feels.
I'd still prefer an easy hotbar swap for different play-styles. It's just that people don't like deciding which sandwich they want; which is the problem. They'll go for the deli every time if there is one.
Juggling all 24 abilities at once during play will be a fair bit more difficult then small/medium/large/boss hotbar swaps, it'll cause delays and pull you out of the game!
Swapping out active skills did not take long at all unless there was lag. At least thats what it looked like in the beta streams.It only took about a second to change a skill and put it in the action bar.
Yes runes may make a big difference but it may not. It appears to me that weapon damage will be the major factor in skills/spells damage. I believe I have seen in one of the streams that the damage went down when he/she swapped to a lower damage weapon(caster). I believe that lower grade runes might be good enough depending on what it did to the skill if you have a strong enough weapon for the damage.
There are only 5 types of runes with 7 grades as far as I know.
Rollback Post to RevisionRollBack
On Strike and supporting Fallout 4 Mod Makers
Some fallout 4 mod makers have had their mods stolen and uploaded and downloaded on Bethesda's site for the Xbox One.
This number was derived from the number of different active skill combinations (7 skill slots and 24 skills per class): 24*23*22*21*20*19*18/(2*3*4*5*6*7) = 346 104
The number that is left when this id divided form the original number is 279936
This number is the number of different rune combinations per skill. At the time there were 7 skill slots, so that's 7 skills.
That number is X to the 7th power
X=6
This means that 6 Runestones were planed.
Now this number is very different:
--------------------------
There are:
24 skills/class
20 passives/class
5 runestones
8 different qualities of runestones
The math:
24*23*22*21*20*19
6*5*4*3*2
number of active skill combinations
5 * 8 + 1
number of different combinations of runes per skill + unruned (if no runes were put into it)
5 different runes * 8 qualities of those runes + unruned
41*41*41*41*41*41 (41^6)
number of different combinations of runes per 6 skills
20*19*18
3*2
number of passive skill combinations
Totaling at:
728 853 334 680 665 040
----------------------------
Recalculated version for less passives:
There are:
24 skills/class
15 passives/class
5 runestones
8 different qualities of runestones
Build combinations: 956 893 437 500 (0,00330/00 of total combinations)
Total combinations:
290 901 988 841 844 380
Barbarian
Number of skill combinations: 94 476 058 707 571 778
Demon Hunter
Number of skill combinations: 83 836 328 480 574 640
Monk
Number of skill combinations: 45 118 631 019 401 728
Witch Doctor
Number of skill combinations: 49 042 259 641 604 104
Wizard
Number of skill combinations: 116 233 880 268 736 912
It has been taken in account that a build consists of a full Tier 7 Runestone in each of the skills and that all 6 active and 3 passive skills have been selected.
In depth math:
Na - Number of active skills (of class)
Np - Number of passive skills (of class)
[Na!/((Na-6)!*6!)] //*Number of combinations of active skills
[5^6] //*Number of Runestone combinations
[Np!/((Np-3)!*3!)] //*Number of combinations of passive skills
Final:
[Na!/((Na-6)!*6!)]*[5^6]*[Np!/((Np-3)!*3!)]
While a skill combination can consist of any Tier or no Runestone in each of the skills and that any number of active and passive skills have been selected.
Na - Number of active skills (of class)
Np - Number of passive skills (of class)
36 - Number of Runestone combinations (5*7+1)
Combinations of selected active skills and passive skills:
Actives Passives
6 3
5 3
4 3
3 3
2 3
1 3
0 3
Actives Passives
6 2
5 2
4 2
3 2
2 2
1 2
0 2
Actives Passives
6 1
5 1
4 1
3 1
2 1
1 1
0 1
Actives Passives
6 0
5 0
4 0
3 0
2 0
1 0
0 0
Final:
(Np*(Np-1)*(Np-2)/6+Np*(Np-1)/2+Np+1)*(Na*(Na-1)*(Na-2)*(Na-3)*(Na-4)*(Na-5)*(36^6)/720+Na*(Na-1)*(Na-2)*(Na-3)*(Na-4)*(36^5)/120+Na*(Na-1)*(Na-2)*(Na-3)*(36^4)/24+Na*(Na-1)*(Na-2)*(36^3)/6+Na*(Na-1)*(36^2)/2+Na*36+1)
References:
http://us.battle.net/d3/en/calculator/barbarian
http://us.battle.net/d3/en/game/whats-new
I think this should be omitted from the equation because we're talking about "builds". Runestone levels only give more of the same thing, and effectively everyone is going to want to upgrade them. I would be considered to have the same "build" as the next person with identical skills and runestone types, even if my runestones were different qualities.
How did you arrive at this number? Each class has a different number of known passive skills (for example the Wizard has 15). It's all quite speculative at the moment, but let's assume ~20 passive skills per class:
I can't take credit for that calculation, but it's closer to Bashiok's number, as was originally referenced on our Runestones page. (http://forums.battle.net/thread.html?topicId=27822642648&sid=3000&pageNo=2#27)
Due to the speculative basis of the passive skills, I will have to remove the number from our wiki. I'll leave a reference to your thread for readers who are interested in precising the numbers.
When I saw that qualities were considered as a par of a build, i had to calculate the new number, because there is a great difference between 15 625 and 4 096 000 000. If hadn't been stated "Runestone qualities", I wouldn't have had a problem with that.
That seems to be the general opinion and the equation you provided in the following quote also uses 20 as the number of passives.
24 skills to choose from.
5 runes.
As far as we can tell, you arn't going to want to use a skill without a rune (ther are runes that simply do flat damage increase for example).
You are only going to use the best runes available to you. Saying the exact same build but with one skill that has a lower level rune is a different build is silly.
6 Skill slots.
Assume 20 traits.
3 trait slots.
((24*5)*(23*5)*(22*5)*(21*5)*(20*5)*(19*5))*(20*19*18)
(120*115*110*105*100*95)*(6840)
10,357,162,200,000,000
10.3 quadrillion possible builds not including items, per class?
Assuming 15 traits it's
4,133,779,650,000,000 (or 4.1 quadrillion possible builds not including items, per class).
My math might be off (let me know), but I would expect this to be a more likely number.
You counted in different positions of skills in the bar as a different build. What you should have done is divide the number by 6! for Active Skills, and 3! for Passive Skills.
If you had done that you would have gotten about 2.400.000.000.000
If it is still easy to change skills when the final version is out then I will call the entire class the build and hope that you do have to use all the skills in different parts of the game to warrant the easy swap.
I agree, the ability to change out skill selections has pretty much ended "builds" as we know them. You can have fun generating some monstrous number of combination possibilities anytime you have multiple variables that relate in a factorial sense. However, you could do the same thing for sandwich possibilities at Subway. It's easy to generate a system with quadrillions of combinations, it only becomes interesting to consider this number when you are forced to pick only ONE.
The difference is that in D2 we had to pick a sandwich and eat it, whereas in D3 we get a sandwich and then sit there and swap out toppings all day. I personally like to eat my sandwich, and think that being able to change skill selections is a horrible idea. For me, much of the end game involved specialty builds. I would build an mf character for a specific area, or try a non-traditional build that I felt may have some potential. These pursuits represented an investment of time, and a sense of finality when skill selections were made. Putting forth the effort to create these builds was rewarding because you would have specialty type characters that others did not have. I would have a Buffing barb, WW barb, Frenzy barb, Singing barb, Goldfind barb, etc, etc. With the current system we will just build one barb that can instantly morph into whatever we want at the time. That sucks!
Maybe runes are what will make people really "commit" to a skillset, specially if removing them is expensive/costly (costly in the sense that the Rune drops a rank or resets its "random affixes", for instance).
If you had written this comment a few days ago, I would agree 100% with you on that. But if you take that Runestones bind to skills rather then not bind at all, you would risk loosing a powerful runed skill by changing the "build" you currently have. Although, I am a fan of the old system, I wouldn't be so fast to judge the new (now). I'd like to try it out and see how it feels.
Also, I love math
Juggling all 24 abilities at once during play will be a fair bit more difficult then small/medium/large/boss hotbar swaps, it'll cause delays and pull you out of the game!
Yes runes may make a big difference but it may not. It appears to me that weapon damage will be the major factor in skills/spells damage. I believe I have seen in one of the streams that the damage went down when he/she swapped to a lower damage weapon(caster). I believe that lower grade runes might be good enough depending on what it did to the skill if you have a strong enough weapon for the damage.
There are only 5 types of runes with 7 grades as far as I know.
EDIT:
New numbers are in!
Just beat me... was too tired for big numbers last night.
GRAND TOTAL: 2,089,314,390,625
Glad I was, glad I was