Category Archives: Tiebreaks

April 12, 2013 · 10:27 am

Robin Haase’s Unlucky 13 Tiebreaks

Yesterday, Robin Haase lost a second-set tiebreak to Kenny De Schepper, a mere blip en route to a three-set victory and a place in the Casablanca quarterfinals.  However, it was yet another set-ending failure for the Dutchman, who has now lost thirteen consecutive tour-level tiebreaks.  And another reason to hate Casablanca.

Yes, thirteen.  No other active player has a streak of more than seven, and no tour-level regular has lost more than his last six.  In fact, Haase is now one lost tiebreak away from tying the all-time ATP record of 14, jointly held by Graham Stilwell and Colin Dibley, two players who accomplished their feats in the 1970s.

As I’ve shown before, tiebreak outcomes are rather random. Aside from a small minority of players with extensive tiebreak experience (such as Roger Federer, John Isner, and Andy Roddick), ATP pros tend to win about as many breakers as “expected.” The good players win more than average, the not-so-good players win fewer than average, but there are few players who seem to have some special tiebreak skill–or a notable lack thereof.

It would be premature, then, to read too much into Haase’s streak.  After all, the last fifteen months haven’t been particularly bad for him in general.  When he last won a tour-level tiebreak, in January of last year, he was ranked 62nd in the world.  Now he is #53, and he will pick up another few spots next Monday.  This despite winning only two of the matches in which he lost one of his consecutive tiebreaks.

If history is any guide, the Dutchman will probably turn things around.  Dibley won six of the 10 breakers that followed his streak, and Stilwell won four. Nikolay Davydenko and Thomas Johansson, two otherwise excellent players who lost 13 tiebreaks in a row, each won 5 of their next 10.  More remarkably, the already-missed Ivan Navarro followed a 10-tiebreak losing streak with a 8-2 record in his next 10.

In the ATP era, 43 players have suffered tiebreak losing streaks of 10 or more (full list after the jump).  32 of those have gone on to play at least 10 more.  Naturally, every tiebreak that follows a losing streak is a win, or else it would be considered part of the streak.  In the nine tiebreaks that follow the streak-breaking win, those 32 players won 134 of 288 tiebreaks, or 46.5%.

While the numbers don’t exactly presage Isnerian greatness for Haase, even a return to his pre-streak tiebreak winning percentage of 41% would be welcome.  Fortunately, that’s much more likely than another 13 losses in a row.

Update: In the Barcelona first round, Haase tied the record, losing a third-set tiebreak to Pablo Carreno-Busta.  On May 6, he lost a tiebreak in the second set of his Madrid first-round match against Alexander Dolgopolov to set a new all-time record of 15 straight lost tiebreaks.

Update 2: On 8 May, Haase lost to Jo-Wilfried Tsonga, 7-6 7-6. (How else?) That’s 17 straight tour-level tiebreaks lost.  The all-time tiebreak winning streak is 18, held by Andy Roddick.

Update 3: On 27 May, in the second set of his first round match at Roland Garros, Haase WON A TIEBREAK. The historical event came against Kenny de Schepper, the Frenchman who appears in the first line of this post.

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February 23, 2013 · 11:21 am

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.

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Filed under Hot Hand, Jerzy Janowicz, Records, Tiebreaks

November 6, 2012 · 11:34 am

The Influence of a First-Set Tiebreak

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.

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Filed under Hot Hand, Tiebreaks

October 30, 2012 · 11:13 am

The Structural Biases of Tiebreaks

There is more to tiebreaks than meets the eye. As we’ve learned recently, big servers don’t seem to have an advantage in tiebreaks over more balanced players, and very few professionals win more tiebreaks than we would expect them to.

In one of those discussions, commenter Håkon Mørk raised a related issue. Is the format of the tiebreak itself biased toward certain types of players? That is: Who benefits by playing tiebreak sets instead of “deuce” sets in which one player must win by a margin of two games?

When we put the question this way, it is straightforward. The primary beneficiaries of the tiebreak format are underdogs.

Think of it this way. The better player is likely to win, regardless of the format. The bigger the margin of victory required, the more likely the better player is to win. If Kenny De Schepper were to play a single tiebreak against Roger Federer, he’d have a decent chance of winning. But in a full-length set, that chance would be much lower. In a best of three match, lower still. Best of five: even lower. Best of five with no tiebreak in the final set: lowest of all.

Any change in the format of a tennis match that causes the match to hinge on fewer points gives the underdog a greater chance of lucking his way into victory.

On average, the underdog’s benefit from tiebreak sets isn’t much, compared to a hypothetical world in which the ATP played only deuce sets. For an individual set in the average tour-level 2012 match, the underdog’s chance of winning was 1.3% higher in a tiebreak set than they would have been in a deuce set.

But there’s more to the story. First of all, matches that are very close (in which both players win about 50% of points) drag down the average, since when the players are evenly matched, the format doesn’t matter — 50% is 50%. Second, matches that are very lopsided also drag down the average–if one player dominates, he has a very high percentage chance of winning a set regardless of the format.

Thus, in a somewhat closely (but not too closely) contested match, the underdog gains quite a bit more from the tiebreak format.

Structural biases

In some of these matches, the gain is much more than in others.

In fact, in six matches this year, the difference between the winner’s chance of winning a deuce set would have been more than ten percent greater than his chance of winning a tiebreak set.

(All of the chances I’m referring to are derived by calculating the winner’s winning percentages on serve and retun points, then running those through my set probability python code, which now provides an option for the probability of winning deuce sets.)

Two of the three most extreme such matches this year (and five of the top 14) were won by–could it be anyone else?–John Isner.

The most extreme case is Isner’s match against Janko Tipsarevic in the London Olympics. Isner won 84.7% of service points and 23.3% of return points, ultimately taking the match 7-5, 7-6(14). Those percentages translate to a 71.1% chance of winning a tiebreak set or an 84.1% chance of winning a deuce set.

If you were Isner, which would you prefer?

Compare that to a match between Jo Wilfried Tsonga and Xavier Malisse at the Miami Masters, which Jo won 7-5 7-5. This match went very differently than Isner-Janko. Tsonga won 68.1% of service points and 43.1% of return points. Those would give the Frenchman an 84.1% chance of winning a deuce set (sound familiar?) or an 82.7% of winning a tiebreak set.

This is just another illustration that fewer pivotal points gives the underdog a better chance. To win a tiebreak against Isner, you need to win one point against his serve (as long as you hold your own). To break an Isner service game, you need to win at least four.

Thus, an extreme big server like Isner appears to suffer from the tiebreak format. If the ATP went back to playing every set as a deuce set, he would have a much better chance of avoiding the lucky upset when he posts stats like those of the Janko match.

The big-serving underdog

There’s still more to this story. As we’ve seen, underdogs benefit from the tiebreak format: A structure with fewer points is more susceptible to luck. And big servers seem to be hurt by the tiebreak format.

What about when big servers are underdogs?

The tiebreak format isn’t biased against big servers, it’s biased against big servers who are better than their opponents. In matches already decided by a small number of points (like a couple of break points or minibreaks in an Isner-Federer match), the underdog benefits from playing tiebreaks.

And when one player has the big-serve/weak-return package, he effectively turns the other player into a bigger server and weaker retuner. We don’t usually think of Philipp Kohlschreiber as a big server, but when he played the serve-and-volleying Dustin Brown in Halle this year, he won 82.1% of service points and only 29.9% of return points. That type of match hinges on a very small number of points, and as such, gives the underdog a greater chance to pounce.

More mathematically speaking, the degree of the advantage given to the underdog by playing tiebreak sets is positively correlated with the overall percentage of service points won.

This presents something a conundrum for the big server. His style of play is beneficial in tiebreak sets while he is the underdog, but it becomes a hindrance once he is the favorite. When so many matches are decided by a single break or even a couple of minibreaks, a big-serving, weak-returning favorite will lose more than his share of matches he “should have” won, simply because of the way he plays.

One solution for such players is to win more tiebreaks than the numbers would suggest they should, as Isner does. Another tactic, of couse, is to hit better returns.

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Filed under John Isner, The Rules, Tiebreaks

October 22, 2012 · 11:29 am

Responding to Pressure at 5-5

In a post last week, I presented some data that suggested that servers weaken a bit under the pressure of a tiebreak.  It’s not a strong effect, but it’s a consistent one.  A possible explanation–that all that time between points gives servers a chance to psych themselves out, yet may not affect returners the same way–would apply almost as much to games toward the business end of a set, such as at 5-5 or 5-6.

In other words, if players don’t serve as well (or they return better) when things get tight, we’d expect to see more breaks toward the end of a set–more breaks than expected at 5-5, but perhaps fewer breaks than expected at 2-2.

This also opens up a possible method for evaluating players, as Carl Bialik has suggested.  If someone is losing more sets 5-7 than they are winning 7-5, it may be that they are wilting under the pressure of 5-5 more than the average player.  It would make sense if the players who consistently exceed tiebreak expectations also regularly outperform 7-5 expectations as well.

Within the constraints of the ATP’s Matchstats, 7-5 sets are a great way to identify these patterns.  While some 6-4 sets end with a break (or a break followed by a set-sealing hold), a 6-4 set doesn’t necessarily end that way.  But a 7-5 set must have reached 5-5 before one player took control.

If the hypothesis is correct that players get tighter on serve as the end of the set approaches, we would expect more 7-5 sets in the real world than simulations would imply.

To estimate the number of sets that should end 7-5, we need to take each player’s service points won from each match.  With that, we can calculate the probabilities that sets will end at any given score.  Repeat the process for every match over a period of time and we get a general idea of how often we should see 7-5 sets.

As it turns out, 7-5 sets should make up about 7.8% of all sets.  In fact, 8.8% of sets end 7-5.  Not a huge difference, but one that is fairly consistent from year to year.  Every year since 1991, where this dataset begins, there have always been more 7-5s than expected.  It certainly adds more weight to the claim that the balance of power swings to the returner toward the end of a tight set.

(My set-prediction model doesn’t exactly replicate reality, since players win more games than their service winning percentages predict, in large part because almost all servers are better in either the deuce or ad court, and the variance between them makes it more likely that the player wins a given service game.  When applying a crude adjustment for this, the crumbling-server hypothesis looks even better–the more games servers are predicted to win, the fewer predicted 7-5 sets.)

Identifying the unbreakable

This type of discussion must make you wonder: Which players are good as this stuff?  If it is true that late-set pressure results in more breaks, it seems obvious that some players are more prone to that pressure, and that other players take advantage of that pressure.

In an ideal world, we’d be able to identify some great 7-5 records, point out some 5-7 records, and have some great new insights into players.

As it is … we might.

As we saw last week with tiebreak analysis, we can’t simply count up a player’s 7-5 sets and compare that total to his 5-7 set losses.  Over the last three years, Andy Roddick won more than 55% of his 7-5 and 5-7 sets, but given the players he faced in those sets and their performances in those matches, he should have won 62%.

There are two ways to quantify player accomplishments in this department.  The first evaluates how well a player avoids losing 5-7 when he reaches 5-5; the other compares his ability to break for 7-5 against his proneness to being broken for 5-7.

Let’s call the first stat Five-Seven AVoidance, or FSAV.  For any player, we first add up the sets that reached 5-5, then count the sets that he won 7-5 or reached a tiebreak.  Then we use the general method described above to estimate how many times the player should have reached 5-5, and how many of those times he should have avoided 5-7.   Since the beginning of 2010, Kei Nishikori has avoided a 5-7 finish in about 92% of the sets in which he reached 5-5.  My model would have expected him to avoid 5-7 only about 84% of the time.  (The model expects that most players will avoid 5-7 about 82-90% of the time they reach 5-5.)

From those numbers, we discover that Nishikori lost 5-7 less than half as often as we would have expected him to.  No other player comes close to that mark. In everyday language, FSAV approximates how often a player was able to hold serve at 5-5 or 5-6.  Important skill, that.

The second stat is more narrowly focused on 5-5 sets that do not reach a tiebreak.  Let’s call this one the Seven-Five Outperformance Rate, or SFOR, similar to the TBOR (TieBreak Outperformance Rate) I introduced last week.

Here, instead of comparing 5-7s to all 5-5 sets, we compare 5-7s to 7-5s.  In other words: Is the player more likely to break for 7-5 or be broken for 5-7?  As with the previous stat, after calculating the simple rate (that is, number of 7-5 sets divided by total number of 7-5 and 5-7 sets), we compare that to the results that the model would have expected the player to post.

Bizarrely enough, our three-year leader in SFOR is Ernests Gulbis, who has won about 73% of his 7-5 and 5-7 sets, compared to the 50% the model expects of him.  (It’s even more impressive when compared to the 7% that I personally would have expected from him.)

As the highlighting of Gulbis suggests, these stats probably don’t yet belong in our everyday toolbox.  There simply aren’t very many 7-5 sets, even if–as I established above–there are a few more than we would expect.  For reference, there are almost twice as many tiebreaks as 7-5s.

And to keep Gulbis in the spotlight, it may be that winning 7-5 sets is more a function of getting to 5-5 when you shouldn’t.  Perhaps many of those 7-5s racked up by the Latvian came when he should have put the set away 6-2.  Once 5-5 came along, he finally decided to get serious.  As Gulbis himself might tell you, it’s anybody’s guess.

Follow the jump for FSAV and SFOR on about 50 or so of the most active players (including all tour-level matches (but excluding Davis Cup) since the beginning of 2010, sorted by FSAV) and decide for yourself.

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October 18, 2012 · 12:55 pm

The Luck of the Tiebreak

Yesterday, I introduced a method to separate “good tiebreak playing” from “good tennis playing.”  For the most part, better players win more tiebreaks, but some guys win more tiebreaks than their general betterness would suggest.

That impels some questions: Why do those players win more tiebreaks than expected?  Do they do so regularly?  Is it their style of play?  Is it magical tiebreak-fu?  Is it possible to get through two paragraphs of a post about tiebreaks without mentioning John Isner?

Here are two hypotheses, which I will discuss in turn:

  1. Players who win more tiebreaks than expected do so because their game is suited to tiebreaks–which probably means that they serve particularly well.
  2. Player who win more tiebreaks than expected do so because, in some intangible way, they are very good at tiebreaks, perhaps due to clutch play, calm under pressure, or intimidation of their opponents.

The server advantage hypothesis

Earlier this week, I reported my results that players seem to serve worse (fewer aces, fewer points won) in tiebreaks than in the sets that preceded those tiebreaks.  If everyone declined the same amount, everyone would win roughly the number of tiebreaks we expect of them.

But much more likely, some players do not see their serves decline in tiebreaks.  Some might even improve in breakers.  If they do, they outperform the average, and they win more tiebreaks than expected.

Another angle here is that for some players, a bit of serve decline doesn’t matter much.  In last week’s match between Isner and Kevin Anderson, Isner won 79% of service points and Anderson won 77%.  Nearly one in five serves for the entire match went for aces–imagine how many more were service winners.  If both players served a bit more conservatively in the breakers, would we even notice?  When Fernando Verdasco starts playing it safe, it’s impossible not to notice–and easier to beat him in a breaker.  Perhaps that isn’t so for the likes of Isner.

These are appealing theories.  (Especially to me–I thought them up myself and believed in them for several hours.)  However, the numbers don’t bear them out.  There is no consistent statistical relationship between big serving and outperforming tiebreak expectations.  To take a few examples: Isner is a tiebreak monster–probably the best tiebreak-player of this generation.  Pete Sampras and Roger Federer are also among the greats.  Below average, though, are the likes of Ivo Karlovic, Sam Querrey, Marc Rosset, and Robin Soderling.

Let’s try another…

The intangibles hypothesis

If there is some intangible mental factor that causes some players to win more tiebreaks than they would otherwise, it’s impossible to test for that effect directly–if it were possible, it wouldn’t be intangible.

But, if some players had that tiebreak-fu, they would probably hold on to it for more than a single season.  For instance, when Novak Djokovic won an impressive 19% and 16% more tiebreaks than expected in 2006 and 2007, respectively, we should have been able to assume that he’s really good at tiebreaks, then predict that he would continue to excel in breakers in 2008.  Yet in 2008, 2009, and 2010, Djokovic barely outperformed average, winning 2% or 3% more than expected.  Ok, so we have a new forecast for Novak in the new decade: just a bit more tiebreak-magic than others.  Yet in 2011, Djokovic won 10% fewer tiebreaks than expected.  He’s 9% below average this year.

Sometimes, these changes might be explained by confidence.  But more often, they are just plain random.  While a few players (including Isner and Federer) put up great numbers every year, the vast majority of the field fluctuates, seemingly at random.  The year-to-year correlation for the population of players with at least 15 tiebreaks in two consecutive years (going back to 1991) is almost exactly zero.  (Set the bar higher if you wish; still barely distinguishable from zero.)

If tiebreak-related intangibles were widespread, there would be some kind of year-to-year correlation.  Perhaps a small number of players do have that magic, but for the purposes of most analysis, it is more accurate to assume that when it comes to a player’s overperformance in tiebreaks, his record one year has very little to do with how he’ll perform the next.

One tiny ray of light

This gets a bit frustrating after a while.  It seems that something should turn up as the cause of tiebreak excellence.  One simple stat does, to a small degree: number of tiebreaks played.  In other words, the guys who play the most tiebreaks tend to be the ones who beat expectations in those tiebreaks.

The connection that immediately springs to mind (after serving prowess, which we’ve already discarded) is practice.  The more match-court breakers you play, the better you become.  Isner, Federer, Sampras–they spend more time at 6-6 than almost anyone, and their tiebreak records are among the best.

Of course, the causation could go the other way.  Perhaps confidence in one’s tiebreak skills cause a player to be more comfortable going to a breaker.  While Djokovic or Andy Murray would press particularly hard for a break a game away from a 6-4 or 7-5 set, Isner is comfortable cruising into a tiebreak.

It’s a minor effect (r < 0.2), one that doesn’t explain anywhere near the observed year-to-year variance in tiebreak under- and over-performance.  But it’s something.

The implications of the luck of the tiebreak

What if overperforming or underperforming your expected tiebreak performance is, essentially, luck?  Or more generally (and safely) speaking, what if it says little about you likelihood of being good or bad at tiebreaks in the future?

For one thing, it would have a major impact on forecasting.  If tiebreak performance one year doesn’t predict tiebreak performance the next, players with extreme under- or over-performances one year can be expected to regress to the mean the following year.  It’s unclear exactly what that would mean in practice, but if you take away Feliciano Lopez‘s five tiebreaks more than expected in 2011, you’re left with a player who probably isn’t ranked within the top 20.  You would expect a decline as he stops winning quite so many breakers.

On a more practical level, these implications might aid the confidence of players with middling tiebreak records.  If you’re Andreas Seppi, who has a career losing record in breakers, you might be excused for some negativity when you reach 6-6 against, say, Karlovic.   But if you know your own poor record is only loosely related to your skills, and Karlovic’s record isn’t nearly as good as it looks, you might take a different approach.  Indeed, Seppi underperformed tiebreak expectations every year from 2006 to 2011, but has won more than expected this season–including one breaker each against Djokovic and Isner.

There’s plenty more work to do here–calling a couple of popular hypotheses into question hardly puts the issue to bed.  But if we’ve learned nothing else this week, it is that tiebreaks are not at all what they seem.  The players you think are masters are often middling performers, and regardless of the conventional wisdom, the breaker is about a whole lot more than a big serve.

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October 17, 2012 · 12:58 pm

Who Actually Excels in Tiebreaks?

I’ve never understood the fixation that some fans and commentators seem to have with tiebreak winning percentage.  Sure, winning tiebreaks is nice, but it seems obvious that the main cause of exemplary tiebreak performance is being good at tennis.  Though some players may in fact be better than others at this facet of the game, a big part of what tiebreak winning percentage tells us is about general tennis skill.

In other words, Roger Federer is very good at tiebreaks because he is very good at serving and returning, the same skills that get him so many wins, regardless of whether any of the sets go to tiebreaks.

If we ignore tiebreak winning percentage, what are we left with?  It’s still tempting to wonder whether some players have a kind of special skill–calm under pressure, a particularly consistent serve–that leads them to outperform expectations in breakers.

The key word there is “expectations.”  Given Federer’s general ability on the tennis court, we should expect him to win most tiebreaks–for example, two of the last three breakers he’s played came against Stanislas Wawrinka, who he should beat regardless of the format.  But our intuition will fail us if we look at Federer’s match record and try to estimate how many tiebreaks he should have won, then compare the “should” to the “did.”

Expected tiebreaks

Sounds like something computers do better than humans.  Given a player’s percentage of service and return points won in a certain match, we can estimate how likely he was to win a tiebreak–on the assumption that his performance level stayed the same throughout the match.

If two players are equally matched, each one would be “expected” to win 0.5 tiebreaks.  That’s nonsensical for a single match, but over the course of this season, we see that of John Isner‘s 53 tiebreaks, the algorithm would expect him to win 29.  In fact, he has won 38, exceeding expectations (in raw terms, anyway) more than anyone else on tour this year.

This gives us two stats that offer more insight into a player’s tiebreak performance than “tiebreaks won” and “tiebreak winning percentage.”  The raw number, the difference between actual tiebreaks won and expected tiebreaks won, tells us how many additional sets a player has taken because of his tiebreak performance.  Call it TBOE: TieBreaks Over Expectations.  A similar rate stat is derived by dividing TBOE by the number of tiebreaks, allowing us to compare players regardless of how many tiebreaks they played.  Call that one TBOR: TieBreak Outperformance Rate.

As we’ve seen, Isner is the 2012 king of TBOE, performing well in tiebreaks and playing far more of them than anyone else on tour.  Yet three players–Steve Darcis, Andy Murray, and Jurgen Melzer–have done better by TBOR, exceeding expectations at a greater rate than Isner has.  Darcis is particularly remarkable, winning 16 of his 19 tiebreaks through last week, despite his serve and return rates in those matches suggesting he should have won only 10 of them.

(And in Vienna on Monday, he won another one, extending his already untouchable lead over the pack.)

I’ll have more to say about this tomorrow, including a look at just how much meaning we can extract from TBOE and TBOR.  In the meantime,  look after the jump for the current 2012 leaderboard–through Shanghai, sorted by TBOR, minimum 15 tiebreaks.

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October 16, 2012 · 12:44 pm

What Matters in Tiebreaks?

Players and fans tend to look at tiebreaks as a unique part of the sport of tennis, perhaps one susceptible to special skills.  The ATP website last week devoted an article to what those skills might be.  Players generally seemed to agree that it was nice to have a good serve, and a good return would also be handy.  Clearly, more analysis is needed.

Let me give you my hypothesis.  Tiebreaks are pressure packed, and pressure can affect any part of a player’s game.  But in general, they should impact some parts more than others.  You could make the case for either side of the ball–on the one hand, serving is a more “automatic” activity; on the other, there’s more time to think before each serve, and thinking can be dangerous when the pressure is on.  This is where it’s nice to have some data.

I found 388 tiebreaks from the last eight ATP slams.  For each one, I compared each player’s winning percentage on serve during the first 12 games of the set to his winning percentage on serve during the tiebreak.  If players were robots, there might be a difference between the set and the tiebreak for any given match, but in general, the numbers should be the same.

But players aren’t robots.  As it turns out, players win more return points than expected during tiebreaks.  The difference is noticeable if not enormous: about one more return point than expected every three matches.

Thus, tiebreaks are different from the sets that precede them in one of two ways.  Either some players are unable to serve up to their usual standard during tiebreaks, or some players manage to raise their return game in tiebreaks.

A breakdown by tournament suggests the answer.  The difference between server winning percentage in sets and tiebreaks is about the same for the Australian Open, the US Open, and Wimbledon, but is less than half as much at the French.  It seems, then, that faster courts give returners a bigger boost in the breaker.  A more likely interpretation is that servers are unable to hold on to their advantage on faster courts.  There’s less of an advantage to lose on clay.

My hypothesis at the outset focused on pressure, and combined with the numbers, it suggests that players are more affected by pressure when serving than when returning.  It’s also possible that players find it more difficult to get into a serving rhythm with only two serve points at a time.  It’s also possible that returners are less likely to concede aces during tiebreaks, meaning that the same serve quality and return potential results in more return points won.

Whether it is a matter of server timidity or returner aggression, there are certainly fewer aces in tiebreaks.  In these 388 tiebreaks, there were 83 fewer aces than would be expected if players kept acing at the rate of their first twelve games.  Given the relative infrequency of aces, that’s a more striking decrease than that of service winning percentage in general.

This analysis is hardly the final word.  But for aspiring tiebreak masters, it does offer a slightly more specific prescription than “get better at tennis.”  Rather than assuming that the tiebreak is all about the serve, recognize that returners have a slight advantage.  On serve, players can improve simply by ignoring the pressure (easy, right?) and serving as well as they did during the set.  When returning, players can be more aggressive in the knowledge that in general, servers will not be.

After all, a good serve may be the key to tiebreak success, but only if the serve is as good as usual in the breaker.

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