Valuing Individual Player Involvements in Norwegian Association Football
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Evaluation of player performance in association football has to a large extent been limited to subjective opinions and simple, easily observable parameters such as goals, passing accuracy and ball recoveries. In this thesis, three models with the goal of objectively rating players by looking at individual actions are presented and documented. An expected goals (xG) model is developed by looking at 13,440 shots attempted in 480 football matches in the Norwegian top division, Tippeligaen. The likelihood of scoring is estimated using binary logistic regression with ten explanatory variables. This model is used as a foundation to evaluate the performance of players with regard to their shot efficiency. Two variations of a zero-sum two-agent Markov game model based on matches from two seasons are developed in order to evaluate other actions than shots. The large state spaces contain three contextual parameters: time period, match status and manpower difference. In addition, different field zones are used in the definition of a state. Reinforcement learning through a Q-function is applied to learn the value of each state and state-action pairs. Players are rated by their impact per 90 minutes played, and results are presented as top 10 lists of players in each position. The reliability of the models is assessed by looking at correlations across seasons. Validity of the two Markov models are examined through comparisons to two subjective player ratings and one provider of market value estimates of players. The models are also tested out of sample. Areas in which extensions of the three models seem possible or appropriate are addressed and highlighted.