ECONOMICS OF HOT HAND: evidence from tennis

In many sports, it is believed that success leads to more successes. In basketball, the term “hot-hand” describes players whose probability to score increases after a streak of successive shots.

Hot hand exists – tennis players who win a point are more likely to win the next one. New research by Romain Gauriot and Lionel Page – published in the November 2019 issue of The Economic Journal – who, using big data from ball tracking on more than 3,000 tennis matches, found that the exact phenomenon exists in tennis: professional male players who win a point are more likely to win the next one.

One of the implications of this new finding will interest all tennis fans: not all points are played with the same intensity in a game of tennis.

To study whether winning a point helps to win the next one, Gauriot and Page focused on situations where winning is partly due to chance: when the balls land within a few centimetres of the court lines.

“When a player hits the ball within a few centimetres in or out of the court, there are negligible differences in strength between players,” says Dr Gauriot. “However, there is a substantial difference in outcome: hitting the ball just out makes you lose the point while you can still win if you put the ball just in. Using these variations in winning chances for balls around the court lines, we can estimate what is the effect of winning a point on the chances of success in the following point.”


Figure: The bounce marks in the data are represented in light grey, and the subset used for the study are represented in black.

Doing so, Gauriot and Page find that male players are 7% more likely to win the next point after winning a point. This effect jumps to 15% in situations like 30-30 and deuce. For Professor Page, this effect can be explained by game theory: “A momentum should exist in a game of tennis. The player ahead plays to win the game, and he should put more effort than the player behind who has to catch up first. Players and commentators sometimes state that players play 100% on each point. But if expending effort is costly (in terms of physical pain or even risk of injury), this is not the optimal strategy.” Instead, Gauriot and Page show in a model that the optimal strategy in a game of tennis is to strategically allocate effort on the most important points. A consequence of this strategy is that a player who trails within a game should save his effort more and therefore be less likely to win the next point.

This strategy indeed echoes the words of one of the most famous tennis coaches, Brad Gilbert. In Winning Ugly (2013) he explains how “specific points and games” can have an impact “on the momentum and outcome of the match”. Within a game, he sees the 30-30 and deuce points as the most important, exactly as predicted by Gauriot and Page’s model. Gilbert states: “Those are the points that really get the juices going. […] These points require more caution. Or to put it another way, they require less casualness or carelessness.” Gauriot and Page’s research, therefore, reveals the dynamic inside tennis matches which emerges from tennis players allocating their effort strategically across points.

Professor Page explains that this research provides insights well beyond the world of tennis: “The type of momentum we observe should exist anytime people have to allocate their effort or resources in competitions taking place over time. What we find is that in such competitions ‘success breeds success’, and therefore early successes are often very important to determine future successes.”

Does Success Breed Success? a Quasi-Experiment on Strategic Momentum in Dynamic Contests” by Romain Gauriot and Lionel Page is published in the November 2019 issue of The Economic Journal

Romain Gauriot

Postdoctoral Associate in Economics at New York University, Abu Dhabi