I'll try to be brief. The first paragraph or so may be irrelevant to answer the question, but I'm including it for context.

For school, a friend and I are developing a strategy game wherein combat units are constructed out of components that offer different benefits (movement speed, damage etc.). We're going to be using automated playtesting to "balance" these components, and I want to make sure I use a logical methodology to do so. From our playtest, we will be pitting a set of 'balanced' units against test-case units that use the new ability we are trying to balance. The components being tested will each have have 1-4 variable values for which we would want to find a balanced curve formula.

For my example, let's say we playtest a component with two variables, +Strength and +Dexterity. We playtest by randomly (within constraints) assigning bonus values to these components for hundreds of battles, throwing them into battle against unit(s) we eventually want to give a 50-50 chance of beating. Though there are random factors that can influence battle, obviously the battles where the bonus values are high give the unit a higher chance of winning and vice versa.

In a slight simplification of our tests, the results data would come out something like this, where STR and DEX stats are random and we get the W/L result of the playtest:

STR DEX W/L

14.3 04.9 W

03.7 07.3 L

01.0 17.8 L

10.2 09.6 W

19.6 06.3 W

02.9 16.1 W

...

And so on. From there we could plot W/L points on a scatter graph, and would want to create a logarithmic curve to define a roughly "balanced" ability, that plots X and Y coordinates for values of STR and DEX where the values on the curve give a 50/50 chance of winning (so p=0.5 in the regression). And beyond that, a methodology of doing so for components with more than 2 variables.

I hope I was clear, I'll reply to any clarification questions

I appreciate any help you could offer to help me in my research of the best/easiest way to calculate this. I've found a lot so far, but better to ask than to remain uncertain I'm going about it correctly.

Thank you!