I have an Excel spread-sheet where I record the games I play, noting the amount of players and the number of games I’ve won. I count month totals, happiness product and winning percentages. It’s an essential part of my game hobby, keeping track of it all.
Lately I’ve been fiddling about with performance measures. Amount of games won is not good: it clearly prefers games I’ve played more. And which one is better achievement, 20 wins out of 40 games or 21 wins out of 80 games?
Win percentage is not good, either. This measure prefers games I’ve played less. One win out of one game is clearly worse than 20 wins out of the 40 games, I’d say. I don’t like setting limits (only games played more than five times count or something artificial like that). No, I want a measure that takes care of it for me.
One solution was the point system used by Seurapelikerho ratings: 10 points for a won game, -1 for rest of the games. This way 20/40 result would be 180 points, while 21/80 would be 151 points. This is all good and well, but I think it still prefers amount of victories over good win percentage too much. Of course I could adjust the point ratios, but that’s not good enough.
I toyed around with my table and dividing the points by won games seemed to result in an interesting results. Basically it’s amount of points per won game. All wins results in a score of 10. There’s no lower bound, as the lost games push the score below zero indefinitely. However, this has two flaws: 1/1 gets the maximum score and zero wins causes a division by zero.
However, both can be fixed with the same small change. The final formula looks like this: (11*won games-total games played)/(won games+c) — the key is the constant c. The value of c can be adjusted to get different results, I use 1.
Now the best game for me is Sunda to Sahul (14/16, 9.20), then Lost Cities (56/95, 9.14), then Ricochet Robot (11.5/13, 9.08), then Carcassonne (35/62, 8.97) — this feels quite correct.