An Approximate Dynamic Programming Approach to Determine the Optimal Substitution Strategy for Basketball




Hughes, David William

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The purpose of this research is to determine a coach’s optimal basketball lineup throughout the course of a game while accounting for players’ changing endurance levels. Coaches currently use a variety of substitution strategies in basketball. These include player rotations, heuristics, playing the “next best” player, and others. However, such strategies may not be optimal in terms of distributing rest over the course of a whole game. In part, this is because live, in-game monitoring of physiological factors, such as heart rates, is not currently authorized by the NCAA. Even with such data, it may not be obvious when to rest a skilled player in order to ensure that player is fresh for later portions of the game. This research develops an approximate dynamic programming (ADP) model of a coach’s basketball lineup decisions accounting for changing players’ endurance levels and the uncertainty of the defensive intensity played against them. The ADP model is quantified via offline endurance data as well as a value hierarchy of player skill sets created from discussions with the head coach of a Division I program. Policy implications resulting from the model are analyzed and compared to other solution methods. The analysis shows that lineups generated from the ADP model consistently provide more overall value when compared with other substitution strategies, such as the “next best” (or greedy) strategy. This difference tends to be greater for games in which low-intensity defense is played. Knowing each players’ current endurance level, their value at each endurance level, and their likelihood of transitioning between endurance levels could help a coach determine a better substitution strategy.



Operations research, Engineering, Basketball Substitutions, Decision-making in Sports, Dynamic programming, Endurance in Sports, Fatigue and Recovery Rates, Optimal Substitution Strategies