I have an idea for a "King of the Hill" contest in the Programming Puzzles and Code Golf Stack Exchange (https://codegolf.stackexchange.com/). The game I have in mind has four players divided into two teams of two players each with a specified play position
(Team 1 White, Team 1 Black, Team 2 White, Team 2 Black) and three discrete outcomes
(Team 1 Win, Team 2 Win, Draw). This would allow me to record each match in the tournament as
Team 1 White Player Name, Team 1 Black Player Name, Team 2 White Player Name, Team 2 Black Player Name, Outcome. My idea was that I could run a tournament where every combination of four unique contestants would play several matches per permutation of players in that combination, record the results, and then determine the contest winner based upon the contestant that participated in the most games where that player won.
A user in that community is concerned that the only way to determine a contestant's strength is to effectively reduce the game to a two-player game by having each contestant play both colors on the team. If this is the case, then I think that may eliminate the fun of the competition.
Is there some statistical method that can be used to determine an individual player's strength in a team game? I think that there might be a way to determine a contribution (correlation, maybe?) between a player's outcomes and his performance as opposed to his teammate's performance. The limited statistics I learned in college does not seem to be helping me much here. I had thought that my best bet would be ANOVA, but the fact that each result between teams AB and CD will be accounted for in each team's observations seems like it might break that test.
If such a test exists, I would appreciate being told its name and being given an explanation for its process.