On Optimal Offensive Strategies in Basketball

TL;DR

This paper uses game theory and dynamical systems to analyze whether basketball teams should predominantly shoot three-pointers, showing that such strategies are not necessarily optimal and depend on various payoff conditions.

Contribution

It introduces a game-theoretical framework to evaluate offensive strategies in basketball, revealing conditions under which two-point strategies may be more stable than three-point strategies.

Findings

Three-point strategies are not always optimal.

Local and global stability analyses identify conditions for strategy stability.

Existence of Nash equilibria depends on payoff constraints.

Abstract

The purpose of this paper is to determine whether basketball teams who choose to employ an offensive strategy that involves predominantly shooting three point shots is stable and optimal. We employ a game-theoretical approach using techniques from dynamical systems theory to show that taking more three point shots to a point where an offensive strategy is dependent on predominantly shooting threes is not necessarily optimal, and depends on a combination of payoff constraints, where one can establish conditions via the global stability of equilibrium points in addition to Nash equilibria where a predominant two-point offensive strategy would be optimal as well. We perform a detailed fixed-points analysis to establish the local stability of a given offensive strategy. We finally prove the existence of Nash equilibria via global stability techniques via the monotonicity principle. We believe that this work demonstrates that the concept that teams should attempt more three-point shots because a three-point shot is worth more than a two-point shot is therefore, a highly ambiguous statement.