A typical approach to quantify the contribution of each player in basketball uses the plus/minus approach. Such plus/minus ratings are estimated using simple regression models and their regularised variants with response variable either the points scored or the point differences. To capture more precisely the effect of each player and the combined effects of specific lineups, more detailed possession-based play-by-play data are needed. 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.

翻译：量化篮球比赛中每位球员贡献的典型方法是采用正负值评估法。此类正负值评分通常通过简单回归模型及其正则化变体进行估计，响应变量为得分或分差。为更精确捕捉每位球员的效应及特定阵容的组合效应，需要更详细的基于球权的逐回合数据。本文即沿此方向展开研究，通过以每次球权得分数为响应的不同正则化模型，探究正则化调整正负值（RAPM）指标的性能表现。为此，我们使用2021-22赛季NBA所有比赛的逐回合球权数据（共322,852次球权）。首先从相关文献标准技术——岭回归的实现出发，展示基于简单回归模型的指标。随后采用Lasso方法，该方法在特定客观验证标准下相比岭回归具有独特优势及更优性能。接着，由于响应变量是主要取值为0至3的离散变量，我们实施正则化二元及多项逻辑回归模型以获得更精确的表现指标。我们最终提出一种改进的RAPM度量方法，该方法基于多项逻辑回归模型的期望得分，其中每位球员的贡献按其参与球队球权的比例进行加权。这一被称作加权期望得分（wEPTS）的指标，在本研究涉及的所有RAPM度量方法中表现出最优性能。