Simulations might be used, but they're of little help because the devs need to balance based off of how players actually play the game.

So for that, they track all sorts of statistics about what characters are used, howe they're used, how effective they are against other characters in general, and specific other characters, and much more.

They take that data and then see if something is too strong, too weak, etc, and try to adjust for fairness.

Or in the case of Riot, they release new characters that are strong so people buy them, then lower the power after.