Category: Tiebreaks

The Dreaded Deficit at the Tiebreak Change of Ends

Italian translation at settesei.it

Some of tennis’s conventional wisdom manages to be both blindingly self-evident and obviously wrong. Give pundits a basic fact (winning more points is good), add a dash of perceived momentum, and the results can be toxic.

A great example is the tiebreak change of ends. The typical scenario goes something like this: Serving at 2-3 in a tiebreak, a player loses a point on serve, going down a minibreak to 2-4. As the players change sides, a commentator says, “You really don’t want to go into this change of ends without at least keeping the score even.”

While the full rationale is rarely spelled out, the implication is that losing that one point–going from 2-3 to 2-4–is somehow worse than usual because the point precedes the changeover. Like the belief that the seventh game of the set is particularly important, this has passed, untested, into the canon.

Let’s start with the “blindingly self-evident” part. Yes, it’s better to head into the change of ends at 3-3 than it is at 2-4. In a tiebreak, every point is crucial. Based on a theoretical model and using sample players who each win 65% of service points, here are the odds of winning a tiebreak from various scores at the changeover:

Score  p(Win)  
1*-5     5.4%  
2*-4    21.5%  
3*-3    50.0%  
4*-2    78.5%  
5*-1    94.6%

It’s easy to sum that up: You really want to win that sixth point. (Or, at least, several of the points before the sixth.) On the other hand, compare that to the scenarios after eight points:

Score  p(Win)  
2*-6     2.6%  
3*-5    17.6%  
4*-4    50.0%  
5*-3    82.4%  
6*-2    97.4%

At the risk of belaboring the obvious, when the score is close, points become more important later in the tiebreak. The outcome at 4-4 matters more than at 3-3, which matters more than at 2-2, and so on. If players changed ends after eight points, we’d probably bestow some magical power on that score instead.

Real-life outcomes

So far, I’ve only discussed what the model tells us about win probabilities at various tiebreak scores. If the pundits are right, we should see a gap between the theoretical likelihood of winning a tiebreak from 2-4 and the number of times that players really do win tiebreaks from those scores. The model says that players should win 21.5% of tiebreaks from 2*-4; if the conventional wisdom is correct, we would find that players win even fewer tiebreaks when trying to come back from that deficit.

By analyzing the 20,000-plus tiebreaks in this dataset, we find that the opposite is true. Falling to 2-4 is hugely worse than reaching the change of ends at 3-3, but it isn’t worse than the model predicts–it’s a bit better.

To quantify the effect, I determined the likelihood that the player serving immediately after the changeover would win the tiebreak, based on each player’s service points won throughout the match and the model I’ve referred to above. By aggregating all of those predictions, together with the observed result of each tiebreak, we can see how real life compares to the model.

In this set of tiebreaks, a player serving at 2-4 would be expected to win 20.9% of the time. In fact, these players go to win the tiebreak 22.0% of the time–a small but meaningful difference. We see an even bigger gap for players returning at 2-4. The model predicts that they would win 19.9% of the time, but they end up winning 22.1% of these tiebreaks.

In other words, after six points, the player with more points is heavily favored, but if there’s any momentum–that is, if either player has more of an advantage than the mere score would suggest–the edge belongs the player trailing in the tiebreak.

Sure enough, we see the same effect after eight points. Serving at 3-5, players in this dataset have a 16.3% (theoretical) probability of winning the tiebreak, but they win 19.0% of the time. Returning at 3-5, their paper chance is 17.2%, and they win 19.5%.

There’s nothing special about the first change of ends, and there probably isn’t any other point in a tiebreak that is more crucial than the model suggests. Instead, we’ve discovered that underdogs have a slightly better chance of coming back than their paper probabilities indicate. I suspect we’re seeing the effect of front-runners getting tight and underdogs swinging more freely–an aspect of tennis’s conventional wisdom that has much more to recommend itself than the idea of a magic score after the first six points of a tiebreak.

Does Serving First in a Tiebreak Give You an Edge?

Italian translation at settesei.it

Tiebreaks are so balanced, with frequently alternating servers and sides of the court, that it seems they must be fair. As far as I know, there is no commonly-cited conventional wisdom to the effect that the first server (or second server) in a tiebreak has any kind of advantage.

Let’s check. In a dataset of over 5,200 tiebreaks at ATP tour events, the first server won 50.8% of the time. Calculating each player’s service points won for the entire match and using those numbers to determine the likelihood that the first server would win a tiebreak, we get an estimate that those first servers should have won only 48.8% of them.

Two percentage points is a small gap, but here, it’s a meaningful one. It’s persistent across each of the three years most heavily represented in the dataset (2013-15), and it holds regardless of the set. While there might be some bias in the results of first-set tiebreaks, since better servers often choose to serve first and lesser servers choose to receive, the effect in each set favors the first server, and the impact of serving first is greater in the third set than in the first.

However, this effect–at least in its magnitude–is limited to ATP results. A survey of 2,500 recent WTA tiebreaks shows that first servers have won 49.7% of tiebreaks, compared to 49.4% that they should have won. Women’s ITF matches and men’s futures matches return similar results. Running the same algorithm on 6,200 men’s Challenger-level tiebreaks confuses the issue even further: Here, first servers won 48.1% of tiebreaks, while they should have won 48.7%.

A byproduct of this research is the discovery that, for both genders and at multiple levels of the game, the first server in a tiebreak is, on average, the weaker player. At first glance, that doesn’t make a lot of sense: We think of tiebreaks as deciding sets when the two players are equal. And since the effect is present for the second and third sets as well as the first, this finding isn’t biased by players choosing who will serve first.

As it turns out, this result can be at least partially explained by another byproduct of my recent research. In my attempt to determine whether it’s particularly difficult to hold when serving for the set, I calculated the odds of holding serve at every score throughout a set, compared to how frequently players should have held. At most holds–including those with the set on the line–there aren’t any major discrepancies between actual hold rates and expected hold rates.

But I did find some small effects that are relevant here. In general, it is a bit harder to hold serve as the second server, at scores such as 3-4, 4-5, and 5-6, than as the first, at scores like 3-3, 4-4, and 5-5. For instance, in the ATP data, players hold serve at 4-4 exactly as often as we would expect them to, based on their rate of service points won throughout the match. But at 4-5, their performance drops to 1.4% below expectations. In the WTA data, while players underperform at 5-5 by 1.4%, they are far worse at 5-6, winning 5.2% less often than they should.

In other words, if two players of equal abilities stay on serve for the first several games of a set, the second server is a little more likely to crack, getting broken and losing the set. Thus, if neither player is broken (or the number of breaks is equal), the second server is likely to be just a little bit better.

That explains, at least in part, why second servers are favored on paper going into tiebreaks. What it doesn’t account for is the discovery that on the ATP tour, first servers overcome that paper advantage and win more than half of tiebreaks. For that, I don’t have a good answer.

Nick Kyrgios, Young Jedi of the Tiebreak

Italian translation at settesei.it

At Wimbledon this year, 19-year-old rising star Nick Kyrgios has shown himself to be impervious to pressure. In his second round upset of Richard Gasquet, he tied a Grand Slam record by surviving nine match points. Against Rafael Nadal, he withstood perhaps the best clutch player in the game. Despite Nadal’s stature as one of the best tiebreak players in the game, the Australian won both of the tiebreaks they contested.

As I’ve shown in other posts, tiebreaks are–for most players–toss-ups. Better players typically win more than 50% of the tiebreaks they play, but that’s because they’re better players, not because they have some tiebreak-specific skill. Only a very few men–Nadal, Roger Federer, and John Isner are virtually alone among active players–win even more tiebreaks than their non-tiebreak performance would indicate.

Kyrgios is making a very strong case that he should be added to the list. In his career at the ATP, ATP qualifying, and Challenger levels, he’s won 23 of 31 tiebreaks, good for an otherworldly 74% winning percentage. Isner has never posted a single-season mark that high, and Federer has only done so twice.

Nick isn’t playing these matches against weaker opponents, and he isn’t cleaning up in non-tiebreak sets. (Too many scores like 7-6 6-1 might suggest that he shouldn’t have gotten himself to 6-6 in the first place.) Based on Kyrgios’s serve and return points won throughout each match, a tennis-playing robot would have had a 52% chance of winning each tiebreak.

Given those numbers, it’s extremely likely that Kyrgios is one of the outliers, a player who wins many more tiebreaks than expected. There’s only a 1% chance that his excellent winning percentage is purely luck. We can be 95% sure that a tiebreak winning percentage of 58% or better is explained by skill, and 90% sure that his tiebreak skill deserves at least a winning percentage of 62%.

Either one of these more modest figures would still be excellent. Milos Raonic, his quarterfinal opponent and a player who represents an optimistic career path for Kyrgios’s next few years, has posted a 58% tiebreak winning percentage at tour level. Tomorrow’s match won’t be enough to prove which player is better in these high-pressure moments, but given each man’s playing style, it’s almost certain that we’ll see Kyrgios tested in another batch of tiebreaks.

The Luck of the Tiebreak, 2013 Edition

Another year, another new set of tiebreak masters.

Despite the conventional wisdom, very few players demonstrate any kind of consistent tiebreak skill over and above their regular, non-tiebreak tennis playing ability.  In other words, while someone like Novak Djokovic is bound to win well over half of the tiebreaks he plays–after all, he’s better than almost everyone he faces–there’s no secret sauce that allows him to win any more than his usual skill level would suggest.

Nowhere is this more evident than in this year’s top tiebreak performers.  I calculated the likelihood of each player winning every tiebreak they played this year, given their typical rates of serve and return points won, giving us a ranked list of those players who most exceeded and most underperformed expectations.  At the top of the list, names like Roberto Bautista Agut, Dmitry Tursunov, Marin Cilic, and Leonardo Mayer.

Maybe Bautista Agut is a clutch monster just waiting for recognition, but it’s more likely he just had a few bounces go his way.  Cilic is an excellent example: While he won 54% more tiebreaks than expected this year, 2013 was only the second season of the last six in which the Croat exceeded expectations in tiebreaks.  Whether tiebreak performance is clutch skill or simply luck, the numbers show that it isn’t persistent.

However, as I’ve noted before, a very few players do consistently outperform tiebreak expectations.  They tend to be players who find themselves in tiebreaks often, and their success may be because they manage to maintain their serve at its usual level.

John Isner and Roger Federer are the usual suspects.  Isner won 20% more tiebreaks this year than expected, in line with his numbers in 2011 and 2012.  (In 2009 and 2010, he was even better.)  Federer beat expectations by 10%, avoiding his first neutral-or-worse season since 2003 by winning a pair of breakers against tough opponents at the Tour Finals in London.

With another year’s worth of data in the books, we can safely add one more active player to this elite group.  Rafael Nadal was fifth overall this year, winning 23% more tiebreaks than expected.  Nadal hovered around the neutral level until 2008, winning almost exactly as many breakers as his overall skill level would suggest.  But since then, he has had only good tiebreak seasons.  No other player besides Isner and Federer has posted more than four better-than-expected tiebreak seasons in the last six.

For the rest of the ATP, it’s best to look at these numbers as indexes of luck.  The men at the top will probably have to win more non-tiebreak sets next year to maintain their ranking, while the guys at the bottom can expect a modest boost with just a little less bad luck.  That is, unless they play too many tiebreaks against John Isner.

—

The complete list of 2013 tiebreak performance is below.  ‘TBOE’ is “Tiebreaks Over Expectations,” the difference between the number of tiebreaks my algorithm expects a player to win and the number he actually won.  ‘TBOR’ is a rate version of the same stat, calculated by dividing TBOE by the total number of tiebreaks played.  TBOE rewards players like Isner who play lots of tiebreaks and play them well, while TBOR identifies those who have been particularly lucky in whatever number of tiebreaks they contested.

Player                  TB  TBWon  TBExp  TBOE    TBOR  
Roberto Bautista Agut   21     16   10.3   5.7   27.0%  
Dmitry Tursunov         21     16   10.4   5.6   26.8%  
Marin Cilic             15     11    8.2   2.8   18.7%  
Leonardo Mayer          15      9    6.8   2.2   14.9%  
Rafael Nadal            25     18   14.6   3.4   13.6%  
Gilles Simon            25     16   12.7   3.3   13.0%  
Ivo Karlovic            29     18   14.8   3.2   11.1%  
John Isner              53     36   30.1   5.9   11.1%  
Andy Murray             23     16   13.5   2.5   11.0%  
Fabio Fognini           23     14   11.7   2.3   10.0%  
Juan Martin Del Potro   33     21   17.7   3.3   10.0%  
Benoit Paire            29     17   14.3   2.7    9.3%  
Philipp Kohlschreiber   33     19   15.9   3.1    9.3%  
Jerzy Janowicz          26     15   12.9   2.1    8.2%  
Jarkko Nieminen         27     14   11.9   2.1    7.9%  
Bernard Tomic           30     16   13.7   2.3    7.6%  
Julien Benneteau        24     14   12.4   1.6    6.9%  
Alexandr Dolgopolov     21     11    9.6   1.4    6.8%  
Ernests Gulbis          23     13   11.5   1.5    6.4%  
Tommy Haas              26     16   14.4   1.6    6.3%  
Jeremy Chardy           21     12   10.7   1.3    6.0%  
Roger Federer           25     15   13.6   1.4    5.4%  
Grega Zemlja            19     10    9.0   1.0    5.3%  
Feliciano Lopez         24     14   12.9   1.1    4.4%  
Jo Wilfried Tsonga      30     17   15.8   1.2    4.2%  
Ryan Harrison           15      7    6.4   0.6    4.1%  
Tommy Robredo           24     14   13.1   0.9    3.8%  
Novak Djokovic          28     19   17.9   1.1    3.8%  
Lleyton Hewitt          16      9    8.4   0.6    3.5%  
Daniel Brands           19     10    9.4   0.6    3.4%  
Fernando Verdasco       24     14   13.5   0.5    1.9%  
David Ferrer            21     12   11.8   0.2    1.0%  
Kei Nishikori           16      9    8.9   0.1    0.9%  
Martin Klizan           15      7    6.9   0.1    0.9%  
Kevin Anderson          35     19   19.1  -0.1   -0.2%  
Marinko Matosevic       16      9    9.1  -0.1   -0.4%  
Mikhail Youzhny         23     11   11.4  -0.4   -1.8%  
Milos Raonic            36     19   19.7  -0.7   -1.9%  
Sam Querrey             31     15   15.6  -0.6   -2.1%  
Stanislas Wawrinka      32     17   17.7  -0.7   -2.3%  
Florian Mayer           18      8    8.4  -0.4   -2.4%  
Gael Monfils            27     13   13.7  -0.7   -2.5%  
Igor Sijsling           19      9    9.5  -0.5   -2.6%  
Andreas Seppi           19      9    9.5  -0.5   -2.8%  
Denis Istomin           24     11   11.8  -0.8   -3.2%  
Richard Gasquet         29     15   16.0  -1.0   -3.4%  
Daniel Gimeno Traver    18      7    7.6  -0.6   -3.5%  
Vasek Pospisil          24     11   11.9  -0.9   -3.6%  
Tomas Berdych           34     17   18.6  -1.6   -4.7%  
Victor Hanescu          24     10   11.2  -1.2   -5.2%  
Ivan Dodig              27     12   13.5  -1.5   -5.7%  
Robin Haase             24     10   11.4  -1.4   -5.9%  
Albert Ramos            16      7    7.9  -0.9   -5.9%  
Benjamin Becker         18      7    8.1  -1.1   -5.9%  
Horacio Zeballos        20      7    8.2  -1.2   -6.2%  
Jurgen Melzer           19      8    9.4  -1.4   -7.4%  
Nicolas Almagro         34     17   19.5  -2.5   -7.5%  
Lukas Rosol             15      6    7.3  -1.3   -8.9%  
Evgeny Donskoy          17      6    7.7  -1.7  -10.2%  
Alejandro Falla         15      6    7.6  -1.6  -10.9%  
Grigor Dimitrov         22      9   11.5  -2.5  -11.4%  
Marcos Baghdatis        20      6    9.5  -3.5  -17.4%  
Carlos Berlocq          18      7   10.2  -3.2  -17.5%  
Juan Monaco             15      5    7.7  -2.7  -18.3%  
Janko Tipsarevic        19      5    8.7  -3.7  -19.5%  
Edouard Roger Vasselin  19      4    8.2  -4.2  -22.3%

Roger Federer and the Missing Tiebreaks (+Updated WTForecast)

For most of his career, Roger Federer has been one of the very few players to play better in tiebreaks than in standard deuce games.  His career record, winning breakers at a 65% clip, illustrates his success at the business end of tight sets.  But there’s more to the story.  Even a player a good as Federer has been should not have won that many tiebreaks.

As I wrote in a pair of posts a year ago, there is very little evidence for any kind of tiebreak-specific skill.  Some players do well in tiebreaks, of course, but their success is almost always due to being good in general–better players win more points, and that translates into tiebreaks.  Plenty of big servers, such as Ivo Karlovic and Milos Raonic, don’t win any more tiebreaks that you would expect simply by looking at the rate at which they win points.

However, a tiny fraction of players defy this regression to the tiebreak mean. Playing a ton of tiebreaks seems to help a bit–John Isner always wins more than expected–and a few other cases might be explained by extreme confidence or intimidations.  These include Pete Sampras and–you guessed it–King Roger.

In the eight seasons from 2004 to 2011, Federer won almost 10% more tiebreaks than his stats say he should have.  In 2006, his outrageous 37-14 tiebreak record was a big part of his equally outrageous overall success.  But even a player as good as Roger was that year “should” have only gone 31-20.  That would still have been an impressive win rate, and let’s not forget, many of his tiebreaks were against excellent players who had already pushed him that far.

As with so much else, that tiebreak magic has eluded Fed in the past two seasons.  Last year was the first season since 2003 when he failed to win more tiebreaks than expected.  He has been neutral this year and last.

It’s tempting to wonder, then, how big a part the disappearance of Roger’s tiebreak magic has played in his overall decline.  If he had won tiebreaks at the “extra” rate he did throughout his peak, he would have claimed two, or possibly three more than he actually did, flipping his pedestrian 13-10 tiebreak record to a more Fed-like 15-8 or even 16-7.  (This post was written before Fed’s tiebreak win over Djokovic in London on Tuesday.  In any event, improving his record to 14-10 doesn’t drastically change anything.)

How much of an impact would those bonus tiebreaks have had?  With a bit of guesswork and a handful of counterfactuals, we can put a number on it.  We’re looking at “flipping” two or three of Roger’s ten lost tiebreaks.  Of those ten, three didn’t end up mattering, as he won the match anyway.   The remaining seven occurred in five matches:

The final match in this list provides the simplest illustration of the math involved here.  Flip the lost tiebreak in the Delpo match, and Federer wins the title, earning 200 additional ranking points.  Since we’re only switching the outcome in two or three tiebreaks, that’s either a 20% or 30% chance of that particular tiebreak counting among those switched, for either 40 or 60 additional points.

It gets much more involved with something like the Stakhovsky loss.  Not only do we need to consider the different outcomes of flipping both tiebreaks (and Roger winning) and flipping just one (and Roger maybe winning), we also need to estimate Fed’s chances of progressing through the draw.  Despite the very early loss, Wimbledon was almost double the lost opportunity of any of the other matches, as his path to the semifinal would’ve gone through Jurgen Melzer, Jerzy Janowicz, and Lukasz Kubot.  To quantify the effect of flipping the Wimbledon outcome, we must consider the probability of his reaching those later rounds and the number of points he would have collected had he gotten that far.

Crunch all the numbers, and if you flip two tiebreaks, Federer gains about 380 ranking points.  Flip three, and it’s about 560.  Either of those numbers would move him in front of Berdych in this week’s rankings and given him a lot more breathing room on the road to London.  These bonus points would still have left a huge gap between him and the top five.

Perhaps more important than a few hundred ranking points, how different would the 2013 Federer storyline look if you flipped just a small number of those results?  Give him the 4th set against Stakhovsky and the 2nd with Delbonis, watch him win the deciders, and there’s a different Fed narrative for the summer.  Whether it’s bad luck, decreased confidence, less intimidation, or something else entirely, it’s crucial that we remember that tiebreaks are often decided by a single bad service point or great return point.  If a narrative can’t hold up against a couple of points going the other way, it probably isn’t telling us very much about a player’s actual performance level.

Yet, if Federer has turned a corner this fall, it would be a mistake to expect improved results to come from a resurgence of his tiebreak mojo.  Whatever mysterious factors cause a tiny minority of players to exceed tiebreak expectations, it seems less likely that fading 30-something Fed has them.  He certainly hasn’t benefited from them for the last two years.  But most of all, unless he gets back into more very high-profile matches–as he may this week–the few hundred points he could gain from tiebreak magic just won’t make much of a difference.

—

London forecast: Today, the results went as expected, with Nadal beating Ferrer and Novak defeating Federer.  Nadal was such a heavy favorite that his win doesn’t affect his chances much, but Djokovic enjoys a bigger bump. The top two seeds are now almost equal, while Federer faces increasingly long odds.

Player     3-0  2-1  1-2  0-3     SF      F      W  
Nadal      50%  42%   9%   0%  91.2%  52.5%  31.5%  
Djokovic   43%  46%  11%   0%  88.5%  54.4%  31.0%  
Ferrer      0%  29%  50%  21%  31.9%  12.2%   4.5%  
Del Potro  22%  50%  28%   0%  71.3%  36.6%  16.7%  
Federer     0%  30%  51%  20%  30.2%  14.1%   6.3%  
Berdych     0%  14%  48%  38%  16.4%   5.7%   2.0%  
Wawrinka   13%  48%  38%   0%  60.5%  21.2%   6.9%  
Gasquet     0%  10%  44%  45%  10.0%   3.3%   1.1%

Click here for the pre-tournament forecast.

John Isner’s Momentary Tiebreak Blip

Tiebreak legend John Isner has now lost four tiebreaks in a row, including a demoralizing two breakers in his match yesterday against 71st-ranked Vasek Pospisil.  Aside from his loss to the Canadian, however, Isner’s sudden tiebreak weakness hasn’t hurt him, nor does it seem to be a sign of poor play or weak nerves.  In fact, he has excelled–as usual–on the North American hardcourts. Twice last week, against both Marcos Baghdatis and Dmitry Tursunov, Isner dropped the first set in a breaker, then came back to win the following two sets with scores of 6-4 or better.

Further, this brief spell of Haase-style tiebreak play follows a much longer stretch of typical end-of-set dominance.  Until losing the first set against Kevin Anderson in the Atlanta final, Isner had won 12 breakers in a row. He immediately bounced back from the setback against Anderson by winning two breakers to claim the match, then won two more in his next match against Alex Kuznetsov.

Summary: The tiebreak mojo is still intact.

At a broader level, Isner has won 70% of his tiebreaks over the last 52 weeks, a rate higher than he has ever sustained for a full season.  Specifically in 2013, he has won 28 of 39 tiebreaks, good for 72%.  By comparison, Anderson has won 57% this season, Roger Federer 59%, and even the inimitable Steve Darcis has never won more than 72% of breakers for a full year.

This isn’t to take away from Pospisil’s achievement, however.  Isner’s career tour-level tiebreak record of 65% suggests that taking two breakers from him in a single match is difficult, and it’s all the more so for a player who most would not consider as Big John’s equal.  In 25 career tour-level tiebreaks before yesterday’s match, the Canadian had won a mere 11.

In fact, of Isner’s 258 career best-of-three-set matches on tour, this was only the seventh in which he lost two sets 7-6.  Given the sheer number of tiebreaks he plays, that in itself quite the accomplishment.  No one had administered such a loss to Isner since last year’s Madrid Masters, where Marin Cilic beat him 7-6 7-6.

When watching the American lose the occasional tiebreak, it’s important to remember that for the vast majority of players, breaker outcomes are essentially luck.  Isner is one of the few players to demonstrate a consistent tiebreak skill, but even that skill can’t prevent the occasional serving outage or an outstanding run of play from a streaky opponent.

With Isner (and by extension, all US men) falling out of the top 20, it’s tempting to point fingers and look for answers.  But don’t blame Big John.  If you must find fault, blame Canada.

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.

Continue reading Robin Haase’s Unlucky 13 Tiebreaks

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.

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.