The Odds of Breaking Back

Perhaps the most unquestioned piece of conventional wisdom in tennis is this: after breaking serve, a player is particularly vulnerable to being broken himself.  It certainly seems to be true–to take just one example, in the Isner/Karlovic match last week, there were only two breaks of serve, and they were consecutive.

As with most bits of conventional wisdom, it’s not clear exactly what people mean by it.  When Djokovic crushes someone 6-0 6-1, do we really think his serve is more vulnerable after each of his five or six breaks than it is after the one game his opponent holds?  When a player does break back, is he then more vulnerable in his next service game?

Today, I’ll try to address the more basic versions of the cliche.  The results are a bit surprising.

The dataset

I’m working with all of the 2011 Australian Open matches from courts where Hawkeye was in place.  That’s about 80 of the men’s singles matches, and roughly the same number of women’s matches.  I’ve run the numbers on both genders but will keep them separate, for reasons that will become clear.

These matches give us over 2,700 men’s games across about 300 sets, and nearly 2,000 women’s games over a bit more than 200 sets.

Breaking back: Men

At this year’s Aussie Open, 24% of all men’s games were service breaks.  If we take the conventional wisdom literally, we would hypothesize that in the game following a service break, another break would occur more than 24% of the time.

But it doesn’t.  In the game following a service break, the server is broken only 19.5% of the time.  (I’m excluding service breaks that end a set or take a set to a tiebreak.)  In other words, in the aggregate, a player is more likely to hold serve after breaking serve than he is after his opponent holds.

Of course, as I suggested by mentioning Djokovic a moment ago, there’s a huge selection bias here.  A player who breaks serve is (all else equal) likely to be a better player than one who doesn’t.  The best players in the most lopsided matches are breaking serve frequently, and because they are the better player, it makes sense that they are more likely (again, all else equal) to hold their own serve.

Without looking at individual matchups, it’s not immediately clear how to address this problem.  For one thing, I’m not convinced it’s a problem.  When Federer broke Kohlschreiber today, a commentator may have said, “Roger is particularly vulnerable here, let’s see if he can consolidate the break.”  One could easily respond: “Roger just showed us he’s in tremendous form; the very fact he just broke serve is an indication that he’s less vulnerable than usual on serve right now.”  And so it proved: Roger broke four times; Kohlschreiber never broke back.

What might be more instructive is to look at situations where the player who broke serve is considered to be roughly equal or inferior to his opponent.  Had Kohlschreiber broken serve early in the match, even given the assumption that he must be playing well in order to do so, the conventional wisdom would suggest that Federer is more likely to break back.  Perhaps that’s true.  It’s not something I can answer today–quantifying the matchups is beyond the scope of this afternoon project.  It’s also problematic in that it would also shrink the size of our already-small dataset.

In any event, it is clear that we can’t take this bit of conventional wisdom at face value.  It may be true in certain scenarios–some players may crumple under the pressure of consolidating a break, and others may rise to the occasion after losing serve.  But it is wrong to say that, in general, players are more vulnerable on serve after a break.

Breaking back: Women

As you might expect, breaks of serve are more prevalent in the women’s game, as are breaks-following-breaks.

At the 2011 AO, women broke serve 36.5% of the time.  In games following breaks of serve, they broke 36.0%.  In contrast to the men’s results, this suggests that in the women’s game, a service break doesn’t tell us as much about the strength of the player who has accomplished the break–or, if it does, that a server is more vulnerable after breaking serve.  Anecdotally, it certainly seems that differences in mental strength play a larger role in WTA matches, so I would expect that the break-back rate would be higher.

As I’ve said, this is far from the final word.  As usual, the conventional wisdom masks many subtleties that only further analysis can unearth.

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2 Comments

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2 responses to “The Odds of Breaking Back

  1. Tom Welsh

    One thing that is in no doubt is that a very good player, having been broken, is very strongly aware of the need to break back as soon as possible – and ideally in the very next game. Psychologically, that is a very powerful counter-stroke: while the exchange of breaks leaves the set equally poised again, the last person to break has the initiative. Break Nadal, Federer, Djokovic or (when he is not out to lunch) Murray, and you will have a fight on your hands. It’s like grabbing a tiger by the tail.

    On the other hand, when a top player breaks one of the things you expect is that he will serve well in the following game. He knows the score, and he is perfectly aware that his opponent is slavering to get a few juicy second serves – or better still a double fault. Even to get into a rally with even chances. So the top player does his level best to prevent any of those outcomes.

  2. First, I appreciate Jeff taking some time to look behind one of the comments which is certainly overused on the air. Just your brief exploration is helpful; whether or not a more full examination would prove anything is unclear, if not doubtful. Tom’s comment on your blog is spot on. It all got me thinking a little more about the intuition behind this sense of imminent peril, and the dynamics at work in television commentators overusing such cliches.
    As players on the court and observers off, all of us have a sense of smell regarding the mental lapses and surges involved in breaks and break-backs. I think most or at least many of the television commentators are very intelligent and qualified to read players as well as to talk tactics, statistics and strokes. The background work done for them and its communication during broadcasts is often informative and sometimes enlightening. That said, however, the nature of how they see their job – using the incredible amount of down time during matches to find some way to keep viewer interest – makes them over-anxious to create a potentially suspenseful moment or hype the dangers in a situation for the clear leader in the match. So when I hear them talk about break back potential, I filter out their hype, assuming their remark wasn’t based on their sense of smell, but on their need to stimulate one in viewers. To the extent that the commentators ‘get away’ with this practice, it is because we are all used to having our own real sense of smell turn out wrong a good portion of the time.
    Does that mean the sense of smell has no more basis than a hunch in a casino roulette game? I don’t think it means that. Such senses are hard-wired into as animals with survival instincts. Our hunches help us prepare for possible disaster and opportunity. Without them, we’d be clueless players and observers, vainly trying to sustain constant momentum with the intensity needed for success, and continuing to play our same game when somehow it should have been clear it wasn’t going to be our lucky day.
    A note re: DOUBLES.
    I’m not sure I’ve heard the cliche used in doubles commentary, where it doesn’t ever feel intuitively the right view. This brings me to the topic of intuiting next breaks, break backs, double faults, etc. I’m not talking about the paranoia of rabid fans of a particular player, who always fear the worst.
    Rick

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