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Lineup Regularized Adjusted Plus-Minus (L-RAPM): Basketball Lineup Ratings with Informed Priors

Christos Petridis, Konstantinos Pelechrinis

TL;DR

Lineup performance in basketball is highly noisy due to sparse data per lineup. The authors introduce L-RAPM, a two-stage regression framework that 1) derives informed player ratings using Regularized Adjusted Plus Minus (RAPM), and 2) regresses lineup-level points per possession with priors informed by those player ratings and regularization toward expected lineup performance. The lineup priors are constructed as $\pi_{\lambda,off}=league\_ppp+\sum_{p\in\lambda}\gamma_{p,off}$ and $\pi_{\lambda,def}=league\_ppp+\sum_{p\in\lambda}\gamma_{p,def}$, and the optimization minimizes prediction error with penalties $\lambda\sum_j(\beta_{j,off}-\pi_{j,off})^2$ and $\lambda\sum_j(\beta_{j,def}-\pi_{j,def})^2$. Empirically, L-RAPM provides predictive improvements over raw lineup ratings, increasing as lineup data become sparser, and yielding noticeable gains for unseen lineups (about 5% RMSE improvement). The approach integrates opponent-adjustment and player-derived priors to stabilize lineup estimates and enhance out-of-sample predictions with practical implications for lineup construction and strategy.

Abstract

Identifying combinations of players (that is, lineups) in basketball - and other sports - that perform well when they play together is one of the most important tasks in sports analytics. One of the main challenges associated with this task is the frequent substitutions that occur during a game, which results in highly sparse data. In particular, a National Basketball Association (NBA) team will use more than 600 lineups during a season, which translates to an average lineup having seen the court in approximately 25-30 possessions. Inevitably, any statistics that one collects for these lineups are going to be noisy, with low predictive value. Yet, there is no existing work (in the public at least) that addresses this problem. In this work, we propose a regression-based approach that controls for the opposition faced by each lineup, while it also utilizes information about the players making up the lineups. Our experiments show that L-RAPM provides improved predictive power than the currently used baseline, and this improvement increases as the sample size for the lineups gets smaller.

Lineup Regularized Adjusted Plus-Minus (L-RAPM): Basketball Lineup Ratings with Informed Priors

TL;DR

Lineup performance in basketball is highly noisy due to sparse data per lineup. The authors introduce L-RAPM, a two-stage regression framework that 1) derives informed player ratings using Regularized Adjusted Plus Minus (RAPM), and 2) regresses lineup-level points per possession with priors informed by those player ratings and regularization toward expected lineup performance. The lineup priors are constructed as and , and the optimization minimizes prediction error with penalties and . Empirically, L-RAPM provides predictive improvements over raw lineup ratings, increasing as lineup data become sparser, and yielding noticeable gains for unseen lineups (about 5% RMSE improvement). The approach integrates opponent-adjustment and player-derived priors to stabilize lineup estimates and enhance out-of-sample predictions with practical implications for lineup construction and strategy.

Abstract

Identifying combinations of players (that is, lineups) in basketball - and other sports - that perform well when they play together is one of the most important tasks in sports analytics. One of the main challenges associated with this task is the frequent substitutions that occur during a game, which results in highly sparse data. In particular, a National Basketball Association (NBA) team will use more than 600 lineups during a season, which translates to an average lineup having seen the court in approximately 25-30 possessions. Inevitably, any statistics that one collects for these lineups are going to be noisy, with low predictive value. Yet, there is no existing work (in the public at least) that addresses this problem. In this work, we propose a regression-based approach that controls for the opposition faced by each lineup, while it also utilizes information about the players making up the lineups. Our experiments show that L-RAPM provides improved predictive power than the currently used baseline, and this improvement increases as the sample size for the lineups gets smaller.
Paper Structure (7 sections, 5 equations, 4 figures)

This paper contains 7 sections, 5 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Studies
  3. Our model
  4. Player ratings: Regularized Adjusted Plus Minus
  5. Regularized Regression for Lineup Matchups
  6. Experimental Results
  7. Discussion and Conclusions

Figures (4)

  • Figure 1: The majority of the lineups during a season appear on the court for a small number of possessions. The distribution (in log-log scale) for the number of offensive (left) and defensive (right) possessions per lineup is right skewed, with a small number of lineups playing for thousands of possessions, while the vast majority of them plays for less than 50 possessions.
  • Figure 2: L-RAPM provides improvements over the baseline throughout the season.
  • Figure 3: L-RAPM's improvements over the baseline are larger when we have observed fewer data for the lineups making predictions for. The prior incorporated in our method allows L-RAPM to obtain lineup ratings with good predictive power with fewer data.
  • Figure 4: L-RAPM provides even higher improvements in terms of predictive power when predicting the points scored in possessions with previously unseen lineups.