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Game Theory in Nadal-Federer Rivalry

The rivalry between tennis stars Rafael Nadal and Roger Federer has been regarded as the greatest sport rivalry of our generation. Nadal, being a left-handed player, can more effortlessly serve and rally to the back-hand side of right-handed players like Federer. Since most male tennis players’ backhand skill is weaker than that of their forehand, for Federer, the key to beating Nadal is to anticipate when Nadal is going to hit to his backhand and move accordingly. However, Federer being over-protective of his backhand side also gives Nadal a chance to attack on his forehand side. The following article discusses why Nadal’s best strategy against Federer is to strike a balance between shots to Federer’s forehand (stronger) side and his backhand (weaker) side, instead of concentrating on his backhand.

To both Nadal and Federer, their competition becomes not only a physical contest, but also a match involving intricate game theory. Without elaborating on the concept of Nash Equilibrium and calculation behind it, the article certainly seems to suggest that although a pure Nash Equilibrium cannot be achieved, a mixed Nash Equilibrium certainly can be. The author suggests that Nadal should be going after Federer’s stronger side more often than he currently does, which is a somewhat unintuitive strategy. Equally unintuitive for Federer, his winning strategy is to move as if he were to hit a weaker backhand shot more often than he does. As Nadal gets better at striking to Federer’s backhand, Federer needs to spend more effort guarding against these kinds of shots. However, doing so leaves Federer’s forehand side, which is supposed to be his stronger side, open for attack. Therefore, as unintuitive as the strategy seem for both players, as the article points out, the key for Nadal’s shot to Federer’s backhand is that “ the threat of using it is enough without having to actually use it”.

 

http://www.gametheorystrategies.com/2011/06/27/game-theory-and-wimbledon/

 

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