Serving First in Marathon Sets

Italian translation at settesei.it

Last night, when Jo Wilfried Tsonga finally defeated Milos Raonic, it was on a match-ending break of serve.  Conventional wisdom suggests that’s often how it goes.  Whoever serves first in a long set seems to have the advantage.  There’s less pressure to hold serve at 7-7 (or 47-47) than there is at 7-8.

Tsonga won his contest with a match-ending break point; Isner finished off his 70-68 set on Mahut’s serve; and when Federer and Roddick went to 14-14 in the 2009 Wimbledon final, Roger held for 15-14 before breaking the American.  Is it a trend?

As it turns out, those three high-profile matches have misled us.  Based on the limited data available, the first server in fifth-set epics has little or no advantage.

(Third-set epics are so rare that we might as well ignore them–the Olympics is the only tournament where men play best-of-three with no tiebreak in the final set.)

We don’t know who served first for every marathon fifth set in tennis history, but we can figure it out for some.  The ATP has limited stats for most matches back to 1991, and those stats include numbers of service games.  When the number of service games is equal for both players, we’re stuck at square one.  When one player has more than the other, that guy must have served the first game of the match–and the last.  Since marathon sets must contain an even number of games, we know who served first in the final set.

The result is a pool of 138 matches in which the fifth set ended at 8-6 or higher and we know who served first.  Of those, the guy who served first–at 0-0, 1-1, 6-6, and so on–won the match 67 times (48.6%).  It’s a coin toss.

If we take pressure out of the equation, this makes perfect sense.  If two guys have gotten to 6-6 in the fifth set, they’re playing as equally as two tennis players can play.  It’s only when we consider the stress of serving to stay in the match that we start to suspect that one player–but not the other–won’t be able to hold up his end.

For a bigger dataset, we can look to similar situations.  Consider 5-setters that end 7-5 in the fifth.  Those don’t have the cachet of matches that go farther, but they are quite epic in their own right.  We know who served first in 86 such matches, and of those, the man who served first won only 38 (44.2%).  It’s not exactly proof that the first server has a disadvantage, but it does cast more doubt on the conventional wisdom.

If want more than 200 or so matches, we need to weaken our definition of “epic.”  Tiebreaks aren’t relevant here, since we’re looking for instances where one player was broken under pressure.  But we can use best-of-three contests that ended 7-5.

With so many more best-of-three matches on the schedule, our dataset is now much bigger.  We know who served first for 753 tour-level matches that ended 7-5 in the third.  Of these, the player who served first went 412-341, winning nearly 55% of matches.

If you want evidence that the conventional wisdom is correct, there you go.  If a match reaches 5-5 in the deciding set and ends with a break, there is, altogether, a 53% chance that the first server wins.

But with our more limited data, it’s impossible to draw the same conclusion about five-setters once they head into the barely-charted territory beyond 6-6.