Game stat madness continues

Hein Hundal contacted me about my game stats madness and described a very interesting rating system, which was easy enough to implement. It's basically a way to calculate what is the probability that one is better than an average opponent.

Here's how it's calculated for each game: First count the harmonic average of number of players in the game. Harmonic average of 2, 3 and 4, for example, is 1/((1/2 + 1/3 + 1/4)/3). Hein says the regular average is ok, but not as good. On a spreadsheet, counting the harmonic average is trivial. Then we need the rating formula f.

f = sqrt(games played) * (win percent - 1/h)

Now the probability you are better than an average opponent can be counted with this formula:

P = 1/2(1+ERF(formula * sqrt(2)))

Where ERF is the error function. There's no ERF in my Excel 97, it's included in some analysis add-on, but Open Office Calc had it. The results look interesting:

Sunda to Sahul: 99,999%
Ricochet Robot: 99,994%
Carcassonne: 99,873%
Puerto Rico: 98,625%
Lost Cities: 95,943%
Battle Line: 81,714%
Go: 0,169%

The low rating of Go is biggest surprise. My win percentage is only 27%, though, and I've played many games, so perhaps the rating system punishes me there. Anyway, it's rather interesting system. If anyone is interested, I have an Excel spreadsheet made by Hein which shows how it works and I can send it those interested.