Scales globallyNeeds scores

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.

FamilyMatrix Methods

Read the shape of this family

Family illustration · not a computed standing

Linear algebra over the whole schedule — fair rankings from messy fixtures. The formula and explanation below describe Massey Ratings.

How it works About 1 min read

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.

Will it fit your results?

Works well with

Games whose results this method reads cleanly

Basketball Soccer Scrabble

Also in Matrix Methods

Linear algebra over the whole schedule — fair rankings from messy fixtures.

Colley MatrixLeagues where people play very different fixtures — it was designed for exactly that problem in college football.