Does Serving First in a Tiebreak Give You an Edge?

Italian translation at settesei.it

Tiebreaks are so balanced, with frequently alternating servers and sides of the court, that it seems they must be fair. As far as I know, there is no commonly-cited conventional wisdom to the effect that the first server (or second server) in a tiebreak has any kind of advantage.

Let’s check. In a dataset of over 5,200 tiebreaks at ATP tour events, the first server won 50.8% of the time. Calculating each player’s service points won for the entire match and using those numbers to determine the likelihood that the first server would win a tiebreak, we get an estimate that those first servers should have won only 48.8% of them.

Two percentage points is a small gap, but here, it’s a meaningful one. It’s persistent across each of the three years most heavily represented in the dataset (2013-15), and it holds regardless of the set. While there might be some bias in the results of first-set tiebreaks, since better servers often choose to serve first and lesser servers choose to receive, the effect in each set favors the first server, and the impact of serving first is greater in the third set than in the first.

However, this effect–at least in its magnitude–is limited to ATP results. A survey of 2,500 recent WTA tiebreaks shows that first servers have won 49.7% of tiebreaks, compared to 49.4% that they should have won. Women’s ITF matches and men’s futures matches return similar results. Running the same algorithm on 6,200 men’s Challenger-level tiebreaks confuses the issue even further: Here, first servers won 48.1% of tiebreaks, while they should have won 48.7%.

A byproduct of this research is the discovery that, for both genders and at multiple levels of the game, the first server in a tiebreak is, on average, the weaker player. At first glance, that doesn’t make a lot of sense: We think of tiebreaks as deciding sets when the two players are equal. And since the effect is present for the second and third sets as well as the first, this finding isn’t biased by players choosing who will serve first.

As it turns out, this result can be at least partially explained by another byproduct of my recent research. In my attempt to determine whether it’s particularly difficult to hold when serving for the set, I calculated the odds of holding serve at every score throughout a set, compared to how frequently players should have held. At most holds–including those with the set on the line–there aren’t any major discrepancies between actual hold rates and expected hold rates.

But I did find some small effects that are relevant here. In general, it is a bit harder to hold serve as the second server, at scores such as 3-4, 4-5, and 5-6, than as the first, at scores like 3-3, 4-4, and 5-5. For instance, in the ATP data, players hold serve at 4-4 exactly as often as we would expect them to, based on their rate of service points won throughout the match. But at 4-5, their performance drops to 1.4% below expectations. In the WTA data, while players underperform at 5-5 by 1.4%, they are far worse at 5-6, winning 5.2% less often than they should.

In other words, if two players of equal abilities stay on serve for the first several games of a set, the second server is a little more likely to crack, getting broken and losing the set. Thus, if neither player is broken (or the number of breaks is equal), the second server is likely to be just a little bit better.

That explains, at least in part, why second servers are favored on paper going into tiebreaks. What it doesn’t account for is the discovery that on the ATP tour, first servers overcome that paper advantage and win more than half of tiebreaks. For that, I don’t have a good answer.