Can someone suggest a rating formula for individuals playing a team game where pairings are made up from a pool of individual players?
I have a game which is always played in doubles. The pairings can be made up of any two players in the pool of players and will change every match. Pairings are random and not affected by previous pairings or skill/ability.
I want a rating system that tracks individual ratings based upon all the games they play in paired matches.
Assumptions
- The simple win probability of a pairing against another pairing is based upon their average rating, nothing more complicated than this.
- Each match provides only two pieces of data - the team that won and the margin of victory (there is no indication of how each player in the team performed, only the team as a whole).
- There are no "cyclic" relationships between pairings or players as in rock, paper scissors.
Requirements
- Accurately tracks the probability of win/loss for a given matchup.
- Not prone to rapid inflation or deflation
- Doesn't encourage players to "protect" their rating
- Doesn't allow manipulation of pairings to create beneficial match ups
- Preferably includes a margin of victory multiplier to encourage teams to continue to play to the best of their ability even when very far behind in a game. This would imply that it can predict the margin of victory as well as the probability of win/loss.
- Low computation requirements and easy to implement in a spreadsheet
Options
Elo is perhaps the best-known rating system made popular from its use by FIDE but has many well-known flaws. It also needs to be adapted to allow tracking individual ratings when only team results are known. Perhaps it can be altered to take into account margin of victory by scaling the scores from 0-1 instead of 0 for a loss, 1 for a win and 1/2 for a draw?
Another system is the KGS rank system.
A frequently-used improvement upon Elo's work is the Glicko-2 system. It introduced concepts such as rating volatility, improves prediction reliability and has replaced the use of Elo on many rating leagues. However, it also doesn't account for teams made of of pairings from a pool.
Rating systems that do account for this include Microsoft's TrueSkill2 but this is a licensed system. Another method would be to use Glicko-2 treating each 2v2 match it as 4 individual simultaneous matches. Nate Silver also apparently uses some sort of algorithm for team sports.
There are some similar questions but, as far as I can see, none take into account both the margin of victory and individual ratings in team matches.
Does anyone have any suggestions for a simple rating algorithm to use?
