Let's say I have the following information for players in a paired game tournament (think tennis doubles where the players all have a chance to play with and against each other):
- P1: 100 matches played, 10% Win rate
- P2: 40 matches played, 80% Win rate
Now, I also have information on the winrates when P1 and P2 play together:
- P1 and P2: 30 matches played together, 30% Win rate
Looking at the above data, it would seem apparent that P2 contributed heavily to the winrate of P1; of the 30 matches they played together, they won 9. That means that 90% (9/10) games that P1 won were with P2.
Basically; P1 drags the team winrate down, and P2 carries the team winrate upwards.
The question is, how do I calculate the relative contribution that P1 and P2 each have on the outcome of (P1,P2)?
Essentially what I'm trying to do is rank a bunch of players independently (like above) by their relative winrate (using a Wilson Score Interval to account for the number of matches played), but also account for the influence of each teammate.