Tennis and Game Theory
Federer’s hopes of winning another US Open were recently squashed by Djokovic in an intense four set championship last Sunday. Although Federer managed to take the second set, at 34, his chances of coming back and defeating Novak late in the match were slim. In tennis, even more than other sports, trying to figure out your opponent’s next move is essential to winning points. Using knowledge of a certain players and opponents, game theory can accurately predict certain statistics in a match, such as ball placement and speed. For example, one of Federer’s strategies is to come up to the net right after serving. Here, if Djokovic hits it back near the center of the court, Federer has a very high chance of winning the point, but if he hits it down the line or lobs it, which are more difficult shots, Federer has almost no chance of winning the point. Given past data of shot percentages for these two player, this example could be easily modeled by game theory, and the best strategy to counter Federer’s serve and volley could be determined.
Another typical aspect of tennis that can described by game theory is serving. Professional tennis players usually try to serve to either the left or right corner of the service box, and knowledge of your opponents’ serving tendencies can improve your returns significantly. Serves can also be labeled as either by high risk (a typical first serve) or low risk (a typical second serve). According to Tristan Barnett, a mathematician witha PhD in tennis statistics, there are two serving strategies: 1) high risk followed by high risk, or 2) high risk followed by low risk. If a player wins a higher percentage of point on high risk serves than their opponent, they are encouraged to use the first strategy, and if not the second. Here are some serving statistics for Nadal and Roddick:
If Roddick were to serve against Nadal on grass he should use strategy 1 (because .535 > .512), but on any other surface, the usual strategy of a high risk serve followed by a low risk serve would work to his advantage. A game theory matrix can then be created and solved, such as the one below describing how much risk Roddick should take on his second serve.
Knowledge is power, and if an average tennis player knew some of his opponents’ statistics, he could easily use game theory to give himself the competitive edge. Pro tennis players develop a natural instinct for game theory, whether or not they know what it is, in split second decisions between hitting an easy return up the middle or a tricky shot down the line.
http://www.strategicgames.com.au/article31.pdf