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Does the “serving-first advantage” actually exist?

Suppose you are watching a tennis match between Novak Djokovic and Rafael Nadal. The commentator says: “Djokovic serves first in the set, so he has an advantage.” Why would this be the case? Perhaps because he is then ‘always’ one game ahead, thus serving under less pressure. But does it actually influence him and, if so, how?

Now we come to the seventh game, which some consider to be the most important game in the set. But is it? Nadal serves an ace at break point down (30-40). Of course! Real champions win the big points, but they win most points on service anyway. At first, it may appear that real champions outperform on big points, but it turns out that weaker players underperform, so that it only seems that the champions outperform. And Nadal goes on to win three consecutive games. He is in a winning mood, the momentum is on his side. But does a ‘winning mood’ actually exist in tennis? (Spoiler: It does, but it is smaller than many expect.)

To figure out whether the “serving-first advantage” actually exists, we can use data on more than one thousand sets played at Wimbledon in order to calculate how often the player who served first also won the set. This statistic shows that for the men there is a slight advantage in the first set, but no advantage in the other sets.

On the contrary, in the other sets, there is actually a disadvantage: the player who serves first in the set is more likely to lose the set than to win it. This is surprising. Perhaps it is different for the women? But no, the same pattern occurs in the women’s singles.

It so happens that the player who serves first in a set (if it is not the first set) is usually the weaker player. This is so, because (a) the stronger player is more likely to win the previous set, and (b) the previous set is more likely won by serving the set out rather than by breaking serve. Therefore, the stronger player typically wins the previous set on service, so that the weaker player serves first in the next set. The weaker player is more likely to lose the current set as well, not because of a service (dis)advantage, but because he or she is the weaker player.

This example shows that we must be careful when we try to draw conclusions based on simple statistics. The fact that the player who serves first in the second and subsequent sets often loses the set is true, but this primarily concerns weaker players, while the original hypothesis includes all players. Therefore, we must control for quality differences, and statistical models enable us to do that properly. It then becomes clear that there is no advantage or disadvantage for the player who serves first in the second or subsequent sets; but it does matter in the first set, so it is wise to elect to serve after winning the toss.

Featured Image Credit: “Balle de Tennis”, Photo by Steve Lorillere, CC by SA 2.0, via flickr.