Personally, the fact that there are 2000 or 2 viable builds, is less important to me than that I can make the build I want to. For example, I I first played LoD, (not sure exactly when It was) I wanted to play a Fissure Durid with some summons. I learned the hard way that this was not possible and I almost put the game down at that point.
Now I have about 5 builds for the Doc (which looks to play more similar to the Druid than the Necro IMHO) some are silly (only dog skills) some are not, and they tell me that I can take at least the serious builds and with the right gear, and a some tweaking (which I can do as I play my first character: How Terrible!) I can play that character. and it will be mine!
I don't care that I can change to be exactly like your character. I don't want to, your character is stupid (as in not interesting to me). If you change your character to be identical to mine, that's your perogative and I may feel proud that my awsome unique build was so cool you wanted one too or I can not care and let you go on your merry way.
In any case I love that there are hundreds of billions of builds fo each class and thank you OP for all the hard work.
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If that made sense to you, Bravo! I think I even confused myself...
*** 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’ve seen a lot of math done out there 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. 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!/13!)] = 7,741,440 total combinations.
There is 7 million, 741 thousand, 440 total possible combinations (not billions). Now what’s great about this is that the way the “sets” are set up makes a vast majority of these combinations 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!/13!)] = 120,960,000,000… not including the “no rune effect” option. This provides us with 15,625 times more variations. In other words, for every 1 of the original 7,741,440 combinations in equation 1, there is 15,625 variations due to rune effects.
[(18x24x24x24x24x18)(16!/13!)] = 361,184,624,640… which does include “no rune effect” option. Likewise with this equation, for every 1 of 7,741,000 combinations, there is 46,656 variations due to rune effects including “no rune”.
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 3,870 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.
I really didn't know that! Thanks for pointing that out. I did play the beta on open weekend but I had not discovered that option. I was the one missing out on something!
I like the analysis, but this is like plotting out chess combinations: it really craps on the bigger picture, or in this case, the more valid one.
Just because you computed permutations doesn't mean that all permutations are actually playable, in the sense that that will provide a considerable amount of utility to the player. So, I propose the following:
Each skill gets an inherent value that mimics that condition when that skill is being used as a "primary", in the sense that it is the focal point of the player. Some skills will score higher than others:
For example, consider a wizard using NOTHING but energy armor, or making a build around energy armor. Not much utility in that. Yes we could argue this, but I think the majority of the players WON'T be doing this because they want to kill shit.
Then each of these skills gets a rune RANGE next to it, i.e. how each rune affects the inherent utility of the skill.
Then this data set gets amplified further by its possible synergies, also a range that represents how that skill would work with other skills. I can't think of a lot of standalone skills, but there are some skills that clearly work better with others, such as the signature spell passive with the wizard signature spells. Thus for each skill, we would have the following array:
Finally we have to consider equipment; some skills will have a considerable benefit over others in that they utilize the equipment of the player more (think of the skills that use multipliers of weapon damage). I propose that be a multiplier between .9 and 1.1 for the all the integers in the dataset above.
From there we pump it into a supercomputer and have it run a script that optimizes the each skill in relation with 8 others, and sums up the total utility/power of each build/combination. Long story short that's a lot of fucking skills, as many permutations as listed above.
I'm willing to bet that there will be a significant utility curve, and that it looks largely like a chi squared curve, and in addition to that, only a certain threshold or higher will actually be viable for completing Inferno with a group.
I really didn't know that! Thanks for pointing that out. I did play the beta on open weekend but I had not discovered that option. I was the one missing out on something!
No worries. Almost no one finds elective mode without somebody pointing it out to them. People have been complaining about this to Blizzard, but their response is that they "are ok with it being tribal knowledge" because they don't want to "confuse" people by putting it in the skill UI. :/ This is one of the few decisions made for D3 that absolutely baffles me.
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...and if you disagree with me, you're probably <insert random ad hominem attack here>.
Monk has the least permutations, and I'm already rewriting how the objects will be handled and have their attributes defined.
Yes, I agree with you. Let's go ahead and cut out the permutations that make no sense, like all defense skills and passives.
Let's define utility as survivability, which will be composed of 50% output of damage and 50% prevention of death. Some skills like Near Death, who have 0 synergy whatsoever, is inherently super useful in Inferno.
I will also like to acknowledge rune variations is just that… a variation on the same skill. A rune effect doesn’t make it a new different skill altogether but only a variation on a theme.
I have to disagree with this. It varies wildly from skill to skill. While Leap runes are all pretty cosmetic variations, for a skill like Shock Pulse, there are 4 very different feeling functions depending on the rune you choose.
Further, a solid build is created by finding synergies between different abilities. In D3, those synergies come much more from the rune options than the skill categories themselves. Even in a skill like Leap, wherein none of the runes changes THAT much about how it works and feels, you can choose to knock enemies back, pull enemies in, slow them, stun them or give yourself more armor. Each fits a very different build concept, and its that runes variety, not the skills that will define the iconic builds we'll all flock to emulate as we works our way through inferno.
You cannot white wash the runes when you talk about build variation.
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I grew up gaming without internet forums. The entire phenomenon of being upset with a game developer makes no sense to me. No sense. I cannot imagine spending my time and energy being upset about something I choose to do for recreation.
I grew up gaming without internet forums. The entire phenomenon of being upset with a game developer makes no sense to me. No sense. I cannot imagine spending my time and energy being upset about something I choose to do for recreation.
I really didn't know that! Thanks for pointing that out. I did play the beta on open weekend but I had not discovered that option. I was the one missing out on something!
Hehe, well now you do, so maybe edit your misinforming post and it's math above ^^?
Edit: Your conclusions seems valid though. And just to poke at you a bit, as for lvl 1 skills, the Necromancers 2 lvl 1 skills for skellys kick ass as does his amplify dmg curse which is also lvl 1, buy overall, yes the lvl 1 skills suck for most classes (also barb passives 1 of them anyway, and claw passive for assassin if your are that kind of assassin) ^^
*** Edit ***
Well the math still holds true to non-elective play but now that I know that we can basically put any active skill in any of the 6 allocated slots, it does greatly magnify the possibilities. Truthfully, I can't understand too many people playing non-electively so I will definitely modify the post to reflect it for non-elective mode. Playing without the elective option on still holds potentially much more play and character variation. Only 18 days left...
People had fun in Diablo 2 making characters and figuring out how to spend roughly 100 skill points by allocating them into roughly 30 skill slots (per class), both active and passive. Some builds were serious business and some builds were just goofy builds where people had fun figuring out how to make them viable.
In Diablo 3, people will shift through different combinations of skills that have very little identity. They aren't builds, just combinations. When somebody says they are making a crit barb or an aoe barb or bash barb, you will have absolutely no way of knowing what the hell their build actually is. It's just another combination of skills that does the same crap as the next guy's.
Do all of the math you want. Go ahead. Slobber over a big passionless number that's at the end of an exponent equation. Big whoopidee doo. It's all generic combinations with very little identity. More doesn't mean better. Every Blizzard fan should know that by heart. Nobody gives a crap if your rogue build is different, They only care if your Combat rogue or your sublety rogue rips into flesh better than the other guy... or if you have the skills or rotation down pat to do so. Who would give a crap if your rogue build is skill combination #3450?
After 6+ years of development, we basically have the same situation where every build has the same purpose of killing crap, while having also having every build have less identity. We might as well just go back to Warcraft 2, where every one of our skills could be perfectly balanced, similar to have every unit in WC2 was a mirror matched unit and they did the exact same thing. Outside of making, let's say, an MF run Demon hunter or a PvM Demon Hunter, what else is there?
Diablo 2 Player: I'm leveling a whirlwind barb.
Diablo 3 Player: Cool. Well you see... my barb will have bash and leap and ignore pain and whirlwind and...
Diablo 2 Playter: Um... so that's a whirlwind barb then, right?
Diablo 3 Player: Well, yeah... but not really. There's more to it then that. You have to see my skills to understand how it all works Plus my runes are...
Diablo 2 Player: Sounds complicated and boring. Too long, didn't listen. Brb, pindleskin run.
Diablo 3 Player: Screw you, noobtrash!
Gems, gear sets and followers will have to be more in-depth to compensate. If not, you'll basically just have a maximum of five characters with an extended stash and maybe mule characters for extra storage. Why? Well every character can switch to another characters "build" simply by switching gear, at absolutely no cost. Almost 12 years have past and all we have done was go from a game where we could have multiple builds of each class (example. having a hurricane druid AND a shapeshifter druid) to a game we just have one character of each class (ex. having one druid that can just switch to any build whenever he wants just by switching skills and gear.)
Math does not make a game fun long-term. If it did, all of you guys and gals would be Actuaries in real life having a great time making a good living.
I've been reading on these forums for a while now and I've become so fed up with this argument that I've decided to actually make a post. Correct me if I'm wrong but it appears that you believe having to re-level a toon to respec is more meaningful than just openning your spellbook and swapping out abilities. I can see how this makes sense to some people since each toon's skills are permanent, and therefore each individual has more of a unique identity. (ie. blizzard sorc and meteor sorc).
The fact that you are ignoring though, is that in D2 it took less that 5 hours play time to level a toon to 80. On top of that, and I admit this is merely my opinion, those ~5 hours felt like a necessary but annoying chore that I had to complete before I could have some real fun. As a result, you are actually arguing that an annoying ~5 hours creates a meaningful identity that a toon in D3 will lack. I for one am glad that Blizzard does not share your opinion.
What really gives a toon a unique identity is the gear. I'd be happy to expand on this but I feel like I've already said too much for my first post.
/rant off
And asfastasican is rebuffed yet again. Don't worry, he won't respond. He never does. He just comes to shit on a conversation by bringing up the D2 vs D3 argument (which this topic is not about) and then leaves. He does not come back.
I will also like to acknowledge rune variations is just that… a variation on the same skill. A rune effect doesn’t make it a new different skill altogether but only a variation on a theme.
I have to disagree with this. It varies wildly from skill to skill. While Leap runes are all pretty cosmetic variations, for a skill like Shock Pulse, there are 4 very different feeling functions depending on the rune you choose.
Further, a solid build is created by finding synergies between different abilities. In D3, those synergies come much more from the rune options than the skill categories themselves. Even in a skill like Leap, wherein none of the runes changes THAT much about how it works and feels, you can choose to knock enemies back, pull enemies in, slow them, stun them or give yourself more armor. Each fits a very different build concept, and its that runes variety, not the skills that will define the iconic builds we'll all flock to emulate as we works our way through inferno.
You cannot white wash the runes when you talk about build variation.
*** Thanks for the reply. I agree with you with the synergy aspect to runes versus the skills themselves and that it really does make a huge difference. I guess what I was trying to say is that the rune changes the skill but not on a fundamental level when calculating the lowest possible build combination and comparing to D2. But you have a good point. if you consider that In D3, "electrocute" is a skill and then a rune modifies to chain lightning. I There are some runes that greatly change the skill. In D2, lightning was a skill by itself and then at lvl 18 you could pick chain lightning. In this scenario you're point seems valid in that a rune could reforge a whole new skill and because of it's effect, change the very nature of how a player plays.
*** Thanks for the reply. I agree with you with the synergy aspect to runes versus the skills themselves and that it really does make a huge difference. I guess what I was trying to say is that the rune changes the skill but not on a fundamental level when calculating the lowest possible build combination and comparing to D2. But you have a good point. if you consider that In D3, "electrocute" is a skill and then a rune modifies to chain lightning. I There are some runes that greatly change the skill. In D2, lightning was a skill by itself and then at lvl 18 you could pick chain lightning. In this scenario you're point seems valid in that a rune could reforge a whole new skill and because of it's effect, change the very nature of how a player plays.
You are the most civil and open-minded forum user ever. You just won the internet.
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I grew up gaming without internet forums. The entire phenomenon of being upset with a game developer makes no sense to me. No sense. I cannot imagine spending my time and energy being upset about something I choose to do for recreation.
Hey Everyone, *** 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’ve seen a lot of math done out there 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. 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!/13!)] = 7,741,440 total combinations. There is 7 million, 741 thousand, 440 total possible combinations (not billions). Now what’s great about this is that the way the “sets” are set up makes a vast majority of these combinations 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!/13!)] = 120,960,000,000… not including the “no rune effect” option. This provides us with 15,625 times more variations. In other words, for every 1 of the original 7,741,440 combinations in equation 1, there is 15,625 variations due to rune effects. [(18x24x24x24x24x18)(16!/13!)] = 361,184,624,640… which does include “no rune effect” option. Likewise with this equation, for every 1 of 7,741,000 combinations, there is 46,656 variations due to rune effects including “no rune”. 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 3,870 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.
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.
# 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....
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"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?"
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.
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.
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.
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.
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.
Rollback Post to RevisionRollBack
If that made sense to you, Bravo! I think I even confused myself...
Now I have about 5 builds for the Doc (which looks to play more similar to the Druid than the Necro IMHO) some are silly (only dog skills) some are not, and they tell me that I can take at least the serious builds and with the right gear, and a some tweaking (which I can do as I play my first character: How Terrible!) I can play that character. and it will be mine!
I don't care that I can change to be exactly like your character. I don't want to, your character is stupid (as in not interesting to me). If you change your character to be identical to mine, that's your perogative and I may feel proud that my awsome unique build was so cool you wanted one too or I can not care and let you go on your merry way.
In any case I love that there are hundreds of billions of builds fo each class and thank you OP for all the hard work.
lolwut? xD thats what i said?
*** 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’ve seen a lot of math done out there 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. 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!/13!)] = 7,741,440 total combinations.
There is 7 million, 741 thousand, 440 total possible combinations (not billions). Now what’s great about this is that the way the “sets” are set up makes a vast majority of these combinations 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!/13!)] = 120,960,000,000… not including the “no rune effect” option. This provides us with 15,625 times more variations. In other words, for every 1 of the original 7,741,440 combinations in equation 1, there is 15,625 variations due to rune effects.
[(18x24x24x24x24x18)(16!/13!)] = 361,184,624,640… which does include “no rune effect” option. Likewise with this equation, for every 1 of 7,741,000 combinations, there is 46,656 variations due to rune effects including “no rune”.
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 3,870 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.
Just because you computed permutations doesn't mean that all permutations are actually playable, in the sense that that will provide a considerable amount of utility to the player. So, I propose the following:
Each skill gets an inherent value that mimics that condition when that skill is being used as a "primary", in the sense that it is the focal point of the player. Some skills will score higher than others:
For example, consider a wizard using NOTHING but energy armor, or making a build around energy armor. Not much utility in that. Yes we could argue this, but I think the majority of the players WON'T be doing this because they want to kill shit.
Then each of these skills gets a rune RANGE next to it, i.e. how each rune affects the inherent utility of the skill.
Then this data set gets amplified further by its possible synergies, also a range that represents how that skill would work with other skills. I can't think of a lot of standalone skills, but there are some skills that clearly work better with others, such as the signature spell passive with the wizard signature spells. Thus for each skill, we would have the following array:
["Skill Name", InherentUtility, RuneLow, RuneHigh, SynergyLow, SynergyHigh]
Finally we have to consider equipment; some skills will have a considerable benefit over others in that they utilize the equipment of the player more (think of the skills that use multipliers of weapon damage). I propose that be a multiplier between .9 and 1.1 for the all the integers in the dataset above.
From there we pump it into a supercomputer and have it run a script that optimizes the each skill in relation with 8 others, and sums up the total utility/power of each build/combination. Long story short that's a lot of fucking skills, as many permutations as listed above.
I'm willing to bet that there will be a significant utility curve, and that it looks largely like a chi squared curve, and in addition to that, only a certain threshold or higher will actually be viable for completing Inferno with a group.
No worries. Almost no one finds elective mode without somebody pointing it out to them. People have been complaining about this to Blizzard, but their response is that they "are ok with it being tribal knowledge" because they don't want to "confuse" people by putting it in the skill UI. :/ This is one of the few decisions made for D3 that absolutely baffles me.
Monk has the least permutations, and I'm already rewriting how the objects will be handled and have their attributes defined.
Yes, I agree with you. Let's go ahead and cut out the permutations that make no sense, like all defense skills and passives.
Let's define utility as survivability, which will be composed of 50% output of damage and 50% prevention of death. Some skills like Near Death, who have 0 synergy whatsoever, is inherently super useful in Inferno.
I'm doing this in Python, want to help?
I have to disagree with this. It varies wildly from skill to skill. While Leap runes are all pretty cosmetic variations, for a skill like Shock Pulse, there are 4 very different feeling functions depending on the rune you choose.
Further, a solid build is created by finding synergies between different abilities. In D3, those synergies come much more from the rune options than the skill categories themselves. Even in a skill like Leap, wherein none of the runes changes THAT much about how it works and feels, you can choose to knock enemies back, pull enemies in, slow them, stun them or give yourself more armor. Each fits a very different build concept, and its that runes variety, not the skills that will define the iconic builds we'll all flock to emulate as we works our way through inferno.
You cannot white wash the runes when you talk about build variation.
Well the math still holds true to non-elective play but now that I know that we can basically put any active skill in any of the 6 allocated slots, it does greatly magnify the possibilities. Truthfully, I can't understand too many people playing non-electively so I will definitely modify the post to reflect it for non-elective mode. Playing without the elective option on still holds potentially much more play and character variation. Only 18 days left...
And asfastasican is rebuffed yet again. Don't worry, he won't respond. He never does. He just comes to shit on a conversation by bringing up the D2 vs D3 argument (which this topic is not about) and then leaves. He does not come back.
*** Thanks for the reply. I agree with you with the synergy aspect to runes versus the skills themselves and that it really does make a huge difference. I guess what I was trying to say is that the rune changes the skill but not on a fundamental level when calculating the lowest possible build combination and comparing to D2. But you have a good point. if you consider that In D3, "electrocute" is a skill and then a rune modifies to chain lightning. I There are some runes that greatly change the skill. In D2, lightning was a skill by itself and then at lvl 18 you could pick chain lightning. In this scenario you're point seems valid in that a rune could reforge a whole new skill and because of it's effect, change the very nature of how a player plays.
You are the most civil and open-minded forum user ever. You just won the internet.
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/
yah I know....D2 had like 5...
Wait! Lower is better right?!? Ya know like golf....
Epicurus
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.
Point:
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.