Colley Matrix
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Linear algebra over the whole schedule — fair rankings from messy fixtures. The formula and explanation below describe Colley Matrix.
How it works About 1 min read
The Colley Matrix method, developed by mathematician Wesley Colley, uses linear algebra to produce fair rankings from win/loss records, even when teams play vastly different schedules.
How it works: It constructs a matrix equation C·r = b, where C captures the schedule and b captures the results. Solving this linear system produces ratings that account for strength of schedule without needing score margins. All teams start at 0.5 (equivalent to "average") and the system adjusts.
When to use it: Leagues or competitions where teams don't all play each other the same number of times. Originally developed for college football rankings (used in the BCS formula), it's ideal for any round-robin with incomplete or uneven schedules.
Watch out for: Computationally heavier than simple standings (requires matrix solve). Only uses win/loss data -- score margins are ignored. Only supports 1v1 or team matches. Results can be non-intuitive since they account for opponent strength indirectly.
Will it fit your results?
Works well with
Games whose results this method reads cleanly
Also in Matrix Methods
Linear algebra over the whole schedule — fair rankings from messy fixtures.