Results of the poll! Most people think game points are the most important points to work for. I’ll argue that, instead, 30-30/deuce is most likely the right answer! Here is a thread for tennis lovers on insights from game theory.https://twitter.com/page_eco/status/1222451143860604930 …
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It is common to hear that players should play each point 100%. See for instance what Djokovic said in 2013:pic.twitter.com/C9RmMCD5W7
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But there are good reasons for players not to do that. In a game of tennis, not all points are worth the same. Consider a player returning serve. Winning at 30-40 gives him a break. Winning at 40-0 will most likely make no difference. So the payoffs of effort vary with the score.
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Here is a stylised tennis game. You start at 0-0 and move in the tree as you win/lose points. To win, you need to win 4 points with at least 2 point difference. Note that 30-30 and deuce are strategically equivalent (2-2).pic.twitter.com/EDvEbC5qwh
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Now suppose we consider a simplified version of a tennis match. Players just decide at the start of each point how much effort they put for this point. The player putting the most effort wins the point. Effort is costly so players don’t want to put more effort than needed.
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Suppose also that players prefer to win quickly (instead of playing 10 advantage<->deuce situations). Then, there is a unique equilibrium in this game, and players do not put the same effort on every point. In particular they put less effort when they are behind!
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As a consequence, symmetric scorelines are key. And the most important situations are 30-30/deuce where you can either get a game point or have to defend one. It is for the 30-30/deuce points that players will expend the most effort in the equilibrium of the game.
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What do professional players do? Brad Gilbert, one of the most successful tennis coaches, stresses in his book “Winning Ugly” that the most important points are not game points but 30-30/deuce.pic.twitter.com/QhbswsYjcw
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All these quotes are from our paper with @GauriotRomain where we find that male professional tennis players seem to follow the predictions of the model. After losing a point on a symmetric scoreline, the player behind is less likely to win the next point.
https://academic.oup.com/ej/article-abstract/129/624/3107/5536246 …pic.twitter.com/PL4esoCa9X
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So if you find yourself on a court, or watching tennis, remember: the most critical points are most likely 30-30 and deuce. It’s an insight from game theory which goes beyond the case of tennis and tells us something about the dynamics of competitions. (End)
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