Success metric

One of my pet projects has been to create a metric to measure my success in various games. I'm not satisfied with the obvious choices: sheer number of victories means the games I've played a lot are on the top, despite the winning percentage, while winning percentage alone lifts the "one win of one game played" games on the top. Not good.

My previous method was pretty good, but still lifted Lost Cities high on the top. I've won Lost Cities 68 times, but 68 out of 112 in a two-player game isn't a record I'd advertise a lot. I'd rather see Sunda to Sahul (18 wins of 21 games) on top, for example.

Well, here's the latest take on the success metric:

Success = (Number of wins - Expected wins) * Winning percentage

That's it. Expected wins means 0.5 for a two-player game, 0.33 for a three-player game, 0.25 for a four-player game and so on - the expected result, if winning the game was based on pure luck. Winning percentage is put on a scale from -1 to 1 and as the first part of the calculation can be negative, there's some fuddling to make sure it stays that way even if the winning percentage is negative as well.

That works, pretty well. There's some oddness to it (for one, if you play a game with two, three and four players and win once, it doesn't matter which one you win even though it probably should), yet I find the results fairly satisfying.