Direct Hit; how much is "enough"?

[nand]

So we know some of the curve's behavior in general:

1. Initially, it's best to put everything into the best (linear) stat available to you.
2. Long-term, it's best to have an exact 50%/50% ratio of both stats.
3. Somewhere in between, there is a transition region from one to the other. We know that this must be smooth and continuous everywhere (because we are only dealing with polynomials).

Since this example was only based on two stats, we haven't necessarily learned anything about actual games here, but I conjecture that these two facts apply to all systems of linear multipliers, i.e. the best initial behavior is to maximize the best stat and the best long-term behavior is to evenly distribute them. The details are left as an exercise to the reader.

It also doesn't directly apply to systems involving quadratic scaling stats like critical hit, but we can at least project the "long-term behavior" result by considering a quadratic scaling stat as two independent linear stats that have the restriction that they must always be exactly equal. But since we already know (under my conjecture) that the optimal long-term behavior is to make them exactly equal, this means that long-term, you want to have twice as much of a quadratic scaling stat as other any linear scaling stat. In general: in the limit, balance each stat weighted by its polynomial degree.

(2/2)