New proposal to manage skill specialisation (and prevent hyperspecialisation):
Each character has a base level defined according to their XP total:
Base level = (5 + (sqrt (XP / 7)))
Hazō has 3141 XP.
You are allowed to have:
3 primary skills at 1.25 * base level (32 for Hazou)
3 secondary skills at 1 * base level (26 for Hazou)
3 tertiary skills at 0.75 * base level (19 for Hazou)
An unlimited number of skills below that.
Questions? Comments? Large thrown objects?
The second one, except replace "past those caps" with "at those caps".
So the difference between a tertiary and other skills is literally 1 level? For Hazo, exactly 3 skills at 27-32; exactly 3 skills at 20-26, exactly 3 skills at 19, and any amount of skills at 18 or lower?
In that case tertiary seems a bit unnecessary.
Someone check my maths, but the XP cost to max out a character, given a base level N:
3 primary skills of L=1.25 * N
P = 3 * L * (L+1) / 2 = (3L^2 +3L) / 2 = 4.6875N^2 + 3.75N /2
3 secondary skills of L = N
P = 3 * N * (N+1) / 2 = 3N*2 + 3N / 2
3 tertiary skills of L =0.75N
P = 3L*2 + 3L / 2 = 1.6875N*2 + 2.25 N / 2
X skills of L = 0.75N - 1 (currently X = 15)
P = X (L*2 + L) / 2 = X * [(0.75N - 1) * (0.75N - 1) + 0.75N - 1] / 2 = X * [0.5625N^2 - 1.5N + 1 + 0.75N - 1] / 2 = X * 0.5625 * N^2 - 0.75XN / 2
Total sum of XP spent is: [(9.375 + 0.5625X) * N^2 + (9 - 0.75X) N] / 2
Substituting and renaming X to S and XP to x: (9.375 + 0.5625S) * (5 + sqrt(x/7)) * (5 + sqrt(x/7)) / 2 + (9 - 0.75S) * ((5 + sqrt(x/7))) / 2
Pasting into wolfram alpha to simplify:
1/2 (9 - 0.75 S) (5 + sqrt(x)/sqrt(7)) + 1/2 (9.375 + 0.5625 S) (5 + sqrt(x)/sqrt(7))^2
Solving 'x - above' for different values of S to find when you have more xp points than required to max all primary/secondary/tertiary and S quartary skills:
S = 0 (when do you get to max your primary/secondary/tertiaries?) : x is 4259
S = 4, x is about 20393. I.e. after you have 20393 skill points you can pick up a 5th skill
S = 6, x is about 81837
S = 7, x is about 284574
S = 8, x is 9.04 * 10^6
S = 9 has no solutions - just the linear term is > x.