The Influence of a First-Set Tiebreak

Italian translation at settesei.it

In the first two rounds of last week’s Paris Masters, 12 matches began with a first-set tiebreak.  Of those dozen matches, nine of them finished as straight-set wins, with the second set more decisive than the first.  Polish qualifier Jerzy Janowicz won both of his first two matches according to this pattern.

This isn’t exactly what we’d expect.  A tiebreak isn’t purely random, but it’s close.  And if two players have reached a tiebreak, the available evidence suggests that they are playing at about the same level.  Thus, the winner of the first set is more likely to win the match–and perhaps a bit more likely to win the second set–but not so highly likely to find it easier going in the following set.

Anecdotally, this seems like a familiar pattern.  Tough fight in the first set, then the tiebreak winner cruises in the second–perhaps due to his own momentum, perhaps because the first-set loser stops trying so hard.

And it is fairly common.  Since 2000, about 9% of tour-level best-of-threes are straight set wins in which a tiebreak is followed by a more decisive set.  When the first set is decided by a tiebreak, by far the most frequent outcome (roughly half of these matches) is a straight set victory where the second set is more decisive than the first.

Evidence or forecast?

So what does it mean?  Does winning a first-set tiebreak actually give a player the boost he needs to run away with the second?  Or are first-set tiebreaks evidence that the tiebreak winner was the better player all along, suggesting that we could have forecast the ensuing 6-3 or 6-4 set before the match even started?

We won’t arrive at a clear answer to this question, but we can try to get closer.

To give us some context, let’s start by comparing matches with first-set tiebreaks to the overall pool of best-of-three contests since 2000:

• In best-of-threes, the first-set winner wins in straight sets 66.1% of the time.  If the first set is decided by a tiebreak, the first-set winner takes the match in straights 60.5% of the time.
• In all best-of-threes, the first-set winner wins the second set by at least one break (that is, without needing to play a breaker) 57.1% of the time.  If the first set was a tiebreak, the first-set winner wins the second set by at least one break 50.0% of the time.
• The first set winner loses a best-of-three match 18.0% of the time.  If the first set is decided by a tiebreak, he loses 22.3% of the time.

Clearly, first-set tiebreaks indicate closer matches than average.  (You probably didn’t need me to crunch the numbers to tell you that.)  It’s still far from clear whether the first-set tiebreak gives the winning player a boost, or it simply reflects the balance between the two competitors.

Factoring favorite status

To isolate the effect of player skill, let’s look at matches with first-set tiebreaks, divided into four categories determined by how much the first-set winner was favored:

             Straights  Easy 2nd   Loss  
Underdogs        48.5%     39.3%  33.8%  
Even(ish)        61.2%     51.4%  19.2%  
Favorite         69.4%     57.3%  14.1%  
Extreme Fav      74.1%     62.0%   9.2%

No surprises here.  The more the first-set tiebreak winner is favored, the more likely he is to win the match in straight sets, the more likely he is to win the second set by at least one break, and the less likely he is to lose the match.

More importantly, a bit more crunching of these numbers shows that almost all–at least 80%–of the variation in these three percentages is determined by the relative skill levels of the two players.  It’s possible that a bit of the remainder can be ascribed to the lingering effects of a tight first-set triumph, but only possible, and only a bit.

A story for every sequence

I suggested at the outset that this pattern–7-6, 6-something–seems like a familiar one.  And of course it is, because there are only so many score permutations in best-of-three matches.

When we watch such a match, it’s easy to come up with a narrative that seems universal.  “Federer won the last three points of the tiebreak, leaving Isner looking overmatched.  No one was surprised when Isner got broken for the first time in the following game.”  The simple story accurately reflects at least part of the match, explains the scoreline, and it’s tempting to theorize that (a) Isner’s break was due to his loss of the first-set tiebreak, and (b) players generally suffer an early break in the second set after losing a tiebreak.

Fine.  Except often (just as often?), we have reason to construct another narrative: “Murray won the last three points of the tiebreak, leaving Tsonga looking overmatched.  No one was surprised, though, when Murray came out a bit stale in the second set and got broken for the first time in the following game.”

Some stories reflect actual trends, and that’s why so many of my posts on this site investigate the most popular stories.  But for any given story, it’s more likely than not that it has been constructed simply to give a bit more meaning to underlying randomness.