OT: Making a Game System (part 2)

[Lokean]

Omni, you mean logarithm again, not exponent. A logarithm flattens for increasing arguments, which is what you're describing. In this case, since its argument is going to be base statistics, you're not going to get into the problem of negative values.

Now, on to the big point that you really need to decide, for definite, before you continue to generate and refine models. What scale of statistics are you looking at? Not only the best parameters for an equation, but even the best equation, is strongly affected by the range of possible input values.

Consider the Gompertz curve that you suggest. You have defined restrictions in the form of an upper asymptote of 1.5 and an intercept of 1, but the Gompertz function is not easily fixed for a specific intercept (The most basic Gompertz function with asymptote 1.5 has intercept 1.5/e = 0.552). One thing I would suggest is that you construct the sigmoid function such that you can adjust the point along the 'shape' of the function which occurs at x=0. By doing this, and incorporating the skill into this parameter of the equation, you can make skilled characters suffer less for lacking physically and benefit more from being stronger and more dexterous than the unskilled fighter. But this depends largely on what possible range of inputs you need the function to be relevant over.

The big balancing act is essentially going to be between 'weapons' and 'tactics'. If they use different equations there will always come a point where it is better to be cunning than accomplished, or vice versa. By incorporating skill into the equations in different ways you may make it easier to control balance, by making a more skilled fighter benefit differently than an unskilled fighter.