The Hangover Effect of a Marathon Fifth Set

Italian translation at settesei.it

Marathon sets are again the talk of tennis.  We won’t soon forget Roger Federer’s 19-17 third-set win over Juan Martin Del Potro … or Roger’s weak performance in the match that followed.

The unusual Olympic format–best-of-three, no final-set tiebreak–brought several issues to the fore.  Should best of three be enough for slams?  It certainly gave us plenty of dramatics last week.  And is it finally time to end the no-tiebreak madness?  For all of the occasional drama, do we really need to see even more service holds in John Isner matches?

Peter Bodo makes the case for a marathon-free world:

[M]y main reason for embracing the final-set tiebreaker is not the obvious one that would be cited by most time-sensitive television producers. The real problem with deuce sets is that when a match goes as long as Federer v. Delpo or even Jo-Wilfried Tsonga v. Milos Raonic (that one went 25-23, for Tsonga) the reward for the winner’s heroic feat is almost always a quick subsequent loss.

As Bodo goes on to illustrate, this seems anecdotally true.  But who cares about anecdotes?  This is a testable hypothesis.

As we’ll see, there is a noticeable hangover effect when a player has fought through a marathon fifth set.  But the alternative–a fifth-set tiebreak–produces nearly the same hangover.

There have been 146 marathon fifth sets–matches in which the final set reached 6-6–in Grand Slam tennis since the beginning of 2001.  The record of those 146 winners in their next round is dreadful: 43-103, or 29.5%.  It’s even worse than that, actually.  Four times, two marathon men went on to play each other, so four of those wins were inevitable.

However, that isn’t the end of the story.  To prove that fifth-set marathons significantly weaken their winners, we need to establish two things: (1) They had a decent shot at beating their next opponents anyway, and (2) if a fifth-set tiebreak were played, their chances would have been better.

Post-marathon underdogs

The first issue is a bit sneaky.  If a player has to go deep into the fifth set to win in the early rounds, he’s hardly a dominating presence in the draw.  Consider the extreme case of Yen Hsun Lu, who in 2010, beat Andy Roddick in a 9-7 fifth set, advancing to play Novak Djokovic in the Wimbledon quarters.  Sure, Lu was tired, but what were the odds of an upset even if Roddick lost in three?  Top players rarely need five hours to push through an early-round opponent.

To quantify this, we can turn to jrank-driven predictions.  Using these measures of each player’s ability level at the time of the match, we can estimate the actual chances of our 146 marathon men.

The marathon men would have been underdogs in their next match no matter what.  On average, each one had a 43.4% chance of winning, meaning that of the 146 matches, they should have won 63 of them.  Even adjusting for their underdog status, they seem to have suffered from their marathons–they won 43 of those matches, barely two-third the number that they “should” have won.

Almost-but-not-quite marathons

We’ve established that once a player enters the uncharted territory beyond 6-6, his chances of winning the next match are substantially weakened.  But surely the fatigue didn’t set in right at the moment the chair umpire called “6-6.”  Even if the fifth set is a bagel, simply playing five sets of professional-level tennis is exhausting, and might impact one’s performance a day or two later.

The most relevant set of matches for comparison are US Open five-setters that went to a final-set tiebreak.  Since 2001, we have 40 of those.  In their next matches, the winners of the almost-marathons went a dismal 11-29 (27.5%)–worse than the marathon men!

Compared to their expectations, though, they did a bit better.  Those forty men, on average, had a 38% chance of winning their next matches, meaning we would expect them to win about 15 of the 40.  Relative to the predictions we would have made at the time, this small sample of fifth-set-tiebreak winners outperformed the marathon men, but just barely.

For a bigger sample, we can turn to the slightly shorter–but still epic–matches that end 7-5 in the fifth.  Of the 95 such matches since 2001, the 7-5 winners went on win 49, or 51.5% of their next matches!  This despite the fact they were collective underdogs, expected to win only 48%, or 46 of those matches.

What now?

Since the 7-5 group performed so differently in their next matches, it’s tempting to speculate why they did so.  My best guess: If a player manages a break before the set goes 6-6, he’s relatively fresh, physically and mentally.  The sort of player who can break at 5-5 or 6-5 is one who can come back a day or two later and plow through another three or four hard-fought sets.

By contrast, matches that get to 6-6–whether they end in a tiebreak or not–are usually battles of attrition.  Think Isner-Mahut: The longer it lasted, the less likely either player could challenge the other’s serve.  That brand of tennis had set in before 6-6 in the fifth: If one of the players pulled out a 7-4 tiebreak, it wouldn’t say much about his fitness or mental stamina, simply that someone is bound to get lucky for a point or two.

Based on the limited data we have, there just isn’t much difference between the after-effects of fifth-set marathons and fifth-set tiebreaks.  In both cases, the marathon men weren’t going to be favored anyway, and their fatigue hurts them even more.  Changing format to fifth-set tiebreaks would have little effect on future outcomes–it would just make those matches a bit more dependent on a lucky bounce.