The Effect of 32 Seeds

Italian translation at settesei.it

In the middle of 2001, the Grand Slams doubled the number of seeds in the draw from 16 to 32, a change “designed to protect star players and satisfy clay and grass specialists.”

The intended beneficiaries of the change were, of course, all seeded players. Those in the top 16 no longer had to worry about facing a fellow top-32 player until the third round. Those ranked from 17-32, who before the change may have faced a top 16 player in the first round, now received the same protection.

The costs of the 32-seed system are borne by two groups: unseeded players, who are now more likely to face a top-ranked player early; and first-week fans, who would like to see more “compelling” early-round matches. While it’s easy to point to shock upsets like Serena Williams’s exit today as a counterpoint, the first two rounds at Slams often feel like warm-up matches for the biggest stars, with fringe players as their hapless foils.

On the other hand, it’s tough to get an intuitive sense of just how much is at stake here. It may not be as much as you think. From 1989 to 2000, men’s seeds were upset 263 times in the first two rounds of slams. Only 51 of those losses were to players in the top 32. In other words, more than 80% of those upsets would have occurred even with a 32-seed format, and presumably, some of the remaining 51 matches would still have resulted in upsets.

From the perspective of the top 16 seeds, there may not be that much difference between opponents ranked in the next 16 and those ranked lower still. To cherry-pick just one example, there are many seeded players Stanislas Wawrinka would have rather faced this week than Guillermo Garcia Lopez.

For top-four women, it hasn’t made a difference at all. In the twelve years before the switch, they reached the third round in 176 of 190 attempts. In the twelve years after the format change, women seeded 1-4 no longer risked facing a top-32 player in the first two rounds, and reached the third round in 178 of 191 attempts.

In fact, for top-16 women’s seeds in general, the 32-seed format has not helped. From 1989-2000, women’s seeds reached the third round 77.6% of the time, the fourth round 63.5% of the time, and the quarterfinals 40.8% of the time. From 2002-13, with lower-ranked early-round opponents, the corresponding numbers were 78.2%, 60.1%, and 37.1%.

It’s likely that some of the differences have to do with the increasing depth of the women’s game, but it’s hardly the case that the 32-seed format has drastically changed the nature of the majors, at least for the players who have been seeded all along. Men’s top-16 seeds have benefited, reaching the third, fourth, and quarterfinal rounds about 10% more often since the switch to 32 seeds, but even here, we’re not seeing radically different second weeks.

The real change, as you might suspect, appears when we consider the balance of power between the new seeds (17-32) and the rest of the field. From 1989-2000, when there were only 16 seeds and those two groups were treated the same way, men’s players ranked 17-32 reached the third round about twice as often (35% to 17%) as their lower-ranked competitors. Women in the 17-32 range held a wider advantage of 39% to 15%.

Now that there are 32 seeds and the 17-32 group is protected, those gaps have substantially grown. From 2002-13, men seeded outside the top 16 have reached the third round 53% of the time, compared to 12% for unseeded players. Seeded women in the 17-32 range have reached the third round 49% of the time, while unseeded women have equaled their male counterparts at 12%.

These differences, big as they are, aren’t going to affect most fans’ enjoyment of the majors. The format change means that Rafael Nadal faces a player ranked 60th in the world in the second round and a player ranked 30th in the third round. He’ll almost always win both matches, so the end result is the same. A surprise run to the quarterfinals isn’t much different if it’s made by world #25 than by #50.

However, the 32-seed format does amplify the gap between tennis’s haves and have-nots. Yes, he Grand Slams have massively increased prize money in the last few years for all main-draw competitors–first-round losers in Paris earn more than $32,000 for their efforts. But players who reach the third round are able to triple that money.

As we’ve seen, the format change has made it much more likely that #32 reaches the third round (and takes home a nearly six-figure purse) at the expense of everyone ranked lower–despite having little effect on the makeup of the field in the fourth round and beyond.  Plus, the ranking points on offer at Slams mean that third-rounders are that much more likely to earn a seed at the next major, starting the next round of the same cycle.

Seeding 32 players instead of 16 doesn’t have much of an effect on the fates of top players, especially on the women’s side. It can, however, lessen interest in the first several days of play, and it certainly supports an arbitrary middle tier of players at the expense of the rest of the field.

If the 32-seed era were to end here, there’s little reason for tennis fans to miss it.

Surprise Semifinalists at the Australian Open

Of the eight singles semifinalists in Melbourne, only two entered the tournament seeded in the top four. Rafael Nadal, the top seed in the men’s draw, has survived, and Li Na, the fourth seed in the women’s draw, is the highest-ranked player still alive on her side.

We haven’t exactly followed the script.

The women’s singles draw, with the top three seeds eliminated, is particularly unusual. It is only the 10th time in the last 35 years that none of the top three seeds have made it through to the final four of a Grand Slam. Such events have been heavily concentrated in the last decade or so–the fourth seed was the highest-ranked surviving player at Wimbledon in 2011 (Victoria Azarenka) and 2013 (Agnieszka Radwanska), and the fifth seed was the apparent favorite at Roland Garros in 2011 (Francesca Schiavone).

You might notice a pattern. In these nine Slams when no top-three seed reached the semifinal stage, the best remaining player didn’t fare so well. Both Vika and Aga fell to lower-ranked opponents when they were the remaining favorites at Wimbledon, and Schiavone lost her shot at the French Open to Li. Only twice in these nine majors did the highest-remaining seed in the semifinals go on to win: Martina Hingis, when she was seed fourth at the 1997 Australian Open, and Anastasia Myskina, when she was the sixth seed at the 2004 French Open.

In a tournament full of surprises, we might not be done yet. It stands to reason that once the favorites are eliminated, the odds of subsequent upsets increase. The lower you go in the rankings, the less difference there usually is between players–there’s a bigger gap between Azarenka and Maria Sharapova than there is between, say, Jelena Jankovic and Angelique Kerber. The smaller the gap, the more likely the upset.

While only one top-four seed remains in the men’s draw, the odds of upsets are moving in the opposite direction. While Nadal can always count on a tough fight from second-seed Novak Djokovic, he typically has little trouble with lower-ranked players. He has won his last 15 matches against the other three players left in the drawRoger Federer, Tomas Berdych, and Stanislas Wawrinka–and lost only 4 of 41 matches against the trio since 2008.

The historical precedent for this sort of semifinal draw also favors Rafa. 14 Grand Slams in the Open Era have featured a semifinal round in which the top seed is the only one remaining of the top four. The top seed has gone on to win 9 of the 14, including 8 of the last 10. The most recent final four that fit this profile was in Melbourne four years ago, when Federer swept the final two rounds without losing a set.

But even this rosy picture for Nadal offers Roger a glimmer of hope.  The last time the top seed was alone in the final four and didn’t go on to win was the 2002 US Open. Lleyton Hewitt was the #1 who failed, paving the way for a 31-year-old Pete Sampras to win one final slam before he retired.

Roger isn’t going to call it quits this week, but he’d sure like to emulate Pete’s success in seizing a wide-open Grand Slam draw.

Bouchard, Halep, and First-Time Quarterfinalists

Two of the final eight women in Melbourne, Eugenie Bouchard and Simona Halep, are playing in their first Grand Slam quarterfinals. Let’s take a look at how other women have done in their first appearances this late in a Slam.

In the Open era, 267 different women have reached the final eight of a Slam. At the time of their debut quarterfinal, their average age was roughly 21 years and four months. Their average WTA ranking was 42, not considering those who predated the ranking system or those who reached their first quarterfinal as an unranked player.

Of the 267, 197 (73.8%) progressed no further in their breakthrough slam. 52 (26.4%) won one more match, losing in the semifinals; 12 (6.1%) reached the final but lost; and the remaining six players won the title when the reached their first Open-era quarter.

However small 6 of 297 sounds, such an outcome is actually even rarer. Three of those six first-time quarterfinalists don’t really count–they reached their first QF in 1968, the first year of the Open era. Billie Jean King, winner of the Australian Open that year, isn’t that great a comp for Bouchard or Halep. The only other players to win a Grand Slam in their first quarterfinal appearance are Chris O’Neil (1978 Australian), Barbara Jordan (1980 Australian), and Serena Williams (1999 US Open).

While we can’t count on Bouchard or Halep winning the tournament this week, their appearances in Slam quarterfinals at relative young ages bodes well. The earlier a player reaches her first major QF, the more QFs she is likely to reach over the course of her career.  In fact, of the 22 women who have reached more than 10 Slam quarterfinals since 1984, only one of them–Jana Novotna–failed to reach her first one in her teens. She didn’t make it until the ripe old age of 20 years and 8 months.

Bouchard has just snuck in before her 20th birthday, which she’ll celebrate next month. Her most age-appropriate comp is Victoria Azarenka, who reached her first major quarterfinal–at the 2009 French Open–just a few weeks younger than Genie is now. Less than five years later, Vika will play her 12th Slam QF.

Less optimistic comparisons for Bouchard are Yanina Wickmayer and Anna Chakvetadze, both of whom reached their first major quarterfinal in the last two months of their teens. Chakvetadze made two more final eights; Wickmayer is still looking for her second.

If history is any guide, Halep’s prospects are bleaker. At 22 years and four months, she is much older than any of the players who have reached double-digit Slam quarterfinals except for Li Na, who is playing in her 10th QF this week. Li didn’t play in the final eight of a Grand Slam until she was 24 years old.

The 61 players who reached their first Slam QF at an older age than Halep did not, on average, achieve much more. They’ve totaled 81 additional QFs–well below two per person.

Of course, the age profile of the WTA is changing, so a 22-year-old debutante isn’t nearly the oddity it was a decade or two ago. It’s no coincidence that Halep’s most optimistic comp is Li, an active player. That’s the most positive outlook for the Romanian, anyway. To rack up an impressive career record, she’ll have to follow Li’s lead and overcome a late start.

The ATP final eight also features a newbie, Grigor Dimitrov. The changing age profile of the ATP is even more drastic, so age-based analysis is less meaningful. But we can take a quick look at the precedents for the Bulgarian’s first Slam quarterfinal.

There have been 329 ATP Slam quarterfinalists in the Open era, and first-timers stand a better chance in the men’s game. 32.5% of debut Slam quarterfinalists have advanced to the semis, and 13 of them (4.0%) went on to win the tournament. Then again, none of them had to beat Rafael Nadal in the quarters.

While Dimitrov is older than Halep–and as noted, 22-year-olds didn’t used to be considered so young on the ATP tour–there are some positive examples for Grigor to follow.

Michael Stich reached his first Slam QF at almost exactly the same age as Dimitrov is now, and he not only reached the semis at that event (the 1991 French Open), but qualified for the final eight in nine more majors. Jo Wilfried Tsonga, David Ferrer, and Nikolay Davydenko all reached their first Slam QF later than Dimitrov, and each has played in the final eight at least ten times.

On average, those optimistic comps are outweighed by all the guys who made it to one or two Slam QFs later in their career. The 153 players who reached their first final eight later than Dimitrov’s current age have returned to a total of 362 additional quarterfinals–good for one or two more appearances per player.

Despite all the hype, Dimitrov’s performance this year isn’t a drastic breakthrough. It’s only a single step in the right direction–especially considering that he reached this milestone by beating the #73 player in the world. He could be the next Tsonga, or he could be the next Robby Ginepri.

Better at Best-of-Five

Italian translation at settesei.it

The best-of-five-sets format used in Grand Slam men’s singles favors the mentally and physically strong. It also gives better players the edge, as it reduces the number of fluky results.

However, simple best-of-five records aren’t always our most useful guide. A player who consistently goes deep in slams faces difficult opponents far more frequently than he would at ATP 250 or 500 events.  We would expect that many players would have worse records in best-of-five matches not because of any tendency, but because of consistently tough draws.

If we accounted for all that–opponent quality and the structural bias toward favorites in best-of-fives–who would come out strongest? Which players outperform expectations the most in Grand Slams?

Let’s start with a few names you might not expect, before we narrow the search down to players with the longest resumes:

  • Of players with 100 career tour-level matches, the man who has outperformed the most at Slams is Bernard Tomic. In 35 matches at majors, he has won 20 despite his rankings suggesting he would win only 11–82% better than expected. Outside of slams, he has precisely played to his ranking.  Modest as Bernie’s track record is, no other active player comes close to this gap.
  • Bump the threshold to 200 career matches, and your man is … Denis Istomin? His 21-21 record at Slams doesn’t seem so impressive until you consider that he has never been seeded. His rankings would imply he should have won only 16 matches.
  • The parade of underdogs continues when we up the standard to 300 career matches. Victor Hanescu has outperformed best-of-five expectations by a solid 20%, going 28-32 while his lowly rankings would suggest he should have won only 23 matches.

Let’s move on to the big dogs. I meant to limit this study to active players, but when you go far enough back to cover the careers of guys like Radek Stepanek and Tommy Haas, you end up getting a lot of notable former stars. And here, Marat Safin stands out.

Safin’s career mark in slams was 95-41, excellent by any standard. His winning percentage of about 70% was about 14% higher than the combination of his rankings and his opponents would have predicted. While he exceeded expectations in Slams, he underwhelmed in other events.  He won almost 10% fewer best-of-three matches than would have been expected over the course of his career.

No current top-ten player displays as big a gap between best-of-five and best-of-three performance than Safin did, but Jo Wilfried Tsonga comes the closest. In this table, I’ve shown each player’s career record at majors, how that compares to the number of wins they should have expected, then the same pair of numbers for non-slams. (I’ve excluded all Davis Cup matches.) Finally, the “ExpRat” column shows how much better each guy played at majors than at non-majors–the ratio of how much more the player exceeded expectations at Slams than elsewhere.

Player                 Bo5 W%  Bo5 Exp  Bo3 W%  Bo3 Exp  ExpRat  
Jo Wilfried Tsonga      76.6%     1.17   66.6%     0.98    1.19  
Tomas Berdych           69.3%     1.06   63.1%     0.95    1.12  
Stanislas Wawrinka      67.0%     1.17   58.6%     1.08    1.08  
Novak Djokovic          85.3%     1.06   79.2%     0.99    1.07  
Rafael Nadal            88.3%     1.07   82.1%     1.01    1.06  
Andy Murray             79.6%     1.05   73.7%     1.03    1.02  
Roger Federer           84.4%     1.01   79.2%     1.00    1.01  
David Ferrer            70.6%     0.95   65.6%     0.96    0.99  
Richard Gasquet         64.0%     1.04   63.5%     1.09    0.95  
Juan Martin Del Potro   72.9%     1.13   72.5%     1.24    0.91

It’s inevitable that the Big Four make up the middle of the pack. When you are as good as they have been for as long as they have been, you can only exceed expectations so much. Most impressive of the group is Rafael Nadal, who has been better at majors than non-majors despite vastly preferring clay courts. Many of the journeyman players who do the worst by this metric are clay specialists–guys like Filippo Volandri and Potito Starace who are virtually guaranteed first-round exits at three slams each year.

While Juan Martin del Potro‘s appearance at the bottom of this list seems particularly timely after last night’s upset, it may be no more than a statistical fluke stemming from his long absence and long comeback in 2010 and 2011.  His ranking lagged behind his skill level for a long time, which explains why he has managed to exceed expectations both at Slams (+13%) and at non-majors (+24%). The loss to Roberto Bautista Agut won’t help his numbers, but it may take several more slams before we can be more confident about Delpo’s best-of-five tendencies.

When Tsonga and Roger Federer clashed in last year’s Melbourne quarterfinals, Federer escaped in five sets. If, as expected, they face off this year as well, these numbers represent one reason why Fed might not be so lucky again.

For further reading, check out Colin Davy’s similar study.