Is Grand Slam Qualifying Worth Tanking For?

Earlier today in Hobart, Naomi Osaka lost her second-round match to Mona Barthel. Coming into the match, she was in a tricky position: If she won, she wouldn’t be able to play Australian Open qualifying. For a young player outside the top 100, a tour-level quarterfinal would be nice, but presumably Melbourne was intended to be the centerpiece of her trip to Australia.

Since she lost the match, she’ll be able to play qualifying. But what if she hadn’t? Is this a situation in which a player would benefit from losing a match?

Put another way: In a position like Osaka’s, what are the incentives? If she could choose between the International-level quarterfinal and the Slam qualifying berth, which should she pick? Or, put more crassly, should a player in this position tank?

Let’s review the scenarios. In scenario A, Osaka wins the Hobart second-rounder, reaches the quarterfinal, and has a chance to go even further. She can’t play the Australian Open in any form. In scenario B, she loses the second-rounder, enters Melbourne qualifying and has a chance to reach the main draw.

Before we go through the numbers, take a guess: Which scenario is likely to give Osaka more ranking points? What about prize money?

Scenario A is more straightforward. By reaching the quarterfinals, she earns 30 additional ranking points and US$2,590 beyond what a second-round loser makes. Beyond that, we need to calculate “expected” points and prize money, using the amounts on offer for each round and combining them with her odds of getting there.

Let’s estimate that Osaka would have about a 25% chance of winning her quarterfinal match and earning an additional 50 points and $5400. In expected terms, that’s 12.5 points and $1,350. If she progresses, we’ll give her a 25% chance of reaching the final, then in the final, a 15% chance of winning the title.

Adding up these various possibilities, from her guaranteed QF points to her 0.94% chance (25%*25%*15*) of winning the Hobart title, we see that her expected rewards in scenario A are roughly 48 ranking points and just under $4,800.

Scenario B starts in a very different place. Thanks to the recent increases in Grand Slam prize money, every player in the qualifying takes home at least US$3,150. That’s already close to Osaka’s expected financial reward from advancing in Hobart. The points are a different story, though: First-round qualifying losers only get 2 WTA ranking points.

I’ll spare you all the calculations for scenario B, but I’ve assumed that Osaka would have a 70% chance of winning qualifying round 1, a 60% chance of winning QR2, and a 50% chance of winning QR3 and qualifying. Those might be a little bit high, but if they are, consider it compensation for the possibility that she’ll reach the main draw as a lucky loser. (Also, if we knock her chances all the way down to 50%, 45%, and 40%, the conclusions are the same, even if the points and prize money in scenario B are quite a bit lower.)

Those estimated probabilities translate into an expectation of about 23 ranking points and US$11,100. Osaka isn’t guaranteed any money beyond the initial $3,150, but the rewards for qualifying are enormous, especially compared to the prize money in Hobart. A first-round main draw loser in Melbourne takes home more money than the losing finalist does in Hobart.

And, of course, if she does qualify, there’s a chance she’ll go further. Since 2000, female Slam qualifiers have reached the second round 41% of the time, the third round 9% of the time, the fourth round 1.8% of the time, and the quarterfinals 0.3% of the time. Those odds, combined with her 21% chance of reaching the main draw in the first place,  translate into an additional 7 expected ranking points and $2,600 in prize money.

All told, scenario B gives us 30 expected ranking points and US$13,600 in expected prize money.

The Slam option results in far more cash, while the International route is worth more ranking points. In the long term, those ranking points would have some financial value, possible earning Osaka entry into a few higher-level events than she would otherwise qualify for. But that value probably doesn’t overcome the nearly $9,000 gap in immediate prize money.

I hope that no player ever tanks a match at a tour-level event so they can make it in time for Slam qualifying. But if one does, we’ll at least understand the logic behind it.

Will the US Open First-Round Bloodbath Benefit Serena Williams?

After only two days of play, the US Open women’s draw is a shell of its former self.

Ten seeds have been eliminated, only the fifth time in the 32-seed era that the number of first-round upsets has reached double digits. Four of the top ten seeds were among the victims, marking the first time since 1994 that so many top-tenners failed to reach the second round of a Grand Slam.

Things are particularly dramatic in the top half of the draw, where Serena Williams can now reach the final without playing a single top-ten opponent. In a single day of play, my (conservative) forecast of her chances of winning the tournament rose from 42% to 47%, only a small fraction of which owed to her defeat of Vitalia Diatchenko.

However, plenty of obstacles remain. Serena could face Agnieszka Radwanska or Madison Keys in the fourth round, and then Belinda Bencic–the last player to beat her–in the quarters. A possible semifinal opponent is Elina Svitolina, a rising star who took a set from Serena at this year’s Australian Open.

The first-round carnage didn’t include most of the players who have demonstrated they can challenge the top seed. Five of the last six players to beat Serena–Bencic, Petra Kvitova, Simona Halep, Venus Williams, and Garbine Muguruza–are still alive. Only Alize Cornet, the 27th seed who holds an improbable .500 career record against Serena, is out of the picture.

What’s more, early-round bloodbaths haven’t, in the past, cleared the way for favorites. In the 59 majors since 2001, when the number of seeds increased to 32, the number of first-round upsets has had little to do with the likelihood that the top seed goes on to win the tournament.

In 18 of those 59 Slams, four or fewer seeds were upset in the first round. The top seed went on to win five times. In 22 of the 59, five or six seeds were upset in the first round, and the top seed won eight times.

In the remaining 19 Slams, in which seven or more seeds were upset in the first round, the top seed won only five times. Serena has “lost” four of those events, most recently last year’s Wimbledon, when nine seeds fell in their opening matches and Cornet defeated her in the third round.

This is necessarily a small sample, and even setting aside statistical qualms, it doesn’t tell the whole story. While Serena has failed to win four of these carnage-ridden majors, she has won three more of them when she wasn’t the top seed, including the 2012 US Open, when ten seeds lost in the first round and Williams went on to beat Victoria Azarenka in the final.

Taken together, the evidence is decidedly mixed. With the exception of Cornet, the ten defeated seeds aren’t the ones Serena would’ve chosen to remove from her path. While her odds have improved a bit on paper, the path through Keys, Bencic, Svitolina, and Halep or Kvitova in the final is as difficult as any she was likely to face.

Roger Federer’s Impressive but Not-Entirely-Relevant Dominance of the Istanbul Field

Roger Federer has faced 14 of the 27 other players in this week’s Istanbul field, and owns a career record of 59-1 against them. His one loss came to Jurgen Melzer, while more than half of his win total is thanks to his decade-long dominance of Mikhail Youzhny (16-0) and Jarkko Nieminen (14-0).

It’s rare that players of Federer’s stature contest such small events, so we don’t expect to see such lopsided head-to-heads very often. In fact, if we limit our view to events where a player faced at least 10 of the other entrants, it is only the 17th time since 1980 that someone has entered an event with a won-loss percentage of 95% or better against the field.

Federer himself represents two of the previous 16 times this has happened. The most notable of them is 2008 Estoril. He had previously faced 14 of the other players in the draw, and had never lost to any of them in 46 meetings. There are only four other instances of players undefeated against a field, all between 1980 and 1984 and in many fewer matches.

The most eye-grabbing of those early-80s accomplishments was Ivan Lendl‘s record entering the 1980 Taipei event. He had faced 15 of the men in the draw, posting a record of 24-0 up to that point. Lendl’s name is the most common on the list, having entered tournaments with a 95% won-loss record against the field on four different occasions, highlighted by a 79-4 mark against the other competitors at Stratton Mountain in 1988.

Federer won the 2008 title in Estoril and Lendl claimed the 1980 trophy in Taipei, but Lendl was ousted in the second round of the 1988 Stratton Mountain event. Federer has also demonstrated that a stratospheric record against the field is no guarantee of success.

After Estoril, Roger’s second-best record entering an event was in Gstaad in 2013. He held a 73-3 record against the field, with each of the three losses coming against different opponents. He lost his opening-round match in straight sets to Daniel Brands. His record against the field of the previous week’s Hamburg event was nearly perfect as well at 137-8, but Federico Delbonis stopped him in the semifinals there.

Rafael Nadal can tell a similar story. His best record against a field was in Santiago two years ago, coming back from injury. He had lost only 1 of 28 career matches against the other players in the draw. That week, Horacio Zeballos doubled Rafa’s loss count.

In fact, of the 16 times that a player went into an event with a 95% or better record against the field, the favorite won only six of them. Expanding the sample to records of 90% or better, the dominant player won 30 of 72 titles. Neither mark is as good as we’d expect if the historically great players continued to win matches at a 95% or 90% clip. In practice, head-to-head records just aren’t as predictive as they seem to be.

As is evident from some of the examples I’ve given, there are mitigating circumstances for many of these losses, and they aren’t entirely random. These days, when a player enters an event that seems below him, there’s a reason for it. Nadal rarely plays 250s; he was doing so to work his way back into match form. Federer rarely seeks out smaller events on clay; he was experimenting with a new racket.

This week, there’s no reason why Fed shouldn’t perform at his usual level–at least his usual level for clay–and win the four matches he needs to claim yet another title. But if he suffers his second loss against the players gathered in Istanbul this week, it won’t be quite as much of a shock as that 59-1 record implies.

The Most Predictable Quarterfinals

This week in Paris, all eight quarterfinalists are among the top nine seeds, the most tightly packed final eight since the 2009 Canada Masters, which was the only Masters or Grand Slam event this century in which all of the top eight seeds reached the quarterfinals.

This quarterfinal lineup is a reminder that, even with the decline of Roger Federer and the temporary absence of Andy Murray, men’s tennis is a top-heavy game.  At the Masters and Grand Slam levels, there have been eight other events since 2000 where all eight quarterfinalists were drawn from the top fourteen seeds–and all eight have been in the last five years.  By contrast, there were only two events between 2000 and 2005 where each player in the final eight came from the top 25.

This year, the average Masters and Grand Slam event has featured 6.5 seeds in the quarterfinals.  That number has hovered between 6.5 and 7 since 2009.  From 2000 to 2009, however, it never topped 6.25.  In 2000 it was as low as 4.4; in 2003 the figure was 4.6.

The median seeds (or ATP rankings, for those players who were unseeded) tell a similar story.  This year, the median quarterfinalist rank at the average Masters or Slam was 7.8, indicating that typically, four of the final eight were seeded 7th or better.  That number didn’t fall below 9.0 between 2000 and 2009 and reached as high as 18.3 in 2003.

What triggered this research, though, wasn’t a desire to quantify the top-heaviness of the men’s game, but to look at whether certain tournaments lent themselves to this sort of late-round predictability.  Given this year’s lineup in Paris and the notable eight-for-eight showing four years ago in Canada, it seems a reasonable guess that, for whatever reason, these two events were particularly prone to a seed-laden final weekend.

They aren’t.  In fact, measured by the median quarterfinalist seeding since 2000, the Canada Masters event ranks as the least predictable among the current slate of Masters and Grand Slam events.  The defunct Hamburg Masters is the only event that compares.  Paris has not been so unpredictable, but it doesn’t rank in the top half of Slam and Masters events by this metric.  Despite the blue clay, the most predictable event has been the Madrid Masters in its years on clay.

Given that seedings are based on ATP rankings, which are in turn based on a season that is hard-court heavy, I’m surprised to find any clay events near the top of the list, even Roland Garros.  More in line with expectations are Monte Carlo, Rome, and most extreme of all, Hamburg.  Another surprise is Shanghai near the top of the list.  Conventional wisdom suggests that players don’t prioritize the Asian swing.

If there’s any rhyme or reason to why some of these tournaments are more likely to see predictable final eights, it is elusive.

Here is the full breakdown, sorted by median quarterfinalist seeding:

Event                 Surface  Yrs  SdQFs  AvgQF  MedQF  
Madrid Masters        Clay       5    6.6   13.1    6.7  
US Open               Hard      14    7.1   14.1    8.5  
Roland Garros         Clay      14    7.0   14.8    8.5  
Shanghai Masters      Hard       4    5.8   17.5    8.8  
Australian Open       Hard      14    6.7   14.6    9.8  
Madrid Masters        Hard       7    5.3   19.1   11.1  
Indian Wells Masters  Hard      14    6.1   20.1   11.3  
Miami Masters         Hard      14    6.8   17.1   11.5  
Paris Masters         Hard      14    5.9   16.9   11.8  
Cincinnati Masters    Hard      14    5.1   18.1   12.2  
Monte Carlo Masters   Clay      14    5.1   22.3   12.7  
Wimbledon             Grass     14    6.3   36.1   13.4  
Rome Masters          Clay      14    4.9   19.8   13.8  
Canada Masters        Hard      14    4.8   22.4   16.1  
Hamburg Masters       Clay       9    3.9   27.7   22.9

The Historically Strong Dallas Challenger

All eyes are on Indian Wells this week, with seven of the top eight-ranked men in the world in the quarterfinals.  (Oh, and one epic streak coming to an end.)  Look a little deeper, though, and you’ll find another ATP event in progress, this one under the guise of a Challenger tournament.

By just about every metric imaginable, this week’s Dallas Challenger has one of the strongest Challenger fields ever assembled.  Many ATP 250s–and a few 500s–are barely at the same level.

Because of Dallas’s timing in between the opening rounds of Indian Wells and the beginning of the Miami Masters, special rules apply to tournament entries.  Higher-ranked players are able to make last-minute decisions to compete, hence the presence of the two top seeds, Marcos Baghdatis and Thomaz Bellucci.  Many other tour-level pros choose to make the stop in Dallas to get a couple of matches under their belt to compensate for a disappointing showing in the California desert.

Measuring field quality is tricky, but here we’re not working with subtle differences.  Here are some simple metrics we could use to the compare main draw strength of the 2500 or so Challenger events since 1991:

  • Average ATP Rank. In Dallas this year, it’s 103, the best ever in a Challenger event.  Second best is 109–that was the same event last year.  Only eight Challengers have ever had an average rank below 130, and the average is a whopping 290.
  • Median ATP Rank. Similar deal, without the risk of a few top players skewing the results.  Dallas’s median is 90; last year it was 90.5–best and second-best ever.  Only two others come in under 100, and the average is 239.
  • 8th seed ATP Rank. I like this metric as it indicates the presumed quality of the quarterfinals–every guy in the last 8 is either this good or has to beat someone this good.  Dallas’s 8-seed this year is #62 Lukas Rosol, the highest-ranked 8-seed ever in a challenger event.  Second place, once again, is the same event last year, where #69 Lukas Lacko was seeded eighth.  Only 18 events have ever had an 8-seed in the top 80, and the historical average is 180.
  • Average seed ATP Rank. Another angle: here Dallas is ousted, coming in 3rd of the 2500 events, at 48.  The 1991 Johannesburg Challenger (46.5) and 1994 Andorra Challenger (47.5) just barely beat it out.  Only 17 events have had an average seed rank better than 60, and the average is 145.
  • Number of top 50 players. Dallas is only the 3rd Challenger event to ever have five top 50 players, after 1991 Jo’burg and 2004 Dnepropetrovsk.  Only 66 Challengers have ever had multiple top-50 competititors, and fewer than 1 in 10 Challengers have a single one.  The average Challenger top seed is ranked #97.
  • Number of top 75/100/125 players.  12 players in the main draw this week are ranked in the top 75, 18 in the top 100, and 25 in the top 125.  All are either new records or tied with the old record.  The average challenger event has 0.13 top-50s, 0.57 top-75s, 1.71 top 100’s, and 3.81 top 125’s.

The one way in which this week’s tournament in Dallas doesn’t rank amongst the best is by a more sophisticated approach, the one that I use in my Challenger strength report on TennisAbstract.com.  By simulating the tournament draw several thousand times, we can estimate the likelihood of a certain level of player winning the event.  For instance, had the 50th-best player in the world entered the Burnie or West Lakes Challenger this year, he would have had about a 25% chance of winning.   But against the more competitive field in Quimper, that number drops to 12%–about the same as the 50th-best player’s chance in the unusually weak Los Angeles ATP event last year.

This week, Jurgen Melzer–ranked in the mid-40s on hard courts by my rating system–had a 9.3% chance of winning the title according to my pre-tourney simulations.  (Go to the tournament forecast page and click ‘R32’ under the ‘Forecast’ header.)  That puts Dallas comfortably among the top 10 toughest Challenger draws in the last year–and better than LA–but nowhere near the top.

It’s one thing to have a deep draw, but another thing entirely to have a tournament that is particularly hard to win.   For the latter, an event needs one or two very highly-ranked players, like Marin Cilic at last year’s Dallas Challenger, or Fernando Verdasco in Prostejov last year.  In theory, if not in practice, someone ranked in the top 20 should waltz to a title, offering an insurmountable obstacle to your typical Challenger-level player.

Dallas may not be the most difficult Challenger event to win, but by any measure of field quality and depth,  it’s one of the very strongest in ATP history.  The fans in Dallas are very fortunate this week.