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. * task is to estimate time-varying ratings for individuals which update following new information (the latest results). Elo ratings have been used for over half a century for rating chess players. Similarly, the Glicko rating system (Glickman, 2012) provides a more theoretically justified model for estimating time-varying ratings of individuals.More recently, attention has moved to using machine learning techniques to estimate player ratings. The TrueSkill rating (Herbrich et al., 2007) developed at Microsoft is a generalisation of the Elo ratings and is used for rating video game players.Rating players in sports teams is more problematic. Players often have different responsibilities with some concentrated on offence (i.e. aiding scoring), whilst others are specialised in defence (i.e. helping to prevent scores for the opposition). A commonly used approach is to assign a value to a set of actions considered to be 'of interest' and to reward the player taking them with the associated value. This method was used for example in the EA SPORTS Player Performance Indicator (McHale et al., 2012) and is still used by the English Premier League as the official player ratings system. Due to its additivity, the previous approach provides simple, user-friendly player ratings and rankings. However, a cost of the simplicity is the lack of context and a deeper understanding of the situations in which actions were committed. Further, the data requirement is not trivial.Models have been used to rate players for specific tasks. For example, Sáez Castillo et al. (2013) and McHale and Szczepański (2014) present methods to identify the scoring ability of footballers whereas López Peña and Touchette (2012), López Peña and Sánchez Navarro (2015), Brooks et al. (2016) and Szczepański and McHale (2016) deal with the passing aspect.But identifying the overall contribution of a player to a team's success (or lack of it) has proven difficult in soccer. However, the concept of the PM ratings provides hope.The concept of the PM rating is fundamentally different to the rating mechanisms discussed above. It directly measures the contribution a player has on a team's success as measured by (the differential) of a ta...

Demographic, physiological, psychological, and on-ice performance indicators predict plus/minus status of recreational ice hockey players across a season

“…boxscore) (Macdonald, 2011). This is in line with previous studies which used plus/ minus values to evaluate individual performance across different sports (Macdonald, 2011;Okamoto, 2011;Kharrat, Peña, & McHale, 2019). However, such metrics are generally only applied to elite hockey players/leagues to date (Macdonald, 2011).…”

Moneyball in Offensive vs Defensive Actions in Soccer

“…Current situation with relative evaluation of offensive and defensive actions in German Bundesliga is examined in this paper. We first find an evidence of undervaluation of top defensive players compared to forwards by an annual prestigious soccer award -Ballon d'Or (Kharrat et al, 2017) together with an evidence of a significant role of defense in a team performance (e.g. Vogelbein et al, 2014;Szwarc et al, 2017).…”

“…The Ballon d'Or -an annual award for the most valuable player in European soccer based on the voting of soccer experts, has nominated only one player with a defensive specialization (goalkeeper) in the top 3, during the period 2011-2016. At the same time, according to the plus-minus rating method, five players with defensive specialization (three defenders, one defensive midfielder and one goalkeeper) should have been included in that list (Kharrat et al, 2017). These two facts together, point out that soccer society is likely to overestimate offensive actions, thus, defensive actions are being underrated.…”

A comprehensive review of plus-minus ratings for evaluating individual players in team sports

“…To resolve this, it was suggested to add a component in the rating of each player corresponding to the competition (league) in which their current team plays. Kharrat, Peña, and McHale (2018) considered three different multiple linear regression models, with independent variables very similar to those of Saebø and Hvattum (2019), but with a slightly different way to adjust for league differences. The three models differ in terms of the dependent variable.…”