Lasso Multinomial Performance Indicators for in-play Basketball Data
arxiv(2024)
Abstract
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.
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