Optimizing NBA Lineup Strategy: Maximizing Predictive Plus-Minus Models with Linear Programming

This research addressed the complex challenge NBA teams face in determining optimal lineups throughout a game. With numerous potential lineup combinations available, identifying the most effective configurations is essential for maximizing team performance. This project aimed to develop a model to predict the performance of any five-man lineup using the plus-minus metric as a proxy for lineup quality. The primary goal was to incorporate these metrics into a linear program to determine optimal lineup combinations for a full, 48-minute game. A new advanced plus-minus metric, Combined Regularized Adjusted Plus-Minus (C-RAPM), was successfully created, combining plus-minus data and box score statistics. This metric was aggregated to provide plus-minus estimates for every five-man lineup. Linear programs were developed with C-RAPM as the optimization target and customizable constraints for maximum player minutes per game, maximum player consecutive minutes per stint and minimum rest periods between stints. The sequential decision analysis program demonstrated meaningful improvements over actual lineups based on the C-RAPM metric. Future work could focus on adding constraints to provide even more realistic lineup outputs and refining the C-RAPM metric. This project established a foundation for further advancements in optimizing NBA lineups across entire games.