Mining Player Ranking Dynamics in Team Sports

Is there a Pythagorean theorem for winning in tennis?

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2015-0057 ◽

2016 ◽

Vol 12 (1) ◽

Author(s):

Stephanie Ann Kovalchik

Keyword(s):

Team Sports ◽

Break Point ◽

Prediction Algorithm ◽

Power Coefficient ◽

Striking Similarity ◽

Point Model ◽

Professional Team Sports ◽

Wide Range ◽

The Individual ◽

Player Ranking

AbstractBill James’ discovery of a Pythagorean formula for win expectation in baseball has been a useful resource to analysts and coaches for over 30 years. Extensions of the Pythagorean model have been developed for all of the major professional team sports but none of the individual sports. The present paper attempts to address this gap by deriving a Pythagorean model for win production in tennis. Using performance data for the top 100 male singles players between 2004 and 2014, this study shows that, among the most commonly reported performance statistics, a model of break points won provides the closest approximation to the Pythagorean formula, explaining 85% of variation in season wins and having the lowest cross-validation prediction error among the models considered. The mid-season projections of the break point model had performance that was comparable to an expanded model that included eight other serve and return statistics as well as player ranking. A simple match prediction algorithm based on a break point model with the previous 9 months of match history had a prediction accuracy of 67% when applied to 2015 match outcomes, whether using the least-squares or Pythagorean power coefficient. By demonstrating the striking similarity between the Pythagorean formula for baseball wins and the break point model for match wins in tennis, this paper has identified a potentially simple yet powerful analytic tool with a wide range of potential uses for player performance evaluation and match forecasting.

Download Full-text

Inverse Reinforcement Learning for Team Sports: Valuing Actions and Players

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2020/464 ◽

2020 ◽

Author(s):

Yudong Luo ◽

Oliver Schulte ◽

Pascal Poupart

Keyword(s):

Reinforcement Learning ◽

Single Agent ◽

Empirical Evaluation ◽

Team Sports ◽

Ice Hockey ◽

Inverse Reinforcement Learning ◽

Reward Function ◽

Player Ranking ◽

The Impact ◽

Q Function

A major task of sports analytics is to rank players based on the impact of their actions. Recent methods have applied reinforcement learning (RL) to assess the value of actions from a learned action value or Q-function. A fundamental challenge for estimating action values is that explicit reward signals (goals) are very sparse in many team sports, such as ice hockey and soccer. This paper combines Q-function learning with inverse reinforcement learning (IRL) to provide a novel player ranking method. We treat professional play as expert demonstrations for learning an implicit reward function. Our method alternates single-agent IRL to learn a reward function for multiple agents; we provide a theoretical justification for this procedure. Knowledge transfer is used to combine learned rewards and observed rewards from goals. Empirical evaluation, based on 4.5M play-by-play events in the National Hockey League (NHL), indicates that player ranking using the learned rewards achieves high correlations with standard success measures and temporal consistency throughout a season.

Download Full-text