Plus-Minus Player Ratings for Soccer

Abstract

The paper presents a plus-minus rating for use in association football (soccer). We first describe the standard plus-minus methodology as used in basketball and ice-hockey and then adapt it for use in soccer. The usual goal-differential plus-minus is considered before two variations are proposed. For the first variation, we present a methodology to calculate an expected goals plus-minus rating. The second variation makes use of in-play probabilities of match outcome to evaluate an expected points plus-minus rating. We use the ratings to examine who are the best players in European football, and demonstrate how the players' ratings evolve over time. Finally, we shed light on the debate regarding which is the strongest league. The model suggests the English Premier League is the strongest, with the German Bundesliga a close runner-up.