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.
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.
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...
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!
*** 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.
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*** 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.
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...
*** 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.