A Hierarchical Approach for Evaluating Athlete Performance with an Application in Elite Basketball

In this paper, we present the ON score for evaluating the performance of athletes and teams that includes a season-long evaluation system, a single-game evaluation, and an evaluation of an athlete's overall contribution to their team. The approach used to calculate the ON score is based on mixed-effects regression models that take into account the hierarchical structure of the data and a principal component analysis to calculate athlete rating. We apply our methodology to a large dataset of NBA games spanning four seasons from 2015-2016 to 2018-2019. Our model is validated using two systematic approaches, and our results demonstrate the reliability of our approach to calculate an athlete's performance. This provides coaches and managers with a powerful tool to gain deeper insights into their players' performance, make more informed decisions and ultimately improve their team's performance. Our methodology has several key advantages. First, by incorporating the hierarchical structure of the data, we can obtain valuable information about an athlete's contribution within their team. Second, the use of principal component analysis allows us to calculate a single score, the ON score, that captures the overall performance of an athlete. Third, our approach is based on classical restricted likelihood methods, which makes the calculation faster than Bayesian methods typically requiring 1,000 posterior samples. With our approach, coaches and managers can evaluate athletes' performance throughout the season, compare athletes and teams over a year, and assess an athlete's performance during a single game. Our methodology can also complement other ratings and box score metrics to provide a more comprehensive assessment of an athlete's performance as our method uses the hierarchical nature of performance data (i.e. player nested within team over season) which is typically ignored in player rating systems. In summary, our methodology represents a significant contribution to the field of sports analytics and provides the foundation for future developments.