Interesting point re: only 3/7 skills can be capped

[starrise]

I posted this on the front page but I know a lot of you probably don't read the comments there. The first part is a math proof, so if you want to skip it find the bold-ital-underlined tl;dr further down.

Ok, for the mathematically inclined reader:

Let n be the number of points you get through your character’s “career” all totaled. There is no way you can get more than n.
Let k be the number of points you can put in any one skill. There is no way you can put more than k points into a skill.

Then if only 3 skills are cap-able, the other 4 must not be capped and must have r = (n-3k) points among them. It must also be true that

r < k

for if we assume r >= k then we could dump k points into a fourth skill, and our assumption that only 3 skills are cap-able is wrong. Proof by contradiction.

tl;dr

This means that no matter what, you’ll have to pick from something approximating one of the following:

Jack-of-all-trades: All of your skills have something like 8/16 or 9/16 points.
Specialist-1: 3 capped skills and one skill with something like 12/16 points, and only 4 skills total.
Specialist-2: 3 capped skills and one skill with 9/16 and three with 1/16.
Specialist-3: 3 capped skills and four with 3/16.

Granted I pulled the specific numbers out of the air, but the math shows that if you only have 3 cap-able skills, you can’t even come close to maximizing the non-capped skills. You will be forced to make some very serious trade-offs in terms of relative skill strengths. Either play a specialist with “one-point-wonder” utility skills as backup, or generalize at half-cap in all the skills.

I can’t stress this enough: I just proved mathematically that you can’t do better than approximately half in all skills, or cap half the skills and mediocre points in the rest, or somewhere in between the two extremes.

The whole argument is moot if skills have variable caps, e.g. slow time caps at 5 and arcane orb caps at 16, but this will be difficult to keep a hard-coded “7 skills at most” and still ensure that you spend all your points. I can’t imagine they would ever want you to purposefully build your character so that you don’t use all your points. I won't go into all the different mathematical ways "7 skills at most" clashes with "can only cap 3 of 7 skills" and "variable caps on skills" because there are a lot of things to consider, but suffice it to say it would take a precarious balancing act to get all three of those propositions to hold at the same time, especially since there are 25 total skills per character (approximately).

My opinion based on the above facts:

There will be serious diminishing returns on most, if not all, skills. This will prompt us to not cap three skills unless it is truly a power-house build and really suits our play-style. That is, we will be "guided" towards playing a generalist character with most skills at 8-9/16 instead of capping three skills, unless the latter works better for our particular playing ability. This means a lot of customization options to accommodate different play-styles and different players, which iirc is one of their stated goals (or will at least earn them the most money).

[cacophony]

First of all, good post. Although things change again if they reconfigure it to 4 capped skills, but the assumptions are still similar. However, I doubt they will "disincentive" a player from capping 3 skills, especially the "terrible terrible damage" type skills. There might be some diminishing returns on certain utility skills, probably crowd control skills (one point in Horrify shouldn't be worthless, but 16 points in Horrify shouldn't mean everybody runs around for 16+ seconds). But for your main damage style skills, I don't think there should be diminishing returns. Still better than one-point-wonders, but maybe they have 4 point or 5 point wonders, instead.

[starrise]

First: thank you!

Now, actually that's an excellent point you've made. To build off what you wrote, it seems like there could be alternatives: you could pick out 4-5 dim-ret skills and cap 2-3 skills that don't suffer dim-ret. Or you could pick 6 skills that only suffer from it a little bit, and 1 that doesn't. In other words, how you distribute your points may be determined by how marginally-effective a given set of skills are. The more effectiveness it loses per point, the fewer you would want to put in it.

Regardless, you're right, there may not be a need for all skills to have diminishing returns. At this point though it becomes an overall game-balance issue.

[Apocalypse]

i wonder if they plan to force us to only be allowed to cap 3 or if it is purely from the amount of given skill points. i had thought that 15 was the max skill point level so when asked i would have thought the answer would be 4 max skills. this would actually be wrong if you are not given a point at level 1 and would mean no skill points for quest rewards. very interested in seeing what they got in store for skills both active and passive

[theeliminator]

just to let you know Cacophony Horrrify was changed, it's now more of a DoT that jumps to another target once it's first target is dead. (if I remember right)

That and a twitter post reconfirms the 3-4 skills being maxed.

Q- "How many skills, active and passive, will we be able to maximize with the 60 level cap?"

A- "It hasn't been nailed down, but probably three, maybe four active skills at highest cap can be maxed out at 60."

[lone_wolf]

it makes a lot of sense since 60/7= 8,571

if we assume 15 is the max cap we can have max 4 skills maxed since 15*4= 60

so who is up for calculation how many different skill builds we can possible have in diablo 3??

[Apocalypse]

this assumes we start with 1 point and receive non from quest rewards

[lone_wolf]

correct apoc that is what i based it on.

[Apocalypse]

correct apoc that is what i based it on.

i hope we get to choose where to place our initial point this time around

[Mad Mantis]

How is this meant to increase the number of skills that one uses in battle? Doesn't this system promote putting all points in one Single Target attack and one AoE attack and the rest into utility skills? Apparently I'm missing something.