Monthly Archives: October 2012

The Most Familiar Faces

In last week’s Basel final, Roger Federer and Juan Martin Del Potro faced off for the seventh time this year, and the 16th time overall.  Seven times in one year is an awful lot, about 10% of Delpo’s matches.  It’s even more remarkable because only two of those contests have been finals — in order to meet so many times, the draws of several tournaments had to complement their consistently strong play.

Making matters even more extreme is that there is a better-than-50% chance that Federer and Del Potro will meet in London next week, bringing the total to 8.  And there’s a slim chance–if they are drawn in the same group, then play again in the final–that the sum will reach 9.

So, what’s the record?  Seven is already pretty good, right?

Single year head-to-heads

In fact, as with so many other records, Federer is #1 in the last 30 years.  He holds the record with Jo Wilfried Tsonga, against whom he played eight times last year.  (In the entire professional era, the mark belongs to Ilie Nastase and Tom Gorman, who played at least nine times in 1972.  I’ve excluded years before 1980 because a variety of factors caused the top players to meet much more frequently than they do these days.)

As long as Fed and Delpo are at seven, they will be tied with four other pairs: John McEnroe and Ivan Lendl in 1984, Jim Courier and Michael Chang in 1995, Novak Djokovic and Rafael Nadal in 2007, and Novak/Rafa again in 2009.  Another 11 pairs met six times in a single year, including Nadal and Djokovic in 2008 and 2011.  (Along with, weirdly, Rajeev Ram and Donald Young in 2007.  Must be the wild cards.)

All-time head-to-heads

Since Djokovic and Nadal show up at the top of the single-year list no more than four times, it stands to reason that they must be near the top of the all-time list, as well.  Indeed, they are.

In fact, assuming Nadal returns to health in anywhere near his historical form, this current pair of stars will almost undoubtedly take over the all-time lead next year.  They could hold it for a very long time.

Player 1       Player 2        H2Hs    W-L  
Ivan Lendl     John McEnroe      35  20-15  
Ivan Lendl     Jimmy Connors     34  22-12  
Pete Sampras   Andre Agassi      34  20-14  
John McEnroe   Jimmy Connors     34  20-14  
Rafael Nadal   Novak Djokovic    33  19-14  
Boris Becker   Stefan Edberg     32  22-10  
Roger Federer  Novak Djokovic    28  16-12  
Rafael Nadal   Roger Federer     28  18-10  
Stefan Edberg  Ivan Lendl        26  14-12  
Roger Federer  Lleyton Hewitt    26   18-8

This is one record that, for all of his dominance, Federer will probably never co-hold.  To find yourself on this list, you not only need to rank among the all-time greats, you need a very-near-contemporary who ranks just as high.

(If you’re interested in head-to-head records, I hope you’re already using the Head-to-Head Matrix on  It’s updated every week, and shows the career H2H records of every matchup within the current top 15.  Each H2H record is linked directly to a listing of the relevant matches.)


Filed under Head-to-Heads, Records

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.


Filed under The Rules, Tiebreaks

How Much Do Wild Cards Matter?

Last week, I presented a lot of data that demonstrated how American (and to a lesser extent, French, Australian, and British) players receive the bulk of ATP wild cards, mostly because there are so many tournaments in these countries.  That leaves nationals of other countries to fight their way up through the rankings more slowly, earning less money and facing tougher odds.

How bad is it?  Does it really help to get a handful of free entries, especially if most wild cards are doomed to lose in the first round or two?

To get a sense of the effect, let’s take a look at Jack Sock, the most gifted recipient of wild cards in 2012.  He entered seven tour-level events this year, all on free passes.  (He was also wildcarded into another three challengers and the Cincinnati Masters qualifying draw.)  If you take away the wild cards, he would’ve played a couple of challengers, some qualifying draws for US 250s, leaving him to fill most of his calendar with futures.

As it is, Sock has boosted his ranking from 381 to 164 in a single year, earning $137,000 along the way.  About half of that comes from his third-round showing at the US Open, which required him to beat Florian Mayer (who retired) and Flavio Cipolla, not a particularly tall order (as it were).  Another $27,000 came entirely from first-round losses–tournaments that he didn’t earn his way into, and where he failed to win a match.

I don’t mean to pick on Sock.  Kudos to him for winning as many matches as he has this year and establishing himself as one of the better prospects in the game.  But if he weren’t from a Grand Slam-hosting country, he would have been lucky to get a single wild card, perhaps benefiting from two or three freebies at the challenger level.  He would have spent most of 2012 on the futures circuit, hoping to pick up the occasional $1,300 winner’s check.

What would have happened then?  A handy test case is Diego Sebastian Schwartzman, a young Argentine about one month older than Sock.  At the end of last year, Schwartzman was ranked 371 to Sock’s 381.  Schwartzman doesn’t exactly constitute a scientific control group, but as a point of reference, we couldn’t ask for much more.

In terms of on-court performance, Schwartzman may well have had a better 2012 than Sock did.  The Argentine won six Futures events on the South American clay, and he added another four doubles titles at that level.  He wasn’t nearly as successful at the next level, going 5-10 in Challenger and ATP qualifiying matches.  Perhaps he was a bit worn down from his 49 Futures singles matches this year.

It’s an open question whether Sock or Schwartzman had the more impressive year.  Some might prefer the American’s challenger title and handful of top-100 scalps; others would prefer Schwartzman’s 30-match winning streak at the Futures level.

But here’s the kicker: While Sock made $137,000 and raised his ranking to #164, Schwartzman made $17,000 and is currently ranked #245.  By showing up at the Indian Wells Masters and losing in the first round, Sock made about as much money as Schwartzman did by winning six tournaments.

The rankings differential isn’t as striking, but it is just as important for both players in the near future.  Sock was able to earn direct entry in the Tiburon Challenger earlier this month.  A ranking inside the top 200 is good enough to get into almost all Challengers and a substantial number of ATP qualifiers.  245 will get you into many of the Challenger events with lower stakes (read: less money, fewer points on offer) and a much smaller number of ATP qualifiers.

Thus, the favors handed to the American–and never considered for the Argentine–will effect the trajectory of both players’ careers for some time to come.

Andrea Collarini, perhaps you’d like to reconsider?


Filed under American tennis, Wild cards

Which Tournaments Award Competitive Wild Cards?

For the last two days, we’ve looked at tour-level wild cards from various angles.  Many top players never received any; others have gotten plenty but never taken much advantage.  Still others have managed to prop up their rankings with occasional wild cards despite not having the game to take themselves to the next level.

Wild cards are perhaps most interesting from a structural perspective.  Every tournament gets to give away between three and eight free spots in the main draw, and what they do with them is fascinating.  Events must pick from among several priorities: Bring in the best possible players to build a competitive field? Award places to big names, even if they are unlikely to win more than a single match?  Support national objectives (and perhaps invest in future fan interest) by handing the places to the best rising stars the home country has to offer?

Obviously, these priorities conflict.  The Canada Masters events give out most of their wild cards to Canadians–56 of the last 59.  But those local favorites have failed to win even one quarter of their matches, the second worst record for home-country wild cards among the current Masters events.  Wimbledon is the least home-friendly of the Grand Slams, but perhaps it is still too friendly, as British wild cards have won barely one in five matches over the last 15 years.  Lately, it has been even worse.

The dilemma is most pronounced for tournaments in countries without a strong tennis presence.  These events generally hand out most of their wild cards to non-locals, saving a few for the best the homeland has to offer.  Dubai, for instance, has only awarded 10 of its last 42 wild cards to Emiratis.  Unfortunately, those guys have gone 0-10.  The story is similar in Doha and Kuala Lumpur.

A different approach is evident in Tokyo, the only remaining tournament in Japan.  These days, the 32-player draw only gives the event three wild cards to work with.  The tournament isn’t wasting spots on outsiders: Every wild card since 1992 has gone to a Japanese player.  The local wild cards have done better than we might guess, winning almost 30% of their matches, good for 45th among the 65 tournaments I looked at.

In fact, there is not a strong correlation between home-country favoritism and poor wild-card performance.  Of long-running tournaments, Newport has seen their wild cards have the most success, winning more than half their matches.  Next on the list is Halle, also a bit better than half.  But the two tournaments take drastically different approaches to local players.  Newport only awards 63% of its WCs to Americans–second-lowest among tourneys in the USA.  Halle, on the other hand, gives nearly all of its free spots to Germans.

When discussing the structural biases of the wild card system, it’s easy to pick on the USA.  America hosts far more tournaments than any other country, and thus US events have the most wild cards at their discretion.  Many of those decisions are made by a single organization, the USTA.  But US tournaments are far from consistent in their approach.

The US Open is by far the most nationalistic of the Grand Slams, having awarded about 85% of its WCs in the last 15 years to US players.  The French comes next at 78%, then the Australian at 69%, followed by Wimbledon at 67%.  But even that understates the case.  Take out the French reciprocal wild cards since 2008 and the Australian reciprocals since 2005, and 100 of the last 105 wild cards in Flushing have represented the home nation.

Yet as we’ve seen, Newport shows less home-country favoritism than almost any other ATP event, and the Miami Masters is even more extreme, living up to its billing as the “South American Slam” by giving barely half of its wild cards to US players.  Even the most biased US tournament (aside from the Open) is the clay court event in Houston, which isn’t even in the top third of all events, handing out “only” 86% of wild cards to Americans.

The problem isn’t the behavior of US tournament officials–if anything, they are more international in their thinking than their colleagues in other countries.  Instead, their priorities–put home-country players on the court; amass a competitive field–combined with the sheer number of US events, result in one wild card after another for a small group of Americans and no equivalent advantages for players from countries that do not host tour-level events.

After the jump, find a table with many of the numbers I’ve referred to throughout this post.  All tour-level events that took place in 2011 or 2012 are included, and data goes back to 1998. homeWC% is percentage of WCs that went to home- country players, WCW% is the winning percentage of all wild cards, and hWCW% is win% of all wild cards from the home country.  I’ve excluded wild cards who were seeded, since those are usually just late entries, and don’t reflect tournament priorities in the same way that other WCs do.  For a sortable table with even more data, click here.

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Filed under U.S. Open, Wild cards

Who Takes Advantage of Wild Cards?

Yesterday, we saw that ATP tour-level wild cards are the privilege of just a small subset of top pros.  If you play for a Grand Slam-hosting country, or you are a major junior prospect, you’ll get plenty.  If you fit neither of those categories, you’re on your own.  Donald Young gets 27 wild cards while better players work for years to earn their way into as many as 27 ATP main draws.

This discrepancy raises plenty of questions, not least the issue of whether the wild card status quo is good for tennis.

The title of this post raises another: Who used those wild cards to rocket to the top?  Andy Roddick is one, having amassed a 20-9 record, including two titles and one Masters-level quarterfinal, from 11 wild cards spots in 2000 and 2001.  On the flip side is Nicolas Mahut, who received 9 tour-level wild cards before his 25th birthday, winning only one match–and that one by retirement.

When players do take advantage of their wild cards and string a few wins together, what are we to make of them?  Roddick was clearly on his way to the top.  After winning Atlanta and Houston in back-to-back weeks in 2001, he never needed a wild card again.  But other highly-touted Americans, such as Jesse Levine and Ryan Sweeting, never manage to get their ranking fully out of wild card territory.  They’ll both probably receive more, taking opportunities to win a tour-level match or two that gives their rankings a boost.

The ranking effect of a tour-level win or two compounds the effects that keep down players like Grega Zemlja.  First, someone like Levine or Frank Dancevic receives a substantial number of wild cards, consistent opportunities to play in a main draw that other, similarly-ranked players don’t get.  Then, unless they really aren’t that good, or they get a slew of unlucky draws, they win a match or two.  A mere appearance in a Grand Slam main draw is worth 10 ranking points; a single win gets you another 35.  In some challenger events, you need to reach the final to earn that many points.

More ranking points, of course, lead to a higher ranking.  A higher ranking leads to more direct entries into tournaments.  And then, somehow, you have Donald Young in the top 50.

Thus, “taking advantage” of wild cards has strong positive and negative connotations.  Guys like Roddick and Federer were ready to compete at the highest level before their rankings said they were, so they took advantage of their opportunities to the fullest.  But when a player gets 10 wild cards and wins four matches, he’s made the best of his situation in a manner that exploits the inequities of the ATP tour.

After the jump, find a table that shows everyone currently in the top 200 who received at least four tour-level wild cards before their 25th birthday.  (I’m using that age as a cutoff to avoid counting wild cards handed to players on the comeback trail or a retirement tour.)  It’s sorted by number of wild cards received pre-25.  For a sortable table, click here.

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Filed under Wild cards

What Grega Zemlja Can Tell Us About American Tennis

Last week, virtually unknown Slovenian qualifier Grega Zemlja reached the final in Vienna.  Like many players–Eastern Europeans in particular–in the back half of the top 100, he has finally established a toehold on tour after putting together a good sequence of challenger results.

The final run in Vienna–only his 16th tour-level event–will help keep him in the top 100 for most of the next year, earning him direct entries into all of the Grand Slams and many smaller ATP events.

Zemlja turned 26 one month ago, so he is hardly a “prospect.”  But I call your attention to him because he has achieved his new berth in the top 50 almost entirely by merit.  When the AELTC awarded him a wild card into the Wimbledon main draw this summer, it was the first tour-level wild card of his career.  In fact, he has only received a single wild card into a challenger main draw.

While the Slovenian has been a fixture in the top 200 since the end of 2008, he hasn’t gotten any favors.

The distribution of wild cards

As it turns out, he’s not alone.  21 players in the top 100 (including Tomas Berdych and Janko Tipsarevic) didn’t receive a single tour-level wild card before their 25th birthday.  Another 16 (Novak Djokovic and David Ferrer among them) got only one, and yet another 23 received only two.

When I started researching this post, I expected to find that Zemlja was uniquely disadvantaged.  But no: Wild cards are the privilege of players who happen to be born in the right places.  Free entries tend to go to home favorites, with a few more awarded to star youngsters like Grigor Dimitrov.

Thus, the geographical distribution of wild cards has everything to do with where tournaments are located.  And tournament locations have an awful lot to do with where the tennis world was centered 20, 50, or even 100 years ago.

The U.S. of Assistance

Much has been said of Donald Young‘s 27 tour-level wild cards.  (Some of it by Patrick McEnroe, recipient of 37.)  But that’s just the tip of the iceberg.  Did you know that the seven active players who received the most wild cards before age 25 play for the USA?  Young is followed by Mardy Fish, Ryan Harrison, Sam Querrey, Jesse Levine, John Isner, and James Blake.  (Blake has been handed by far the most career wild cards, but the majority have come in his more recent comeback attempts.)

The current top 200 players received 748 wild cards before the age of 25.  139, or 18.6% of those, have gone to these seven, or 3.5% of players.

Put simply, the distribution of tennis tournaments doesn’t match the distribution of tennis talent.  The US is the only country with more than one Masters 1000 event–it has three.  Plus a slam.  And two 500s.  And another seven 250s, at least in 2012.

All those tournaments have at least three wild cards to give out.  This year, seven of them handed main draw spots to Jack Sock, who at age 20 has already amassed 10 career tour-level wild cards, more WCs than 90% of the top 200 have received.

A structural problem

This is an easy subject to get worked up about, especially if you prefer to root for players like Zemlja.  Yet it’s difficult to blame anyone in particular.

Tournaments fiercely guard the few wild card spots they are given, so it would be difficult for the ATP to meddle.  The events want to attract fans, and an up-and-comer with an easy-to-pronounce name is a great way to sell tickets.  And you certainly can’t blame a player for accepting main draw berths.

Here’s a modest proposal: Convert a few more “wild card” spots to merit-based spots.  The USTA is doing more of this, setting up playoffs for reciprocal wild card placements at the Australian and French Opens, among other strategies.  But that doesn’t help with geographical distribution, since only Americans can compete!

Better yet is a version of how Zemlja got into Wimbledon.  He won the Nottingham challenger two weeks previous, and the AELTC wasn’t going to give away all the free spots to Brits.  The Slovenian was a deserving up-and-comer, even though he doesn’t play under the right flag.

Perhaps every Slam and Masters event should reserve a spot for the winner of a corresponding challenger.  Or every tournament with a 48-or-bigger draw should be required to hand at least one wild card to a non-national.

If a player is good enough, he’ll break in eventually.  But wouldn’t the sport be better off if some players didn’t have to wait longer than others, based simply on how many tournaments are played in the country they play for?


Filed under American tennis, Wild cards

Daniel Brands and Ace Records in Context

In the Vienna round of 16 last week, Juan Martin Del Potro beat Daniel Brands in a three-set, three-tiebreak match.  The courts are fast, Delpo serves big, and apparently Brands has quite the weapon of his own, as both players hit at least 30 aces.  Brands hit 32.

We can’t help but be impressed at the sheer numbers.  As it turns out, it’s an ATP first, at least since 1991, when the ATP started keeping such stats.  Never before had both players hit at least 30 aces in a three-set match.

Here are the top nine matches in the ATP record books, in which both servers reached a certain ace milestone:

minAces  Winner                 Loser              Year  Event               Surface  Score                 wAces  lAces  
30       Juan Martin Del Potro  Daniel Brands      2012  Vienna              Hard     6-7(5) 7-6(4) 7-6(6)     30     32  
29       John Isner             Gilles Muller      2010  Atlanta             Hard     4-6 7-6(6) 7-6(7)        33     29  
28       Andrei Pavel           Gregory Carraz     2005  Milan               Carpet   7-6(0) 6-7(5) 7-6(3)     28     33  
25       Greg Rusedski          Joachim Johansson  2004  Moscow              Carpet   7-6(5) 6-7(1) 7-6(7)     25     26  
25       Arnaud Clement         Thomas Johansson   2008  Cincinnati Masters  Hard     7-6(4) 6-7(5) 6-3        25     28  
24       Mark Philippoussis     Greg Rusedski      2002  Queen's Club        Grass    6-7(1) 7-6(3) 7-6(5)     25     24  
24       Joachim Johansson      Kristof Vliegen    2006  Stockholm           Hard     6-7(5) 7-6(5) 7-6(7)     24     24  
24       Andy Roddick           Ivo Karlovic       2009  Queen's Club        Grass    7-6(4) 7-6(5)            24     26  
24       Richard Gasquet        Joachim Johansson  2009  Kuala Lumpur        Hard     4-6 7-6(1) 6-2           26     24

(There are several matches in which both players hit 23, including two on clay, both from 2011: Isner/Karlovic in Houston, and Federer/Feliciano Lopez in Madrid.  Both went to three tiebreaks.)

Aces in a losing effort

Even independent of Del Potro’s 30 aces, it stands out that Brands racked up 32 aces in a best-of-three losing effort.  But that’s not a record–it ties him for 16th of all time with several others, including Sam Querrey, Milos Raonic, Ivo Karlovic, and Goran Ivanisevic, who did it twice.

Mardy Fish may not be proud of this record, but he simply blows away the rest of the field, having served past the eminently ace-able Olivier Rochus 43 times despite losing to the Belgian.  Though Karlovic may not sit atop the list, he makes up for it by dominating the middle.

lAces  Winner              Loser             Year  Event             Surface  Score                  wAces  
43     Olivier Rochus      Mardy Fish        2007  Lyon              Carpet   6-7(5) 7-6(6) 7-6(15)      2  
37     Yevgeny Kafelnikov  Alexander Waske   2002  Tashkent          Hard     6-7(6) 7-6(5) 7-6(6)      10  
35     Pete Sampras        Goran Ivanisevic  1996  Tour Finals       Carpet   6-7(6) 7-6(4) 7-5         17  
35     Andy Roddick        Feliciano Lopez   2011  Queen's Club      Grass    7-6(2) 6-7(5) 6-4         15  
35     Feliciano Lopez     Ivo Karlovic      2004  Madrid Masters    Hard     6-4 6-7(10) 7-6(5)         8  
35     Yen Hsun Lu         Ivo Karlovic      2012  Queen's Club      Grass    6-7(3) 7-6(6) 7-6(7)       6  
35     Rafael Nadal        Ivo Karlovic      2008  Queen's Club      Grass    6-7(5) 7-6(5) 7-6(4)       6  
35     Arnaud Clement      Ivo Karlovic      2004  's-Hertogenbosch  Grass    7-6(8) 6-7(5) 6-3          2  
34     Thomas Johansson    Ivan Ljubicic     2002  Canada Masters    Hard     4-6 6-4 7-6(6)            17  
34     Lars Burgsmuller    Wayne Arthurs     2006  Tokyo             Hard     6-7(5) 7-6(7) 7-6(3)      10  
34     Richey Reneberg     Richard Krajicek  1997  Halle             Grass    4-6 7-6(2) 7-6(6)          6

Total aces in a single match

If there has never been a match in which both players hit 30 aces, a match total of 62 aces must be pretty impressive, right?

Indeed it is.  Del Potro and Brands are now tied for the record, initially set by John Isner and Gilles Muller two years ago in Atlanta.  It’s only the fourth time that two players have combined for 60 or more aces in a best-of-three contest.

totAces  Winner                 Loser             Year  Event               Surface  Score                 wAces  lAces  
62       Juan Martin Del Potro  Daniel Brands     2012  Vienna              Hard     6-7(5) 7-6(4) 7-6(6)     30     32  
62       John Isner             Gilles Muller     2010  Atlanta             Hard     4-6 7-6(6) 7-6(7)        33     29  
61       Andrei Pavel           Gregory Carraz    2005  Milan               Carpet   7-6(0) 6-7(5) 7-6(3)     28     33  
60       Goran Ivanisevic       Magnus Norman     1997  Zagreb              Carpet   7-6(5) 6-7(4) 7-5        40     20  
58       Frank Dancevic         Peter Wessels     2007  Stockholm           Hard     6-1 6-7(7) 7-6(6)        35     23  
55       Jan Michael Gambill    Wayne Arthurs     2002  San Jose            Hard     7-5 6-7(5) 7-6(4)        22     33  
55       Bohdan Ulihrach        Goran Ivanisevic  1999  Rotterdam           Carpet   6-7(6) 7-6(3) 7-5        23     32  
53       Andy Roddick           Wayne Arthurs     2006  Memphis             Hard     6-7(4) 7-6(9) 7-6(2)     20     33  
53       Andy Roddick           Sam Querrey       2010  San Jose            Hard     2-6 7-6(5) 7-6(4)        21     32  
53       Arnaud Clement         Thomas Johansson  2008  Cincinnati Masters  Hard     7-6(4) 6-7(5) 6-3        25     28  
53       Joachim Johansson      Gregory Carraz    2004  Canada Masters      Hard     7-6(4) 6-7(3) 7-6(4)     30     23

The higher bar of ace rate

If you want to set a record in a best-of-three-sets match, getting to those three tiebreaks is a good idea.  The more points you play, the more likely you’ll hit more aces, as evidenced by Fish’s losing performance, where he not only reached three tiebreaks, but played at least twelve points in each one!

For greater context, we should open up the field to all matches regardless of length, and compare them by ace rate.

Del Potro’s 30 aces came in 125 service points, for an ace rate of 24%.  Brands hit 32 in 131, for an ace ate of 24.4%.  It’s not often that one player (not named Isner, anyway) hits nearly one-quarter of his serves for aces, so it is particularly unusual for both players to do so.

In all tour-level matches (including grand slams) since 1991, a minimum ace rate of 24.0% is only good for 17th.  Andy Roddick was particularly adept at bringing about these kinds of matches, appearing in 6 of the top 11 on this list:

minA%  Winner            Loser              Year  Event            Surface  Score                wA%    lA%  
33.3%  Andy Roddick      Ivo Karlovic       2009  Queen's Club     Grass    7-6(4) 7-6(5)      33.3%  35.1%  
29.8%  Mikhail Youzhny   Ivan Ljubicic      2007  Rotterdam        Hard     6-2 6-4            29.8%  29.8%  
29.2%  Gregory Carraz    Martin Verkerk     2004  Milan            Carpet   6-3 7-6(3)         30.4%  29.2%  
27.3%  Goran Ivanisevic  Boris Becker       1996  Antwerp          Carpet   6-4 7-6(5)         30.8%  27.3%  
27.1%  John Isner        Gilles Muller      2010  Atlanta          Hard     4-6 7-6(6) 7-6(7)  27.5%  27.1%  
27.0%  Robin Soderling   Andy Roddick       2008  Lyon             Carpet   7-6(5) 7-6(5)      27.0%  27.2%  
26.7%  Janko Tipsarevic  Peter Luczak       2010  s-Hertogenbosch  Grass    6-3 6-3            26.7%  27.1%  
26.1%  Andy Roddick      Gilles Muller      2008  Memphis          Hard     6-4 7-6(4)         27.4%  26.1%  
25.4%  Andy Roddick      Joachim Johansson  2004  San Jose         Hard     6-3 7-6(7)         36.5%  25.4%  
25.4%  Andy Roddick      Nicolas Mahut      2008  Lyon             Carpet   7-6(5) 6-4         29.0%  25.4%  
25.3%  Andy Roddick      Feliciano Lopez    2008  Dubai            Hard     6-7(8) 6-4 6-2     26.2%  25.3%

Ace rate in a losing effort

While losers rarely hit as many aces as Brands did last week, losers often hit aces at a much higher rate.  Brands doesn’t register anywhere near the top of this all-time list.

Think of it this way: The shorter the match, the more likely a player will do something off-the-charts, rate-wise.  Karlovic tops this list, with 28 aces in his 70 service points.  Brands didn’t maintain anywhere near the same rate that Ivo did, but Brands did have to hit nearly twice as many serves!  Had Karlovic continued for 61 more serves, he probably would’ve done better than 24.4%, but it is very unlikely he would have continued at a 4-in-10 pace.

This is also a reason why we haven’t seen many best-of-five matches on the ace-rate leaderboards.  Even if one player is acing like a madman while quickly losing, he still has to keep up the pace for three sets.

lA%    Winner              Loser               Year  Event               Surface  Score                     lAces  
40.0%  Florent Serra       Ivo Karlovic        2009  Basel               Hard     7-6(5) 6-4                   28  
37.5%  Alex Obrien         Mark Philippoussis  1996  Cincinnati Masters  Hard     6-4 6-4                      21  
36.6%  Thomas Johansson    Ivan Ljubicic       2002  Canada Masters      Hard     4-6 6-4 7-6(6)               34  
35.8%  Richey Reneberg     Richard Krajicek    1997  Halle               Grass    4-6 7-6(2) 7-6(6)            34  
35.1%  Andy Roddick        Ivo Karlovic        2009  Queen's Club        Grass    7-6(4) 7-6(5)                26  
34.8%  Paul Henri Mathieu  Ivo Karlovic        2009  Cincinnati Masters  Hard     7-6(9) 6-4                   23  
34.8%  Paul Henri Mathieu  Chris Guccione      2008  Adelaide            Hard     4-6 6-3 6-4                  24  
34.2%  Andre Agassi        Joachim Johansson   2005  Australian Open     Hard     6-7(4) 7-6(5) 7-6(3) 6-4     51  
33.8%  Jonas Bjorkman      Mark Philippoussis  2002  Memphis             Hard     7-6(6) 7-6(1)                26  
33.3%  Thomas Johansson    Wayne Arthurs       2001  Nottingham          Grass    7-6(3) 7-6(3)                24  
33.3%  Yevgeny Kafelnikov  Marc Rosset         2002  Marseille           Hard     6-3 7-6(5)                   19  
33.3%  Andre Agassi        Goran Ivanisevic    1994  Vienna              Carpet   6-4 6-4                      19

Combined ace rate

As you might have guessed by now, 24% isn’t going to be good enough to crack this final all-time list.  Roddick, Karlovic, and Mark Philippousis simply played too many matches to allow that to happen.

Indeed, the Brands/Del Potro combined rate of 24.2% isn’t even close to the top of this list.  To show up here, it’s necessary to come within an ace or two of the 30% mark.  With Andy’s retirement and Ivo’s decline, this leaderboard looks particularly safe at the moment.

totA%  Winner              Loser              Year  Event                 Surface  Score          totAces    wA%    lA%  
34.2%  Andy Roddick        Ivo Karlovic       2009  Queen's Club          Grass    7-6(4) 7-6(5)       50  33.3%  35.1%  
31.6%  Andy Roddick        Thomas Johansson   2004  Bangkok               Hard     6-3 6-4             31  38.2%  23.3%  
31.6%  Andy Roddick        Joachim Johansson  2004  San Jose              Hard     6-3 7-6(7)          42  36.5%  25.4%  
31.6%  Martin Verkerk      Thomas Enqvist     2003  Milan                 Carpet   6-3 6-4             30  46.0%  15.6%  
30.6%  Robin Soderling     Gregory Carraz     2004  Marseille             Hard     6-3 6-4             30  42.6%  19.6%  
30.4%  Jonathan Stark      Goran Ivanisevic   1997  Indian Wells Masters  Hard     7-5 6-3             34  37.7%  23.7%  
29.9%  Mark Philippoussis  Lionel Roux        1996  Paris Masters         Carpet   6-4 6-4             35  49.1%  11.7%  
29.8%  Mikhail Youzhny     Ivan Ljubicic      2007  Rotterdam             Hard     6-2 6-4             28  29.8%  29.8%  
29.8%  Gregory Carraz      Martin Verkerk     2004  Milan                 Carpet   6-3 7-6(3)          36  30.4%  29.2%  
29.0%  Jonathan Stark      Thomas Enqvist     1993  Halle                 Grass    6-4 6-2             27  37.8%  20.8%  
29.0%  Goran Ivanisevic    Boris Becker       1996  Antwerp               Carpet   6-4 7-6(5)          38  30.8%  27.3%

Andy, we’re missing you already.

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Filed under Records, Toy stats

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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Filed under Research, Tiebreaks

More New Toys on

If you’re not yet using as your go-to ATP results and stats resource, it might be time to switch.

Last week, I added tournament pages for every ATP and Challenger event.   For instance, you can now see every match (and all of its stats, and every player’s ranking) for any tournament, like last week’s Shanghai Masters, or the 2001 Milan event.  Most sites require that you click a pop-up window to get match stats.  Now you can compare every match (including qualies, for the last several years) by  ace rate, return points won, and dozens of other stats.

As with the player pages, the match table is sortable by almost every column, and a handful of filters in the left-hand sidebar allow you zero in on the matches you are interested in.

One feature I particularly like is the ability to select subgroups of players in the top-right table.  Each tourney page defaults to displaying event totals for the eight men who reached the quarters, so you can compare tournament-long statistics for the top contenders.  By clicking the links at the bottom of that table, you can get a quick glimpse of the seeds, qualifiers, or wild cards … or stats for everyone in the main draw.

These tournament pages are accessible from every player page (and vice versa).

There are several more new features that I hope you find interesting:

  • If you haven’t already seen TA’s current tournament pages, this is a great week to check them out, with three tournaments in action.  These pages show all completed matches, all upcoming matches, and jrank-derived odds given who is left in the draw.
  • A small recent adjustment to those pages is particularly handy.  For the projections, you can click on previous round names (e.g. “R32”) to see what the projections looked like at that point in the tournament.  Find out who scored the biggest upsets, who has increased their odds the most, or just hunt for my model’s most egregious errors.
  • Many of you have asked for regularly updated surface rankings.  Here you go!
  • The first of several new reports is the Head-to-Head Matrix.  See H2H records for the current top 15.  Click on the records themselves to see a fuller view of all of the relevant head-to-heads..
  • Also new: Current Rankings by Age.  Find the top players under 19, under 21, and under 23, along with those 28+, 30+ and 32+.  Use the dropdown menu to see similar reports for each year’s year-end rankings back to 1984.
  • Inspired by a long-ago blog post, see which players are performing the most and least consistently.
  • Finally, compare tournaments by field quality.  This is fascinating stuff, so much so that I made a report for the last 52 weeks of Challengers, as well.

All of the reports are accessible from the home page.  I hope you enjoy them, and that you keep an eye out for the next wave of new toys, as well.


Filed under Tennis Abstract

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.


Filed under Tiebreaks