A RAPM Model for Soccer Player Ratings
Date:
One of the most well-known frameworks for constructing all-in-one player performance metrics is the plus-minus model, which in the most rudimentary form has been applied in hockey since the 1950s. The plus-minus model considers the number of goals scored minus the number of goals conceded when a given player is in the game. A huge problem with this approach is that it does not control for the impact of teammates or opponents. It is important to acknowledge that every player on the pitch, either directly or indirectly, is contributing to the overall team’s performance. Several academic studies have started to utilize linear regression as an adjusted plus-minus (APM) framework to include other players’ influence on that individual’s rating. APM and its variations have most commonly been seen in basketball and hockey, achieving substantial improvements in these fields, an example being ESPN’s widely known real plus-minus (RPM).
As a sport, soccer has numerous inherent disadvantages when it comes to APM, especially compared to basketball or hockey. Soccer is a low-scoring game with few substitutions, which means a traditional APM for the sport will have collinearity issues and an infrequent response variable. The collinearity comes from the low number of substitutions since some players will share the same minutes on the court together in almost every segment, which eventually makes them indistinguishable. Out of these three sports, basketball is the best sport to calculate APM for, and whereas hockey is low-scoring, it has an extremely high number of substitutions every game. Several scholars have tried to handle this challenge, considerably the paper from the Department of Statistics at Carnegie Mellon University, which introduces the use of video game ratings from FIFA as a prior in the APM model.
This paper aims to build up on the foundations of calculating individual player ratings using a plus-minus framework. This procedure ensures that the one-number statistics for soccer players accurately represent the individuals’ skill level as well as their team contribution by adding the traditional box-score rating into the measurement of the APM model. Our approach also uses expected goals instead of the actual goals as we believe this will better measure the team’s performance within a match.
Joint presentation with Edvin Tran Hoac, and Phong Hoang.