#### Event Title

Optimal Risky Strategies in Tennis - Preliminary Research

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#### Faculty Mentor

Dr. Marco Castaneda

#### Document Type

Poster Presentation

#### Date of Publication

2021

#### Abstract

In the game of tennis, players must make risk-reward calculations in order to determine the optimal risk level for a given strategy. Low-risk strategies come with few unforced errors but allow the opponent to capitalize on weaknesses. High-risk strategies, however, minimize these weaknesses but lead to a greater number of unforced errors which can offset the gains of a higher risk strategy. From the standard game theory analysis, the optimal strategy for a player should not vary across points within a game against a given opponent. That is, the Nash Equilibrium does not change depending on the score within the game. However, in practice players are often observed adopting lower risk strategies when behind in a game. Conversely, players tend to play more aggressively when ahead. In this research paper, I will evaluate how professional tennis players change their strategy in reference to the score within a game. I use service speed as a measure of risk. I compare it to the player's average for a given match to determine if differences are correlated to the players game score. In addition, I will evaluate the efficacy of changing strategies across scores within a game. Lastly, I will discuss the psychological factors and motivations that may explain this deviation from the predictions of the standard analysis.

#### Keywords

Game Theory, Tennis, Nash Equilibrium

#### Persistent Identifier

http://hdl.handle.net/10950/3025

*Caitlyn Cox Poster PDF*

Optimal Risky Strategies in Tennis - Preliminary Research

In the game of tennis, players must make risk-reward calculations in order to determine the optimal risk level for a given strategy. Low-risk strategies come with few unforced errors but allow the opponent to capitalize on weaknesses. High-risk strategies, however, minimize these weaknesses but lead to a greater number of unforced errors which can offset the gains of a higher risk strategy. From the standard game theory analysis, the optimal strategy for a player should not vary across points within a game against a given opponent. That is, the Nash Equilibrium does not change depending on the score within the game. However, in practice players are often observed adopting lower risk strategies when behind in a game. Conversely, players tend to play more aggressively when ahead. In this research paper, I will evaluate how professional tennis players change their strategy in reference to the score within a game. I use service speed as a measure of risk. I compare it to the player's average for a given match to determine if differences are correlated to the players game score. In addition, I will evaluate the efficacy of changing strategies across scores within a game. Lastly, I will discuss the psychological factors and motivations that may explain this deviation from the predictions of the standard analysis.

## Comments

Zachary Tucker commented "This is awesome Caitlyn!"