Tennis Tournament Game Theory
We have discussed the application of game theory to sports in class, in the context of penalty kicks in soccer. A similar research article I found discusses the tennis tournament techniques and tactics through a game theory lens. The recent conclusion of the US Open may already be prompting similar analyses and new strategy development; however, this article reflects on select conventional plays and responses to evaluate the best offensive and defensive strategies. Games can be categorized into two distinct types: a static game, in which the players make a simultaneous and independent decision on their strategy, and a dynamic game, in which decision-making occurs sequentially. Though the reaction time is relatively short in tennis, a dynamic game model is the approach investigated in the study, and is best suited to the action-response rally that occurs in practice. One characteristic of games in which moves are carried out sequentially is the presence of first or second-move advantage. In tennis, service is often considered a first-move advantage, as it gives the player an opportunity to control the court and places greater stress on the opponent. In light of these factors, the paper examines a particular snapshot of the momentous 2009 Australian Open, in which Roger Federer and Rafael Nadal faced off in the men’s singles final. The players prepared for the championship point, in which a win for Federer would mean continuing the game, but a win for Nadal would ensure victory and end the match. The serve was to be played by Federer, while Nadal was on the receiving end.
Following the procedures discussed in class, we can identify the three essential components of the game: players, their corresponding strategies, and the payoffs of each strategy pair.
The players are the server, Federer, and the receiver, Nadal, whose strategies vary based on these roles. Federer’s options are an outer angle serve or inner angle serve, while Nadal’s responses may be returning a crosscourt shot, which would send the ball diagonally back toward the service box, or a linear ball, directed toward the adjacent box. The payoffs are dependent on each player’s strength in returning a forehand or backhand shot, and are analyzed in the study as follows:
If Federer’s outer angle serve is returned with a linear ball, no player has a strict advantage and the game continues, leaving the score at 0,0. However, if it is returned crosscourt, Federer assumes the advantage of playing forehand and gains 1 point, while Nadal loses 1 point.
An inner angle serve, by contrast, will give Nadal a forehand advantage, which if returned with a linear ball would exploit Federer’s weaker backhand, gaining Nadal 1 point and at a cost of 1 point for Federer. Finally, a crosscourt response will give Federer a forehand advantage, resulting in a payoff of 1,-1. The payoffs are summarized by the following matrix:
We can observe that this game already defines a dominant strategy for Nadal: returning a linear ball is always preferred to a crosscourt. The paper denotes crosscourt returns as a dominated strategy for this reason. For Federer, the researchers identify the outer angle serve as a best strategy, as it exploits the opponent’s weaker backhand. Moreover, the concept of first-move advantage is illuminated as Federer has fewer opportunities to lose the point.
A continued and more general analysis is made on specific shot types and their “costs” in terms of space and time, assessing how particular shots affect opponent mobility and response time. I found it very interesting to consider how, even in games that operate at an incredible pace, such strategic decisions are critical to a successful match. While spectators may not easily be able to predict when one player may lose the offensive play and the other gain control of the court, through game theory analysis it is possible to model these situations and uncover the underlying “game” that truly governs the match.
Source: Journal of Chemical and Pharmaceutical Research, 2014 : http://jocpr.com/vol6-iss3-2014/JCPR-2014-6-3-257-265.pdf