Thread by @page_eco

Roger Federer game theorist.

Professional tennis players are not just amazing athletes. They are also brilliant decision makers. If you like tennis, this thread will change your view of the game.

Varying serve direction is critical to be the least predictable.

Walker & Wooders (AER 2001) found that players' success in each serve direction appears equal as predicted by game theory (N=10 matches).

Graph: test pvalues vs theory (45 degree line)
aeaweb.org/articles?id=10…

Using ball tracking data with a much larger dataset (>3000 matches) we find that winning percentages are not just roughly equal but actually very close from being equal.
The distribution of test statistics is stunningly close from theory (45 degree line).
ideas.repec.org/p/qut/qubewp/w…

Are tennis players too conservative on their second serve?

Klaassen & Magnus (2009) found that professional players are quite good at taking the right amount of risk on first and second serve.
sciencedirect.com/science/articl…

We replicated this result using a quasi-experiment: when a serve bounces off the net, players get a 1st serve if the ball lands in, a 2nd serve if it lands out.
The following 1st/2nd serves appear in very similar situations and can be directly compared.
ideas.repec.org/a/eee/joepsy/v…

Do tennis players use their challenge calls smartly?

Abramitzky et al. found that players approximate the optimal strategy which takes into account the value of keeping a challenge for later (in case a close call is made on a more important point).
onlinelibrary.wiley.com/doi/abs/10.111…

Do tennis players allocate their effort well in a match?

In best-of-3 matches, players ahead should increase effort relative to players behind as they are closer from victory.

Malueg & Yates found results compatible with this prediction (N=351 matches).
mitpressjournals.org/doi/abs/10.116…

We looked at how players allocate effort within a game of tennis using ball tracking data on more than 3,000 matches.

We find that male players are more likely to win a point when they are just ahead (e.g. 30-15), as predicted by our game theoretic model.
ideas.repec.org/p/qut/qubewp/w…

Finally, have you ever wondered why favourites seem to surprisingly struggle against weak opponents in the first week of Grand Slam tournaments?

It is optimal for them to save energy for later rounds. The cost is a higher risk of upsets in early rounds.
onlinelibrary.wiley.com/doi/abs/10.109…

Conclusion:

The athletic performance of tennis players is for all to see.

But careful studies have also shown that professional tennis players are excellent decision makers who have learned to approximate optimal/equilibrium behaviour in many dimensions of the game.