Optimizing serve strategies in tennis: A focus on Nash equilibrium and different court surfaces

This study analyzes 120 men's singles tennis matches using the Stroke Performance Relevance (SPR) metric and Nash equilibrium from game theory, focusing on serve strategies across different court surfaces. The SPR metric quantifies the impact of each stroke on match dynamics, providing a comprehensive alternative to traditional outcome-based metrics. Results show that on hard courts, first serves to the outside placement achieve the highest expected return (27.3), while on clay courts, the outside has the highest probability distribution (22.1%). For second serves, hard courts favor the inside with the highest expected return (2.3), whereas grass courts demonstrate the highest probability in the outside (6.0%). These findings underscore the critical need to adapt serve strategies to court-specific characteristics, enabling players to maximize strategic efficiency. Coaches can utilize these insights to develop targeted training programs. By integrating the SPR metric and Nash equilibrium, this study combines stroke impact quantification through SPR with game-theoretic strategy optimization. This integration enables players to dynamically adapt serve strategies during matches and empowers coaches to design surface-specific training regimens, thereby enhancing competitive performance through data-driven tactical adjustments.