Hypergraph adjusted plus-minus (2403.20214v3)
Abstract: In team sports, traditional ranking statistics do not allow for the simultaneous evaluation of both individuals and combinations of players. Metrics for individual player rankings often fail to include the interaction effects between groups of players, while methods for assessing full lineups cannot be used to identify the value of lower-order combinations of players (pairs, trios, etc.). Given that player and lineup rankings are inherently dependent on each other, these limitations may affect the accuracy of performance evaluations. To address this, we propose a novel adjusted plus-minus (APM) approach that allows for the simultaneous ranking of individual players, lower-order combinations of players, and full lineups within a team. The method adjusts for the complete dependency structure and is motivated by the connection between APM and the hypergraph representation of a team. We discuss the similarities of our approach to other advanced metrics, demonstrate it using NBA data from 2012-2022, and suggest potential directions for future work.
- Dan Rosenbaum. Measuring how nba players help their teams win. http://www.82games.com/comm30.htm, 2004.
- Brian Macdonald. A regression-based adjusted plus-minus statistic for nhl players. Journal of Quantitative Analysis in Sports, 7(3), 2011.
- Lars Magnus Hvattum. A comprehensive review of plus-minus ratings for evaluating individual players in team sports. 2019.
- Superior value creation in sports teams: Resources and managerial experience. M@ n@ gement, (3):284–312, 2012.
- Nba chemistry: Positive and negative synergies in basketball. International Journal of Computer Science in Sport, December, 2013.
- An extended regularized adjusted plus-minus analysis for lineup management in basketball using play-by-play data. IMA Journal of Management Mathematics, 32(4):385–409, 2021.
- Bayesian inferences on uncertain ranks and orderings: Application to ranking players and lineups. Bayesian Analysis, 18(3):777–806, 2023.
- Konstantinos Pelechrinis. Linnet: Probabilistic lineup evaluation through network embedding. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pages 20–36. Springer, 2018.
- Basketball lineup performance prediction using edge-centric multi-view network analysis. Social Network Analysis and Mining, 10:1–11, 2020.
- Identifying group contributions in nba lineups with spectral analysis. Journal of Sports Analytics, 6(3):215–234, 2020.
- Joseph Sill. Improved nba adjusted+/-using regularization and out-of-sample testing. In Proceedings of the 2010 MIT Sloan sports analytics conference, 2010.
- Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1):55–67, 1970.
- Statistical analysis of network data with R, volume 65. Springer, 2014.
- Applied functional data analysis: methods and case studies. Springer, 2002.
- Kernels and regularization on graphs. In Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003, Washington, DC, USA, August 24-27, 2003. Proceedings, pages 144–158. Springer, 2003.
- Basketball-reference. https://www.basketball-reference.com.
- A starting point for analyzing basketball statistics. Journal of quantitative analysis in sports, 3(3), 2007.