Measuring player quality

Latent-skill rating models

xV-style metrics value actions. A latent-skill rating values the player — a single (or low-dimensional) quantity meant to be portable across opponents, contexts, and seasons. Football's player-rating literature borrows heavily from basketball and chess.

Bayesian per-player ratings

Treat each player as a latent skill θ_p with a prior, observe minutes-weighted action values, fit by MCMC or variational inference. Partial pooling shrinks low-minutes players to position-and-age priors. The natural framing for a "career-stable" rating system. Few public implementations for football specifically; the framework is borrowed from baseball (Albert/Bennett-style models) and chess (Glickman).

Plus-Minus / Adjusted Plus-Minus

Originally an NBA tool. Regress goal difference per minute on a sparse design matrix where each player gets a +1 (on the pitch) or 0 column. Coefficients are per-player rating impacts. Two issues, both severe in football:

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