The game you're writing sound interesting, and yes, there is a formula that allows us to obtain the percent bonuses you've given. The percentages can be listed as follows:

(Sorry, I haven't figured how to display percentages yet.) Now we need a function that will map the Stat points as follows:

On the left, we see multiples of increasing in powers of , and on the right we see increasing one power at a time. To get the power of from a number on the left, we may therefore divide by , take the base logarithm of the result, add in this case, and raise to that power:

This operation can be summarized as

which gives us the formula