In sports analytics, the topic of streakiness–the “hot hand“–is a popular one. Nearly everyone believes it exists, that players (or even teams) can go on a hot or cold streak, during which they temporarily play above or below their true level.
To a certain extent, streakiness is inevitable–if you flip a coin 100 times, you’ll see segments of 5 or 10 flips in which most of the flips are heads. That’s not because the coin suddenly got “better,” it’s a natural occurence over a long enough time span. So if you watch an entire tennis match, there are bound to be games where one player seems to be performing better than usual, perhaps stringing together several aces or exceptional winners.
The question, then, is whether a player is more streaky than would occur purely at random. To take just one example, let’s say a player hits aces on 10% of service points. If he did occasionally serve better than usual, we would observe that after he hits one ace, he is more likely (say, 15% or 20%) to hit another ace. A missed first or second serve might make it more likely than he misses his next try.
One of the most popular subjects for hot hand research is basketball free throw shooting. Researchers like it because it’s as close as basketball players get to a laboratory: every shot is from the same distance, there’s no defensive quality to consider, and even better, players usually get two tries, one right after the other. There’s nothing like it in tennis.
The one thing that seems a bit akin to free throw shooting is serving, especially for more dominant players. John Isner, Roger Federer, and Milos Raonic seem to go on serving streaks; certainly they can play game after game and control play with unreturnable serving. But when we look closer, their experience is much more nuanced. As we’ve seen, players generally are better in the deuce or ad court. It would be as if basketball player shot one free throw, then took two steps to the left and one step forward before attempting his next shot.
And, of course, there’s another player on the court. If Federer uses a relatively slow serve out wide in the deuce court for a service winner at 15-15, he is much less likely to use the same tactic at 30-30 or 40-15. Even if he was capable of hitting 50 perfect serves of that nature, he would never do so in a match. If it has any relevance for professional tennis, the hot hand must refer to something broader than a single skill.
On a more general level, the rules of tennis involve alternation more than more sports. Sure, most sports give the ball to the other team after a goal, but the length of possession–or in baseball, the length of an inning–can vary widely. In tennis, you can only add one game to your tally before handing the ball to your opponent. And even within that game, you are constantly moving from your stronger court to your weaker court; your opponent might be doing the same.
My question to you is this: If there is a hot hand in tennis, where would you expect to find it? Consecutive aces? Aces specifically in the deuce court? Service winners? Short service points? Points won? Return points won? Games won? First serves in? Point-ending winners? Avoidance of unforced errors? It’s possible that any or all of these things could occur in bunches, but which of them would indicate what we think of as a tennis player on a hot streak?