Hot Hand – Heavy Topspin

Do Players Get Broken More Often After Failing to Convert Break Point?

The headline is a bit unwieldy, but it refers to one of the most common nuggets of conventional wisdom in tennis. When a player has the opportunity to break and doesn’t do so, this viewpoint holds that they are more likely to get broken in their following service game.

Like so much conventional wisdom, this assumes that momentum plays a role. Break points are crucial moments, and if a player doesn’t capitalize, the momentum will turn against him. That momentum then carries into the following game, and the player who failed to convert gets broken himself.

Or so the story goes.

However, data from almost 3,000 2013 tour-level and qualifying-round matches suggests the opposite. The likelihood that a player holds serve has almost nothing to do with what happened in the previous game.

Let’s start with some general numbers. To make sure we’re comparing apples to apples, I’ve ignored the first game of every set. This way, we compare “games after missed break point chances” to “games after breaks” to “games after holds.” In other words, we’re only concerned with “games after something.” I’ve also limited our view to sequences of games within the same set, since the long break between sets (not to mention other psychological factors) seem to put those multi-set sequences of games in a different category altogether.

Once those exclusions are made, this set of several thousand ATP matches showed that players got broken in 21.7% of their service games. Compare that to break rates after various events:

after a hold of serve: 22.6%
after a break of serve: 19.3%
after a hold including a missed break point chance: 21.2%
after a hold including three missed bp chances: 20.9%
after a hold including four or more missed bp chances: 19.4%

These are aggregate numbers, not adjusted for specific players, so they don’t tell the whole story. But they already suggest that the conventional wisdom is overstating its case. After failing to convert a break point, players hold serve almost exactly as often as they do in general. In fact, they get broken a bit less frequently in those situations (21.2%) than they do following a more conventional hold without any break points (22.6%).

Let’s see what happens when we adjust these numbers on a match-by-match basis. For example, if Tomas Berdych gets broken by Novak Djokovic 6 times in 15 tries, we can use that 40% break rate as a benchmark by which to measure more specific scenarios. If Berdych fails to convert break point twice, we would “expect” that he gets broken in 40% of his following service games, or 0.8 times in the two games. Of course, no one can get broken a fractional amount of a game, but by summing those “expected” breaks, we can see what the aggregate numbers look like with a much lesser chance of particular players or matchups biasing the numbers.

Once that cumbersome step is out of the way, we discover that–again, but more confidently–there is virtually no difference between average service games and service games that follow unconverted break points.

In my sample of 2013 ATP matches, there were 5,701 service games that followed missed break point opportunities. Players held 4,493 of those games (78.8%). That’s almost precisely the rate at which they held in other games. Had those specific players performed at their usual level within those matches, they would’ve held 4,488 times (78.7%).

We see the same findings when we focus on the most high-pressure games, ones with three or more break points. This sample contained 722 games in which the server held despite three break points. Servers held the following game 571 times. Had they performed at their usual, average-momentum rate, they would’ve held 570 times. After holds with four or more break points (206 in all), servers held 166 times instead of an “expected” 162.

There’s no evidence here that these particular service games have different results than other service games do.

Envoi

Momentum, the basis for so many of the beliefs that make up tennis’s conventional wisdom, is surely a factor in the game, but my research has shown, over and over again, that it isn’t nearly as influential as fans and pundits tend to think.

Once we hear a claim like this one, we tend to notice when events confirm it, reinforcing our mostly-baseless belief. When we see something that doesn’t match the belief, we’re surprised, often leading to a discussion that takes for granted the truth of the original claim. Our brains are wired to understand and tell stories, not to recognize the difference between something that happens 77% of the time and 79% of the time.

It may turn out that some players are unusually likely or unlikely to get broken after failing to convert a break point. Or perhaps this particular sequence of events is more common at certain junctures in a match. But barring research that establishes that sort of thing, there is simply no evidence that momentum plays any role in the service game following unconverted break points.

Jerzy Janowicz and the Frequency of Tiebreak Shutouts

In Marseille this week, Jerzy Janowicz played two dominant tiebreaks. In his second-round win over Julien Benneteau, he put away the first set with a 7-0 breaker en route to a straight-set victory. In the quarterfinals, he won another 7-0 tiebreak to even his match with Tomas Berdych before falling in three.

Amazingly, this is not the first time anyone on the ATP tour has won two tiebreaks by a score of 7-0 in back-to-back matches. It is, however, the first time it’s been done in best-of-3 matches. In 1992, Brad Gilbert won both his 2nd- and 3rd-round contests at the US Open in five sets, winning 7-0 tiebreaks in the 5th set both times. If that’s not a case for fifth-set tiebreaks at slams, I don’t know what is.

Janowicz’s accomplishment and Gilbert’s feat are the only two times anyone on tour has won two shutout breakers in the same event. That’s not much of a surprise, since there are typically fewer than 25 such tiebreaks at tour level per year.

What’s particularly odd here is that Jerzy’s two shutouts weren’t the only ones in Marseille. In the first round, wild card Lucas Pouille was 7-0’d by Benneteau, the same guy who Janowicz victimized first. Weirdly, both losing and winning 7-0 breakers in the same event is slightly more common than winning two. It has happened three times before, most recently at the 2009 Belgrade event by Lukasz Kubot, who shut out Karlovic in a semifinal tiebreak then got 7-0’d by Novak Djokovic in the final.

Finally, while we’re wallowing in trivia, here’s one more. Only once has a player lost two 7-0 tiebreaks at the same event. This is quite the feat, because to pull it off, you have to win the first match despite losing a set in painful fashion. The only man to do it is Simone Bollelli, who beat Dmitri Tursunov in the 2nd round of the 2007 Miami Masters despite losing the first set in a 7-0 tiebreak, then lost in the 3rd to David Ferrer, who threw in another tiebreak bagel on the way to straight-set win.

Rare, but not rare enough

Shutout tiebreaks don’t occur very often, but they occur more often than we might expect. On tour since 1991, there have been 30,259 tiebreaks, and 524 of them–about 1.7%–have been by the score of 7-0. That’s barely more than the number that end 11-9.

However, if we assume that players who reach a tiebreak are reasonably equal, that’s almost double the frequency we would expect. A discrepancy like that has serious implications about player consistency.

The arithmetic here is simple. Say that both players have a 70% chance of winning a point on serve. In order to win a tiebreak 7-0, the player who serves first must win three points serving and four points returning. The probability of pulling that off is about (0.7^3)(0.3^4) = 0.28%. It’s easier if you serve second. You must win four points serving and three returning: (0.7^4)(0.3^3) = 0.65%. In this scenario, both players have equal skills, so each one has the same chance of winning 7-0, and the chance of the breaker ending in a shutout is the sum of those two probabilities, 0.93%.

Of course, this simple model obscures a lot of things. First, players who reach a tiebreak aren’t necessary equal. Just last month, Bernard Tomic got to 6-6 against Roger Federer, and even more recently, Martin Alund played a tiebreak against Rafael Nadal. Second, any competitor’s level of play fluctuates, and some guys seem to fluctuate quite a bit when the pressure is on.

Still, the gap between predicted (no more than 0.93%) and observed (1.7%) is enormous. To predict that 1.7% of tiebreaks would end in a 7-0, we’d need to start with much more extreme assumptions. For instance, if one player is likely to win 77% of serve points and the other only 64% of serve points, the likelihood of a 7-0 tiebreak is 1.7%. Those assumptions also imply that, if each man kept up the same level of play all day, the better player has a 93% chance of winning the match. Perhaps true of Nadal/Alund or even Federer/Tomic, but certainly not Janowicz/Benneteau or Janowicz/Berdych, or most of the other matches that reach a tiebreak.

This is all a roundabout way of saying that–breaking news!–players are inconsistent. Or streaky, or clutch, or unclutch … pick your favorite. Were players machines, 7-0 tiebreaks wouldn’t come around nearly as often. As it is, we shouldn’t expect more from Jerzy for a while … unless Brad Gilbert is planning a comeback.

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.