Massey Ratings
A least-squares fit where every game says 'A's rating minus B's rating should be about this margin', solved across all games at once.
Least-squares: r_A - r_B ≈ margin for all games
Best at
Scored competitions where beating someone by thirty says more than beating them by one.
Where it misleads
Needs real score data, and it rewards running up the score — worth a thought if your group finds that unsporting.
How it works
Massey Ratings, developed by Kenneth Massey, use score differentials in a least-squares framework to produce ratings that reflect not just who won, but by how much.
How it works: It sets up a system of equations where each game contributes a row: rating_A - rating_B ≈ margin. The least-squares solution minimizes prediction error across all games. The result captures both win/loss information AND margin quality.
When to use it: Score-based competitions where the size of victory carries meaningful information (e.g., basketball, where beating a team by 30 says more than beating them by 1). Also used in college sports ranking systems.
Watch out for: Requires meaningful score data -- won't work with placement-only or winner-only results. Running up the score is rewarded, which may not match your group's values. Consider capping margins if sportsmanship is a concern.