Action Calculus Research and Optimal Focus

[mdlthree]

Hey forums. I have been sitting on this research for a quite a while. I have mentioned in a few posts in the past but I was constantly refining it. I finally was able to succinctly describe the theoretical relationship between hit and value mechanics with simple math (high school calculus is simple right?). Check out the post here on Tumblr.
https://herdingdice.tumblr.com/.../action-calculus

Using those results I have created a table to describe when you should be picking focuses to maximize value. The difference between this table and the one in the blog post is that I have made the TN11 the base to compare with (ability of zero means a optimal base action value of 5).

Ability	Optimal Focus
-4	-8
-3	-5
-2	-3
-1	-1
0	0
2	1
4	2
9	3
16	4
31	5
67	6
211	7

Current rules gives you focus in a +2 then +1 fashion. The table shows that the +2 is best focus unless your spell/attack value is 9 or better. With value between 9 and 15 +3 is best.

In conclusion, while I have been advocating for change in a lot of mechanics, I can now be 100% confident what are the best choices for character progressions.