How strong a player am I?
I have a game my friends and I like to play (Farkle - Wikipedia, the free encyclopedia). We keep score on a spreadsheet that's able to record game history after each game. We've played for awhile now and have amassed a nice little bit of game data.
What I'd like to do is come up with some means of determining how "strong" a player is. For instance, if 4 people are playing, it can be said that any person has a 1 in 4 chance of winning. If I always play in 4 person games and I end up winning half the time, then this is statistically significant and I can be thought of as a "strong" player. In other words, my strategy is helping me win more often than simple chance would.
Our games, however, have a variable number of players. For each game, I know who played, whether they won or not, and how many other players they played against. How can I determine the "strength" of the players with this data?
I apologize in advance if there is some really simply/obvious statistical model for this and I just don't know what it is!