Lasso Multinomial Performance Indicators for in-play Basketball Data

Abstract

A typical approach to quantify the contribution of each player in basketball uses the plus-minus method. The ratings obtained by such a method are estimated using simple regression models and their regularized variants, with response variable being either the points scored or the point differences. To capture more precisely the effect of each player, detailed possession-based play-by-play data may be used. This is the direction we take in this article, in which we investigate the performance of regularized adjusted plus-minus (RAPM) indicators estimated by different regularized models having as a response the number of points scored in each possession. Therefore, we use possession play-by-play data from all NBA games for the season 2021-22 (322,852 possessions). We initially present simple regression model-based indices starting from the implementation of ridge regression which is the standard technique in the relevant literature. We proceed with the lasso approach which has specific advantages and better performance than ridge regression when compared with selected objective validation criteria. Then, we implement regularized binary and multinomial logistic regression models to obtain more accurate performance indicators since the response is a discrete variable taking values mainly from zero to three. Our final proposal is an improved RAPM measure which is based on the expected points of a multinomial logistic regression model where each player's contribution is weighted by his participation in the team's possessions. The proposed indicator, called weighted expected points (wEPTS), outperforms all other RAPM measures we investigate in this study.