Possible number of passive tree combinations

I think it would be better to count builds by keystones and skill gems.

I find it funny that 'counting' is actually a robust field in mathematics and particularly statistics.

I still contend that once you pass up perhaps 1000's of builds, the concept of builds starts becoming meaningless.

So in terms of meaningful builds, I feel you have to divvy things up into build categories, and then combine them with keystones. These are the only meaningful differences in builds.

Even with 20 keystones given 1 2 or 3 as choices, there are about 1200 possible builds with just that.... Given 100 skills and a choice of 4 there are nearly 4 million builds. These two combined immediately put the possible meaningful builds into the millions or billions.

So I contend that there are even so many meaningful builds that counting them is too large to be practical. Ironically out of millions or billions of meaningful builds, only perhaps 10 will be top tier used by players.

(In all reality, if you divvy them up into categories of perhaps 10-20 skills and choosing 4 or perhaps 5 skills, then you are back to thousands of builds)

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zeto wrote:

I think it would be better to count builds by keystones and skill gems.

Keystones are very powerful and build enabling but you certainly don't need them to create viable builds. Most of my characters don't use keystones.

I think zeto is right though that the main limitation on build variety currently isn't the passive tree but the number of viable active skill gems.

Obviously, even if there are more than 2^116 possible builds, we can't say that they are all viable, nor are all of them significantly different from each other.

But if you look at my earlier statistic - Baldur's Gate? It has under 5000 possible character archetypes (your character can't change too much once you build it from level 1) and it has a fairly diverse number of options, but nowhere near as many as POE.

And it's wrong to count keystones only. Most of my characters are defined by their active skill focus, not their passive skills. I take Blood Magic on most of my Marauders, but I have a fire-mage marauder and a ground slam marauder, they take similar passives, but play very differently.

True game/character complexity is the result of passive interaction with active skills (and support gems, which add obviously more complexity to the equation). This is why I think GGG should endeavor to release as many active and support skills as they can during 2013, adding a few more "game changing passive skills" to influence their use. Also, support gems have a larger impact overall on most builds, as most of your damage comes from support gems and not passives (notable exception being pain attune, cast/attack speed increases, weapon elemental damage increases and critical damage increases) which I think is something which should be addressed.

I cannot give you a formula, but the possible number of combination is a lot lower than these astronomical numbers... but still very high, sure.

For an example of 3 points:
you wrote 2*3*8 but it's only 6+(2+1)+(2+1) (6* three in a row, then splitted)
48 >> 12

quite a diffence... and related to the number of nodes, there are few connections...

But anyway, I'd really like to know how big the number would be :)

It's more than 12 if you count ALL valid non-unique passive trees, which I was. I'd like to run through it by hand for the first 3 points using the witch start. I dunno if 2*3*8 is right, I think I may have counted wrong 8 should probably be 6? But anyway... for unique combinations...

At level 2 you have 2 choices: 40% mana, 10% spell dmg
At level 3 you have 2 new choices: +10 int x2 or more spell damage or 8% mana
At level 4 you have 6 new choices: 2x int, 1x spell crit, 1x spell cast, 1x mana regen, 1x flat mana

But at level 3 and 4 you cannot ignore the possibility of taking older nodes. So I'm going to make things easy by doing chains by hand

A: spell damage 10%
A2 = 8% spell dmg
B: 40% mana reg
C: 8% mana
B2 = 20% mana reg
C2 = 8% mana
D: 25% spell crit
E: 3% cast spd
F: 10 int
G: 10 int
H: 10 int
I: 10 int

here we go I'm listing all unique possible combinations for a level 4 witch

<empty passive tree>

A
B

AB
AA2
BC
AF
BG

ABC
ABG
ABF

AA2F
AA2D
AA2E
AA2B

BCB2
BCC2
BCG

BGH
AFI

I think that's all of them? Let's see. 1+ 2 + 5 + 3 + 4 + 3 + 2 = 20. It is twelve if you ONLY look at level 4 possibilities and don't count the empty passive tree (where a player chooses not to use his passives), so you're right on that.

yeah ok, if you also count unused points...

btw, would be a nice "build" to completely ignore skills and see how far you can get :)

To be honest I don't know what you're trying to do with the number? Knowing it just for fun? I mean pretty obviously it's worthless... it doesn't matter if there are 10^99 oder 10^100 possible combinations, it doesn't say anything about the game.

If you want to have a guess for the number of possible builds, you first have to define what a "unique build" is. Let's assume we both play the same bow-ranger... but you spent 5 passive skill points different and you're using an aura I don't use... do we use the same build?

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Asphael wrote:

To be honest I don't know what you're trying to do with the number? Knowing it just for fun? I mean pretty obviously it's worthless... it doesn't matter if there are 10^99 oder 10^100 possible combinations, it doesn't say anything about the game.

If you want to have a guess for the number of possible builds, you first have to define what a "unique build" is. Let's assume we both play the same bow-ranger... but you spent 5 passive skill points different and you're using an aura I don't use... do we use the same build?

It was an exercise to show relative complexity. Yes, there is not too much difference between 10^99 and 10^100, but the point I'm trying to make is one about how the complexity of a game is directly related to its depth.

Of course, poor balancing and design can make all 1350 nodes worthless and make 10^100 possible builds suck, except for one - you have low actual complexity. But if you have good balancing and design and make most of the 1350 nodes compelling and useful, you have a balanced, deep game, because there are so many possible combinations, viable combinations well exceeding 10000 - that means there is so much room for growth and experimentation. It's this kind of deep strategical, long-term planning and thinking that obviously appeals to a group of players who are being neglected by most of the video game industry these days.

My overall point, that I will be making for the video, is that Path of Exile demonstrates there is room for incredible complexity in video games. That such complexity is beneficial. While many developers are copying World of Warcraft and making their games simpler, thinking KISS (keep it simple stupid) is the only viable method to game design, they are missing out on a key demographic of players.

I will also make the point that most RPGs have ALWAYS been about integer games. Exploiting these number games, making them deeper, more involved, but logical and conveyable, is key to making a good game, a good RPG.

The video is a thorough examination of DA2, which demonstrates what goes wrong when you make a spiritual successor to BG2 that isn't complex.

the thought of beginning how to calculate the possibilites gives me a headache, and im a pretty intelligent person. how many splits there are makes it insane.

Strolls into the room wielding a large tuna shouting "BUBBLES BUBBLES BUBBLES"!!!!

Recovers from the effects of reading the schollars and mathmeticians mashinations and feels infinatly smarter.............if not a little worse for ware. Lets just hope an episode like that never happens again.

On a serious note though. I agree, the depth of the game is reflected in both the numbers which are literally nothing more than a reflection of the depth within the developers.

:)