Game Theory’s Application in Tennis
As it does in many sports, game theory has relevant applications in tennis. Though players’ decision making during rallies (continuous hits of the ball back and forth mid-point) employs strategic thinking in its own right, the context in which game theory, and specifically John Nash’s equilibrium, is most plainly evident, is the moment in which the server chooses the direction in which to serve the ball.
As with penalty kicks in in soccer, a tennis server faces several choices when serving the ball- serve to the receiver’s right, or serve to their left (the particular study I will go on to discuss did not mention alternatives to these two options, presumably assuming that a serve directly at the receiver is suboptimal in all scenarios). Given the binary nature of the decision facing the server, John Wooders, a professor of economics at NYU Abu Dhabi, authored a scholarly paper analyzing tennis serves through the lens of game theory. Wooders, along with two other economists, gathered data for the trajectory and bounce points of nearly 500,000 serves from over 3,000 professional matches. The key distinction between this particular study and previous similar studies lay in the sheer sample size as well as the fact that professional matches were interpreted. Wooders notes that unlike experiments conducted with an undergraduate population, the stakes in a professional environment were much higher, meaning the players’ level of experience was greater, resulting in more accurate results (Kappler, 2017).
The economists were able to gather that tennis players do, in fact, behave in a way that is consistent with the Nash equilibrium- a theory that we covered in our course content describing a game in which neither player faces an incentive to choose any strategy other than one that persists as optimal regardless of what the other player chooses to do. In tennis, the server’s payoff is the same regardless of whether or not they choose to serve to the left or the right of the receiver; the implication of this is that the receiver’s optimal strategy is to stand in a place that leaves the server indifferent regarding whether to serve left or right (Kappler, 2017).
Additionally, the study looked at “serial independence,” which is defined as the idea that the direction of the subsequent serve does not depend on the direction of any previous serves (Kappler, 2017). In essence, serial independence implies pure randomness, and the economists found that at the highest level, the most skilled players were more likely to exhibit this sort of tendency in their serve pattern, yielding greater overall success.
Game theory’s application in tennis and in sports more broadly is both pertinent and utile. The more that scientists are able to understand about players’ game theoretical tendencies, the more sophisticated players’ decision making can potentially become in-game, leading to both increased winning chances as well as more entertaining events for fans.
Source: https://nyuad.nyu.edu/en/news/latest-news/world-and-societies/2017/june/experts-test-game-theory-on-world-s-top-tennis-players.html