John Wooders, an economics professor at NYU Abu Dhabi, has discovered a fascinating application of game theory within the realm of professional tennis. Although he does not play the sport himself, Wooders has developed a passion for tennis, particularly through watching his son compete. His academic pursuits focus on analyzing the strategic choices made by elite tennis players, especially regarding their serve direction.
In collaboration with economists Romain Gauriot from the University of Sydney and Lionel Page from Queensland University of Technology, Wooders has co-authored a research paper that utilizes data from 500,000 serves across 3,000 matches. This extensive dataset, gathered through Hawk-Eye technology, provides accurate tracking of ball trajectories and bounce points, enabling the researchers to apply Nash’s game theory in a practical context.
The findings of their study indicate that professional tennis players, particularly men, often adhere to the Nash equilibrium – a concept for which John Nash received the Nobel Prize in 1994. This theory posits that when a server randomizes their serve direction, the likelihood of winning the point remains stable, irrespective of the chosen direction. Wooders observes that higher-ranked players tend to follow this theory more closely than those ranked lower.
Additionally, the research uncovers a notable distinction between male and female players. Men, whose serves average a speed of 160 kilometers per hour, align more closely with the Nash equilibrium compared to women, whose serves average 135 kilometers per hour. The increased speed of male serves provides less reaction time for female receivers, making deviations from optimal strategies less impactful.
Analyzing Strategy and Predictability in Tennis
The second key finding of the paper addresses the concept of “serial independence,” which suggests that the direction of a serve should not be influenced by previous serves. However, the study reveals that players frequently change serve directions too often to achieve true randomness. This indicates that while players strive to be unpredictable, they may not be as effective as they believe.
Despite this tendency towards predictability, higher-ranked male players demonstrate less serial coordination, suggesting a closer alignment with randomness and, as a result, greater success on the court. The challenge lies in recognizing these patterns during a match, as thorough statistical analysis is typically necessary to pinpoint deviations from randomness.
Wooders references a well-known anecdote involving Andre Agassi, who once detected a “tell” in Boris Becker’s serve direction but had to keep this insight hidden to maintain his competitive edge. This story highlights the significant influence that strategic understanding can have on match outcomes.
Similar to the Moneyball phenomenon in baseball, where data analytics revolutionized player assessment, Wooders’ research has the potential to reshape tennis strategies. While he does not intend to provide consulting services to players, the increasing recognition of such studies may inspire players and coaches to integrate these insights into their training and match strategies.