Category: Research

The Speed of Every Surface

Italian translation at settesei.it

Last week, I wrote an article for the Wall Street Journal noting the relatively slow speed of this year’s U.S. Open.  It’s not clear whether the surface itself is the cause, or whether the main factor is the humidity from Hurricane Irene and Tropical Storm Lee.  For whatever reason, aces were lower than usual, creating an environment more favorable to, say, Novak Djokovic than someone like Andy Roddick.

The limited space in the Journal prevented me from going into much detail about the methodology or showing results from tournaments other than the slams.  There’s no word limit here at Heavy Topspin, so here goes…

Aces and Server’s Winning Percentage

Surface speed is tricky to measure–as I’ve already mentioned, “surface speed” is really a jumble of many factors, including the court surface, but also heavily influenced by the atmosphere and altitude.  (And, possibly, different types of balls.)  If you were able to physically move the clay courts in Madrid to the venue of the Rome Masters, you would get different results.  But teasing out the different environmental influences is little more than semantics–we’re interested in how the ball bounces off the court, and how that affects the style of play.

So then, what stats best reflect surface speed?  Rally length would be useful, as would winner counts–shorter rallies and more winners would imply a faster court.  But we don’t have those for more than a few tournaments.  Instead, I stuck with the basics: aces, and the percentage of points won by the server.

Important in any analysis of this sort is to control for the players at each tournament.  The players who show up for a lower-rung clay tournament are more likely to be clay specialists, and the men who get through qualifying are more likely to be comfortable on clay.  Also, the players who reach the later rounds are more likely to be better on the tournament’s surface.  Thus, the number of aces at, say, the French Open is partially influenced by surface, and partially influenced by who plays, and how much each player plays.

Thus, instead of looking at raw numbers (e.g. 5% of points at Monte Carlo were aces), I took each server in each match, and compared his ace rate to his season-long ace rate.  Then I aggregated those comparisons for all matches in the tournament.  This allows us to measure each tournament’s ace rate against a neutral, average-speed surface.

The Path to Blandness

The ace rate numbers varied widely.  While the Australian Open and this year’s US Open were close to a hypothetical neutral surface speed, other tourneys feature barely half the average number of aces, and still others have nearly half-again the number of aces of a neutral surface.   I’ve included a long list of tournaments and their ace rates below; you won’t be surprised to see the indoor and grass tournaments on the high end and clay events at the other extreme.

But there’s a surprise waiting.  I also calculated the percentage of points won by the server, and like ace rate, I controlled for the mix of players in every event.  While ace rate varies from 53% of average to 145% of average, the percentage of points won by the server never falls below 90% of average, rarely drops below 95%, and never exceeds 105%.  53 of the 67 tournaments listed below fall between 97% and 103%–suggesting that surface influences the outcome of only handful of points per match.

That may defy intuition, but think back to the mix of players at each tournament.  Big-serving Americans don’t show up at Monte Carlo, while South Americans generally skip every non-mandatory event in North America.  The nominal rate at which servers win points varies quite a bit, but that’s because of the players in the mix.

Also, this finding suggests that, as a stat, aces are overrated.  They may be a useful proxy for server dominance–if a players hits 15 aces in a match, he’s probably a pretty good server–but they come nowhere near telling the whole story.  Aces on grass turn into service winners on hard courts, and then become weak returns and third-shot winners on clay.  The end result is usually the same, but Milos Raonic is a lot scarier when the serves bounce over your head.

Finally, it would be a mistake to say that a variance of 3-5% in serve points won is meaningless.  It may be less than expected, but especially between good servers, 3-5% can be the difference.  Move Saturday’s Federer/Djokovic semifinal to a surface like Wimbledon’s, and we’d be looking at a different champion.

All the Numbers

Here is the breakdown of ace rate and serve points won, compared to season average, for nearly every current ATP event.

Since I am using each season’s average, you may wonder whether the averages themselves have changed from year to year.  I’ve read that courts are getting slower, but in the five-year span I’ve studied here, the ace rate has actually crept up a tiny bit.  Each tournament varies quite a bit–probably due to weather–but generally ends up at the same numbers.

Below, find the 2011 ace rate and percentage of serve points won, as well as the average back to 2007.   Again, these are controlled for the mix of players (including how much each guy played), and the numbers are all relative to season average.

The little letter next to the tournament name is surface: c = clay, h = hard, g = grass, and i = indoor.

Tournament          2011Ace  2011Sv%    AvgAce  AvgSv%  
Estoril          c    57.5%    96.6%     53.3%   94.3%  
Monte Carlo      c    52.0%    92.1%     53.9%   91.2%  
Umag             c    58.6%    95.2%     58.7%   94.3%  
Serbia           c    54.2%    93.5%     61.0%   94.8%  
Rome             c    62.5%    95.9%     62.9%   94.4%  
Buenos Aires     c    61.9%    99.0%     62.9%   98.6%  
Houston          c    64.9%    97.2%     66.6%   96.8%  
Valencia         i                       68.0%   96.4%  
Barcelona        c    55.7%    94.3%     68.0%   96.2%  
Dusseldorf       c    45.7%    96.5%     72.8%   97.2%  

Hamburg          c    78.0%    96.6%     74.3%   96.4%  
Bastad           c    63.8%    94.5%     76.8%   97.7%  
Roland Garros    c    78.0%    98.4%     77.1%   97.5%  
Santiago         c    84.5%    98.5%     81.5%   99.4%  
Costa do Sauipe  c    83.4%   101.7%     84.2%   98.9%  
Nice             c    88.5%    97.4%     84.3%   98.1%  
Casablanca       c    79.1%    99.0%     84.9%   98.2%  
Acupulco         c    70.9%    95.6%     86.0%   98.7%  
Madrid           c    77.0%    98.5%     86.1%   98.0%  
Munich           c    87.9%   100.1%     86.5%  100.0%  

Beijing          h                       86.7%   97.3%  
Los Angeles      h    84.7%    97.2%     87.7%   97.3%  
Kitzbuhel        c    95.8%    97.9%     89.0%   98.6%  
Toronto          h                       89.6%   98.3%  
Chennai          h    82.3%    98.0%     89.6%   98.7%  
Stuttgart        c    77.0%    95.8%     89.7%   98.1%  
Indian Wells     h    88.9%    99.0%     90.9%   98.0%  
Doha             h   125.5%   101.9%     91.2%   97.6%  
Auckland         h   103.1%   102.0%     93.9%   98.7%  
Miami            h    94.5%    97.9%     94.4%   98.0%  

Shanghai         h                       94.6%   98.1%  
Australian Open  h    97.6%    97.3%     96.5%   96.9%  
Kuala Lumpur     h                       97.1%   97.3%  
Sydney           h   105.8%   100.0%     97.4%   99.1%  
St. Petersburg   i                       97.8%  101.7%  
Montreal         h    91.3%    98.4%     98.1%   98.2%  
Delray Beach     h   106.2%    99.9%     99.1%   98.6%  
Gstaad           c   104.5%   100.1%    101.2%  101.4%  
Dubai            h   102.7%    96.5%    103.2%   98.2%  
US Open          h   101.3%    97.4%    104.0%   98.7%  

Vienna           i                      105.8%  101.4%  
Johannesburg     h   110.0%   102.7%    106.0%  101.0%  
Washington DC    h    97.5%   100.1%    106.8%   99.8%  
Newport          g    93.3%    99.0%    107.5%  101.7%  
Winston-Salem    h   108.1%    99.6%    108.1%   99.6%  
Atlanta          h   110.0%   100.9%    108.4%   99.0%  
Bangkok          h                      110.5%  101.6%  
Cincinnati       h    96.2%    98.9%    111.7%  100.5%  
Zagreb           i   107.0%    99.2%    112.3%  102.3%  
Moscow           i                      113.0%  101.3%  

Brisbane         h   130.6%   100.3%    113.4%  100.0%  
Eastbourne       g   111.2%   101.8%    114.1%  102.9%  
Paris Indoors    i                      115.4%   99.6%  
Rotterdam        i   123.8%   103.7%    115.9%  101.0%  
Basel            i                      117.7%  101.3%  
San Jose         i   108.6%   103.0%    120.0%  102.7%  
Wimbledon        g   119.4%   102.8%    120.7%  103.0%  
Queen's Club     g   113.3%   101.8%    121.5%  103.2%  
Halle            g   122.9%   104.7%    123.2%  102.5%  
Marseille        i   127.4%   102.8%    124.2%  102.2%  

Stockholm        i                      124.4%   99.8%  
Metz             i                      124.6%  101.7%  
Tokyo            h                      124.7%  100.5%  
s-Hertogenbosch  g   110.9%   102.1%    126.3%  104.0%  
Memphis          i   117.1%   101.2%    129.1%  102.0%  
Montpellier      i                      145.4%  104.5%

US Open Draw Datasets

Earlier today, I published a thorough analysis of the last ten years of US Open draws, showing that while first and second seeds have had extremely easy first-round matchups, there is no other credible statistical evidence that suggests any nonrandom manipulation of the draw.

If you want to take a look at the draws yourself, I’ve made it easier.  The following files not only have the full draws going back to 2001, but they also include each player’s ATP or WTA ranking at the time of the tournament, their ordinal ranking among the players in the draw, the ordinal ranking of their first-round opponent, and the ordinal ranking of their best-possible second round opponent.

Click to download the files:

Here’s a quick rundown of the columns you’ll find in each sheet:

  • Year — each file contains the entire draws for the last ten years.
  • Draw Pos[ition] — numbers 1 to 128, so you can always sort the sheet to show the players in draw order.  (For instance, the #1 seed is 1, that player’s opponent is 2, and so on.)
  • Player
  • Country
  • Seed — the seeding assigned by the US Open
  • Rank [ATP/WTA] — the player’s official ranking the Monday that the tourney began.
  • Ordinal — the player’s rank among the 128 players in the field.  Last year, Shelby Rogers’s WTA ranking was 344, which made her ordinal ranking 124 out of 128.
  • 1stRdOpp — the ordinal ranking of the player’s first-round opponent.
  • Best2nd — the ordinal ranking of the player’s best possible second-round opponent.
Let me know if you find anything interesting!

Is the US Open Draw Truly Random?

Italian translation at settesei.it

Last week, an ESPN “Outside the Lines” article called into question the fairness of the U.S. Open main draw.  A researcher discovered that the top two seeds (both men and women) have gotten very easy first-round assignments.

This is one small step away from a direct accusation of draw-rigging by the USTA.  It’s a serious claim, and while the article’s author leans heavily on a single academic who supports the methodology used, it’s not at all clear that anything unacceptable is going on.

What they found

For some reason, the study focused on the top two seeds.  It’s not at all clear why it did so–I have no idea what the USTA’s motive would be for rigging the draw in favor of the top two seeds, regardless of their identity.  Sure, there were a few years when a Federer-Nadal final would have been particularly mouthwatering, or when American viewers craved a Serena-Venus showdown in Flushing, but why would the USTA be tweaking a draw in favor of Gustavo Kuerten?  Marat Safin?  Amelie Mauresmo? Dinara Safina?

For the moment, let’s set that major concern aside.  To quantify the difficulty of each player’s first-round opponents, the ESPN study invented a metric called “difficulty score.”  We’ll come back to “difficulty score” in a bit.

A simple look at the lists they assembled of first-round opponents does suggest that something untoward is going on.  In the last ten years of men’s draws, a top-two seed has faced a top-80 opponent only four times, and not once in the last five years.  Seeded players should face top-80 opponents about half the time.

If we are truly interested in the first-rounders assigned to top-two seeds, it’s clear that these players have been given an easier path than what would be statistically expected.  But it’s not yet clear that it’s anything other than good luck.

Breaking down “difficulty score”

Here’s the explanation of the metric that ESPN used:

So if a top two seed faced the 33rd-ranked player in the first round, he/she would get a difficulty score of 0.995 for that round; if he/she faced the 128th-ranked player in the first round, the score for that round would be 0.005. An average opponent (ranked around 80th or 81st), would correspond to a difficulty score near 0.500, which should be the average difficulty score over several years of draws.

I don’t understand why the ESPN study needed to switch from ordinal rankings (1 to 128) to difficulty scores between 0.005 and 0.995.  But I replicated the work using ordinal rankings instead of difficulty scores, and came up with the same results.

The average first round opponent for the top two seeds in each year’s men’s draw has been about the 98th-best player in the draw.  Given that seeds can draw anyone from 33 to 128, the average “should” be around 80.  With difficulty scores, ESPN says that the likelihood of the last ten years of easy draws is 0.3%.  With ordinal rankings, I found approximately the same.  The last thing the sports-analysis world needs is another superfluous metric, but at least this one doesn’t appear to be misleading.

What about better reasons for rigging?

The core problem here is this: Why do we care  specifically about the draws for the first two seeds?  Or, why would the USTA care enough to compromise the fairness of the draw?

As ESPN highlighted, some of the first-round victims are American wild cards.  Scoville Jenkins, for instance, was fed to the wolves twice, once each against Federer and Roddick.  If we’re really fishing for an explanation, perhaps the USTA wants to put up-and-coming stars such as Jenkins, Devin Britton, and Coco Vandeweghe on a big stage, either to showcase these players, or to make otherwise pedestrian blowouts more interesting.  I suppose I’d rather watch Nadal play Jack Sock than, say, Diego Junqueira.

But that’s ex post facto reasoning of the most blatant sort.  If the USTA were going to rig the draw, wouldn’t they be more likely to do so in favor of top Americans?  Or in favor of a broader range of seeds, to better ensure marquee matchups for the second week?  Or rig second-round matchups for top players, to ensure that the big names make it to the middle weekend?

If no evidence of draw manipulation appears in any of those other scenarios, it would seem that ESPN discovered something more like the famous correlation between the S&P 500 and butter production in Bangladesh.  If your search for a newsworthy conclusion is sufficiently wide, you’re bound to find something.

The top seeds

As I’ve said, there’s no doubt that the top two seeds in the men’s draw have had an easy go of it in the last ten years, since the draws started seeding 32 players instead of 16.  The same is true of the women.

The top two in both the men’s and women’s draws faced an opponent who ranked roughly 98th out of the 128 field.  The odds of this happening on either side are tiny–about 0.25%.  The chances that a single tournament would randomly produce draws so easy for the top two men and women for ten years are effectively zero.

Beyond the top two, however, any suspicions quickly disappear.  The average opponent for the top four seeded men has been ranked about 89 out of 128, meaning that #3 and #4 face opponents around #80–dead average.  The average first-round assignment for the top eight seeded men has been around 87, meaning that seeds 5-8 face average opponents in the mid-80s.  Nothing to cause a raised eyebrow there, and the numbers are almost identical on the women’s side.

To go one step further, there’s no evidence of manipulation in the second-round draws.  In fact, the top two women’s seeds faced particularly tough 2nd round opponents–there was only a 20% chance that those twenty women would be given as tough of 2nd round assignments as they have.

Before looking at the draws of U.S. players, a quick summary.  While the top two seeds were given very low-ranked opponents in the first round, the effect did not extend to the second round, or to any seeds beyond the top two.

The American draws

If the USTA were to tweak the draws, you’d expect them to do so in favor of the home players, if for no other reason than television ratings.  But they haven’t.

Let’s start with the American men.  The top two ranked American men each year have faced opponents ranked, on average, 79 of 128.  That’s a bit tougher than average.  If we expand the analysis to the top four ranked Americans, or just seeded Americans, the results stay around average.  If anyone is manipulating the draws in favor of American men, they are either doing it without regard for ATP rankings, or they aren’t doing a very good job.

More surprising is the average opponent of all American men.  The average opponent of an American man in the last ten years has been 61.2 — considerably lower than 80, in part because unseeded men may draw seeded players in the first round.  But the average shouldn’t be that low.  In fact, there is only a 20% chance that American men would be given such a tough assignment.

Results for the women are mostly similar.  The top two American women each year have gotten a slightly easy draw–the average opponent rank is 83 of 128.  Keep in mind, however, that this overlaps with the analysis of the top two seeded women–five of the 20 top-two-seeded women were Americans, and in almost each one of those five cases, those women faced one of the weakest players in the draw.  In other words, there’s more evidence that the draw is skewed in favor of the top two seeds than the top two Americans.

As with the men, American women in general have been given tough assignments.  In fact, there is only a 16% chance that American women would face such tough first round opponents as they have.

What this means

If the USTA (or anyone else) is messing with the US Open draws, they are doing so in a nearly inscrutable way.  The only evidence of manipulation is with each year’s top two seeds, as ESPN highlighted.

The theory I mentioned above–that it might be desirable to pit top players against up-and-coming Americans–is appealing, but also not supported by the evidence.  Only five of the 20 opponents of top-two men’s seeds (and six of 20 women’s opponents) has been American, despite the fact that the U.S. contributes five or six lowly-ranked wild cards each year, in addition to a disproportionate number of qualifiers.

It’s an odd situation.  The first-round opponents of the top two seeds makes for a plausible target of draw manipulation, if not the most obvious one.

Postscript: One more question

I mentioned earlier that I’d rather watch Nadal play Jack Sock than Diego Junqueira.  I like up-and-comers, and it’s always interesting to see whether a new opponent forces a top player to change tactics.  It makes for a more interesting match than Nadal (or any top-tenner) against a 29-year-old who has hovered for years around #100.

My question, then: If you’re Rafa Nadal, and (presumably) you want to go deep at the U.S. Open, who would you rather play?  The American wild card ranked #450, or the veteran ranked #99?  A tougher question: Sock, or a veteran who was nearly seeded, like Fabio Fognini?  I can see different players making different choices, but I don’t think it’s clear cut.

It is the draws of Jenkins, Britton, Glatch–in other words, the Jack Socks of previous years–that give us this evidence of manipulation.  On paper, the 127th-highest-ranked player in the draw looks like the 127th-best, but in practice, it’s not nearly so clear cut.  And if these wild cards really are “wild cards,” what looks like an easy draw may not be much easier than yet another dissection of Sergiy Stakhovsky or Albert Montanes.

It may be true that at some stage, the US Open draws are being manipulated for (and only for) the top two seeds in each field.  But that doesn’t tell us whether those players are gaining anything from it.  It’s far from clear that the lowest-ranked players in each draw are the easiest opponents.

The High-Quality Cincinnati Draw

It’s tough to imagine a Master’s series event featuring a higher-quality field than the one assembled in Cincinnati this week.  With the exception of Robin Soderling, virtually every “name” player is present.  Just as importantly, almost all of the players awarded wild cards are legitimate competitors at this level.  The same is true of most of the seven men who qualified.

For tennis fans, it’s an enjoyable outcome: With the possible exception of Robby Ginepri, everyone present “deserves” to be here.  The event gave the other three wild cards to Ryan Harrison, Grigor Dimitrov, and James Blake, three men inside the top 85 who excel on hard courts.  Four of the top seeds in qualifying advanced to the main draw, all of whose current rankings put them right on the cusp of making the cut in the first place.

All this made me wonder: How does the Cincinnati draw compare to other 56-player Masters fields?  Is Cinci always this strong?

I’ve previous looked at the field quality of ATP 250s, so it was a small step to point the guns at the bigger tourneys.  Here are all 48- and 56-draw Masters events since 2009, along with the average entry rank and median entry rank of players in the field, sorted by the latter:

Year  Event        Field  AvgRank  MedRank  
2011  Madrid          56     37.7     30.0  
2010  Paris           48     38.1     30.5  
2011  CINCINNATI      56     50.1     31.5  
2010  Shanghai        56     56.5     31.5  
2009  Paris           48     57.5     31.5  
2009  Cincinnati      56     38.5     32.0  
2009  Montreal        56     83.6     32.5  
2010  Cincinnati      56     38.5     33.5  
2009  Rome            56     42.0     33.5  
2009  Shanghai        56     54.8     33.5  
2011  Rome            56     42.2     34.5  
2009  Madrid          56     43.6     34.5  
2011  Montreal        56     50.7     35.5  
2009  Monte Carlo     56     45.1     36.5  
2011  Monte Carlo     56     51.9     36.5  
2010  Rome            56     43.1     38.5  
2010  Toronto         56     57.7     40.5  
2010  Madrid          56     59.5     43.0  
2010  Monte Carlo     56     50.6     43.5

There’s not a huge difference in quality–after all, players are required to show up for most of these events–but there is a noticeable differentiation into “haves” and “have-nots.”  Of course Monte Carlo is near the bottom, as it is not mandatory.  Rome is required, but it does get skipped.  Madrid is an interesting case, as this year’s new schedule meant all the best players showed up, while last year, it was near the bottom of the list.

Setting aside Paris, which is near the top of the list because its field has eight fewer players, Cinci appears to consistently offer one of the best Masters fields.  This makes sense, as even if it weren’t a required stop on the tour, it’s a perfectly scheduled warm-up for the U.S. Open.

How Long Does the Server’s Advantage Last?

In professional tennis, it’s a given that the server has an advantage.  The size of that advantage depends on the abilities of the two players and the surface, but especially in men’s tennis, it’s a sizable edge.  On average, a server in an ATP match starts a point with a roughly 65% chance of winning.

But how long does it last?  It seems that, at some stage in the rally, the server’s advantage has disappeared.  Four or five strokes in, the server may still be benefiting from an off-balance return.  But by ten strokes, one would assume that the rally is neutral–that the advantage conferred by serving has evaporated.

As usual with tennis analysis, one question begets several more.  Does the server’s advantage last longer on faster surfaces?  Do women settle into “neutral” rallies sooner than men do?  Do dominating players, like this year’s edition of Novak Djokovic, take away the server’s advantage faster than the average player?

Using the rally counts provided by Pointstream at the last three majors, we can start to answer these questions.

Neutralizing the serve

The first step is to take all the matches we have rally-count data for, and average them out.  Then, for each point length, we calculate the odds that the server wins a point of at least that length.  So, for instance, we look at all points of five shots or more, and figure out how many of those the server wins.

Each one of these numbers is biased, because a rally of exactly five-strokes is, by definition, won by the server.  The server either hits a winner on his third shot (the fifth overall), or the returner makes an error attempting to hit his own third shot (the sixth overall).  Thus, if we look at all points of at least five strokes, the exactly five-stroke rallies virtually guarantee that the server will have the advantage.

However, the same reasoning shows us that a six-stroke rally will be biased in favor of the returner.  When we do the math for at-least-five, at-least-six, at-least-seven, and so on, we’ll see a yo-yo effect.  When the biases have equal effect, that means the serve is neutralized.

Here are the results for the approximately 150 grand slam matches with Pointstream data so far this year:

At least…  Win%  Notes                          
0          63%   before point begins            
1          66%   if serve goes in               
2          50%   if serve is returned           
3          60%   if server makes second shot    
4          46%   if returner makes second shot  
5          58%                                  
6          45%                                  
7          57%                                  
8          44%                                  
9          56%                                  
10         44%                                  
11         56%                                  
12         43%                                  
13         56%                                  
14         43%                                  
15         56%

In the table, “Win%” refers to the server’s chance of winning the point.  The biases even out somewhere between the 4th and 8th shot, meaning that in that zone, the server’s advantage is neutralized.

While the server retains the advantage at least until the fourth shot, it is interesting to see how quickly it decays.  Dropping from 66% upon making a serve to 56% once the advantage is neutralized, it loses more than half the difference between the first and third shots.  Thus, the returner doesn’t negate the server’s advantage simply by getting the ball back in play, but he does take a large step toward doing so.

Does surface matter?

As usual, it sure does.  The numbers for the Australian and French Opens are similar, and since they make up 2/3 of the data set, they are close to the aggregate numbers shown above.  But Wimbledon, as is so often the case, seems to play by a different set of rules:

At least…    Wimby    Austr    French  
0            66%        62%       62%  
1            68%        64%       67%  
2            52%        50%       48%  
3            62%        59%       58%  
4            48%        46%       45%  
5            61%        57%       57%  
6            47%        44%       44%  
7            61%        55%       56%  
8            47%        44%       44%  
9            59%        55%       54%  
10           47%        43%       43%  
11           60%        54%       55%  
12           46%        43%       43%  
13           59%        55%       55%  
14           43%        45%       42%  
15           56%        54%       56%

The biases don’t balance out until the very bottom–at 14 or more shots!  That’s only about 3% of points.  I’m not sure how to explain this, except perhaps psychologically, that on grass (considered the best surface for servers), players are less successful in return games simply because that’s what they expect to happen.  Regardless of surface, I can’t understand why else the server’s advantage would persist into double-digit shot counts.

What about the ladies?

WTA players (on average) start each service point with a smaller advantage than their male counterparts, and as it turns out, that advantage evaporates more quickly.

We saw a moment ago that, by putting the return in play, an ATP returner gives himself a 50% chance of winning the point–at least until his opponent hits another shot.  Women, however, knock the server’s winning percentage down to 47% by making the return.

The returner clearly neutralizes the point by the fourth stroke overall, and–here’s the good part–takes over a slight advantage herself by her third shot, the sixth stroke overall.  By making that sixth shot, the returner has a 57% chance of winning the point, while the server will never reach 57% again.  The advantage is only a percentage or two, but from the sixth stroke on, the returner has the edge.

Finally, presenting Novak Djokovic

Pointstream has tracked 17 of Djokovic’s slam matches this year, giving us a good set of data to work with.  When a man is having a season like this one–in large part because of his return game–it’s fascinating to see how comprehensively he is outplaying his opponents.

In the same terms as the tables above, here are Djokovic’s serve and return points across those 17 matches.  The return points are shown with the server’s winning percentages:

At least…    ND Sv    ND Ret  
0            70%         57%  
1            72%         60%  
2            59%         42%  
3            68%         50%  
4            56%         39%  
5            68%         49%  
6            57%         38%  
7            68%         47%  
8            58%         38%  
9            68%         45%  
10           55%         34%  
11           65%         44%  
12           55%         33%  
13           66%         38%  
14           52%         29%  
15           65%         40%

After seeing the averages above, you might reasonably conclude that these numbers are out of this world.  Even with the bias of 4-, 6-, and 8-stroke rallies, as discussed above, Djokovic still maintains an edge.  For everyone else, once fifth or sixth shot is struck, the point is a 50/50 proposition.  For Novak, it’s at least 60/40 in his favor.

The amazing stats are on his return.  When he gets his return back in play, he’s more than likely to win the point.  That may not surprise anyone who has watched Djokovic play this year, but consider how remarkable that is in the context of modern men’s tennis.  By the 8th stroke or so, he’s back to the 60/40 odds of the service points that turn into longer rallies.

Thanks to Carl Bialik for suggesting this topic.

The Most (and Least) Consistent Players on the ATP Tour

“Consistency” is one of the many terms that commentators frequently use but rarely define.  It’s often misused, too: we say we want a player to be more consistent, when we really just want him to stop playing badly.

To me, consistency for a tennis player is similar to the notion of “playing up to his ranking.”  In other words, if a player is consistent, he usually beats players ranked lower, and he usually loses to players ranked higher.  No player is perfect in this regard, but clearly, some are much more reliable than others.

A recent poster boy for inconsistency is Ernests Gulbis.  At Roland Garros, he lost to Blaz Kavcic, ranked 82nd in the world.  That was on clay, a surface on which Gulbis had posted some excellent results the previous year.  Two months later, in Los Angeles, he beat Juan Martin del Potro, someone he shouldn’t have even challenged on a hard court.

Quantifying consistency

With my player rankings and match prediction system, I’m able to assign a win probability to each player for every match.  For instance, when Ivan Dodig beat Nadal last week, I had given him a 14.4% chance of doing so.  As you might imagine, that’s a major upset–as I wrote the next day, it was the 10th-biggest upset of the season.

In these terms, an ideally consistent player will never be on either end of an upset.  If he is the favorite, he wins; if he is the underdog, he loses.  In practice, no tour-level player accomplishes this, though over the last two years, Florent Serra and Eduardo Schwank have come very close.

I’ve come up with a metric to measure consistency.  This is how it works:

  • Gather a list of all ATP-level matches for the desired time period.  (Today, I’m using everything from January 2010 through Montreal last week.)
  • Eliminate matches that ended in retirement or walkover, as well as those where we don’t have enough information to make an educated prediction.  (e.g. the first few comeback matches of Tommy Haas, or one with a wildcard playing his first professional match.)
  • For each player, count how many matches he played.
  • For each player, find the matches where he was the favorite and lost, or was the underdog and won.
  • For each of those matches, take the probability than the eventual winner would win (e.g. 18% — always under 50%), multiply by 100 (e.g. 18, not 18%),  subtract it from 50 (e.g. 50 – 18 = 32), and square the result (e.g. 32*32 = 1024).
  • Sum all of the squares, then divide by the number of total matches–not just the ones where the favorite lost.

Whew!  In something more like layman’s terms, we’re taking all the upsets a player was involved in, coming up with a number to represent how big (or surprising) the upset was, then averaging the results.

Using this method, we give big upsets considerably more weight than mini-upsets.  If a player had a 45% chance of winning a match and ends up winning, it barely counts as an upset–and this system treats it accordingly.  By dividing by the total number of matches, we give consistency credit to players who win the matches they’re “supposed to” win, and lose those they are supposed to lose.

Most importantly, the numbers this algorithm spits out are completely believable, matching up well with the conventional wisdom of which players are consistent and inconsistent.

The consistency of the top ten

The most consistent player on the tour, since the beginning of 2010, has been … Florent Serra.  Amazingly, Igor Kunitsyn comes in second.  But I doubt many of you care much about the consistency of guys like that.

Let’s start with the current top 10, ranked from most to least consistent:

Player              Upsets  Matches    Up%  UpsetScore  
David Ferrer            25      119  21.0%          55  
Rafael Nadal            16      131  12.2%          68  
Novak Djokovic          18      119  15.1%          69  
Roger Federer           21      123  17.1%          69  
Jo-Wilfried Tsonga      20       80  25.0%          75  
Mardy Fish              19       77  24.7%          82  
Tomas Berdych           32      113  28.3%         106  
Gael Monfils            24       89  27.0%         107  
Robin Soderling         23      115  20.0%         130  
Andy Murray             24       97  24.7%         151

The relevant column is the rightmost, “UpsetScore,” which is the result of the algorithm described above.  Ferrer has been part of more upsets than any of the top three (“Up%”), but his upsets are more minor.  Except for losses to Ivo Karlovic and Jarkko Nieminen early in the year on hard courts, Ferrer has not lost a match he had a 60% or better chance of winning.

The two ends of this list certainly line up with what I would have expected: Ferrer and Nadal are rock-solid (last week’s loss to Dodig notwithstanding), while Soderling and Murray both can be picked off by anybody, and frequently threaten higher-ranked players.

Right now, you may be tempted to put Djokovic higher on the list–after all, he’s ranked #1 and he’s beating everybody.  However, in the slightly longer term of 20 months, his movement around the top three has included some unexpected results, like losing to Ljubicic at Indian Wells last year, and victories over Federer and Nadal before his ranking suggested he would do so.

Tour wild cards

Outside of the top 10, there are a handful of players who are almost impossible to predict.  Some names that come to mind are Marcos Baghdatis, Ernests Gulbis, and Nikolay Davydenko, men who can take out one of the top three on a good day (well, maybe not Gulbis), but can lose to a qualifier on the next.

Player                 Upsets  Matches  Up%  UpsetScore  
Nikolay Davydenko          32       73  44%         273  
Marin Cilic                27       91  30%         180  
Marcos Baghdatis           38       89  43%         177  
Olivier Rochus             20       52  38%         164  
Milos Raonic               16       41  39%         164  
Juan Martin del Potro      11       48  23%         154  
Andy Murray                24       97  25%         151  
Jurgen Melzer              28       96  29%         150  
Fernando Verdasco          40      104  38%         150  
Ivan Ljubicic              27       69  39%         149  
Florian Mayer              30       72  42%         147  
Samuel Querrey             26       66  39%         146  
Andrei Goloubev            24       55  44%         143  
Ernests Gulbis             22       69  32%         140  
Jeremy Chardy              31       65  48%         133  
Juan Monaco                26       73  36%         131  
Robin Soderling            23      115  20%         130  
Michael Llodra             26       67  39%         130  
Rainer Schuettler          15       42  36%         119  
Mikhail Youzhny            25       78  32%         116

The “upset score” number tells the story for Davydenko.  The man who beat Nadal at the beginning of the year and threatened Djokovic last week recently suffered defeat at the hands of Cedrik-Marcel Stebe (twice!) and Antonio Veic.

While no one is in Davydenko’s league, names like Cilic, Baghdatis, Murray, and Verdasco seem appropriate.  Verdasco, along with Melzer and Milos Raonic suggest a flaw in this approach: the algorithm reads very fast improvement or decline as inconsistency, which isn’t quite right.  Yes, Raonic has shocked the tennis world repeatedly this season, but he hasn’t mixed in too many disastrous losses alongside the surprise upsets.  I tinkered with ways to include that in the model, but nothing worked very well.

A couple more interesting notes from the “most inconsistent” players are found in the upset percentage column.  Guys like Davydenko, Baghdatis, Mayer, Goloubev, and Chardy are involved in upsets nearly half the time.  Chardy is highest in that category.  In fact, if I expanded the study to challenger events, he might rocket to the top of this list, as he plays quite a few, and often manages to lose against players outside the top 100.

The consistent ones

The flip side is considerably less star-studded.  In the 20 most-consistent players of the last 19-20 months, Ferrer is the only top-10 guy present, though #11 Nicolas Almagro is there as well.

Here’s my seat-of-the-pants theory.  In this sense, “consistent” isn’t good.  Yes, “consistent” sounds good, especially when “inconsistent” means Davydenko losing to Antonio Veic or Mayer falling to Federico del Bonis.  But inconsistent means Davy beating Federer and Mayer beating Soderling.  So, the players who show up on as “most consistent” are in fact consistent, but they are also mediocre.  Their consistency (perhaps a mental advantage) has helped them move up from the top 200 to the top 50 or 100, but that’s all they can do.

Ferrer and Almagro are good examples of this, actually.  Neither has the weaponry that makes commentators say, “This guy could be number one!”  But they’ve earned their rankings by regularly reaching the quarters and semis of tournaments, not suffering the boneheaded losses that afflict the likes of Cilic and Baghdatis.

All that said, here’s the list:

Player            Upsets  Matches  Up%  UpsetScore  
Florent Serra         11       56  20%          23  
Igor Kunitsyn         14       40  35%          33  
Ilia Marchenko        14       46  30%          40  
Potito Starace        28       81  35%          46  
Victor Hanescu        26       77  34%          50  
Tobias Kamke          12       41  29%          52  
Andreas Seppi         24       81  30%          53  
Julien Benneteau      23       59  39%          53  
Viktor Troicki        25      101  25%          54  
David Ferrer          25      119  21%          55  
Fabio Fognini         18       71  25%          55  
Pere Riba             13       41  32%          56  
Lukas Lacko           14       44  32%          57  
Igor Andreev          17       62  27%          58  
Lukasz Kubot          26       63  41%          59  
Nicolas Almagro       22      112  20%          59  
Frederico Gil         15       40  38%          60  
Denis Istomin         25       76  33%          65  
Jarkko Nieminen       25       74  34%          66  
John Isner            21       82  26%          67

These lists hardly represent the final word on who is or is not consistent–for one thing, I haven’t said anything about consistency within matches, which may be a completely separate issue.  But this approach does, I think, provide some insight into who is more likely to be part of an upset, and suggests that consistency might not be such a good thing after all.

Andy Murray and The Worst Upsets of the Year

On Tuesday in Montreal, Andy Murray played an ugly, listless match against world #35 Kevin Anderson, losing 6-3 6-1.  While Murray has played some solid matches this year and is in no immediate danger of losing his top-four ranking, the Anderson loss is hardly the first disaster of his season.  Back in Indian Wells and Miami, he managed to lose to Donald Young and Alex Bogomolov in successive matches.  Ouch.

Using my rankings and match projection system, I’ve generated win probabilities for every ATP match of the season.  Combined with match outcomes, that allows us to find the upsets that were least expected on that surface, at that time.

Pre-match, my system gave Anderson a 16.3% chance of beating Murray–only a smidge better than Dodig’s 14.4% against Nadal.  (My system has never given the South African much credit; his hard-court ranking right now is #58.)  In fact, Anderson was the 4th-biggest underdog going into the 2nd round, ahead only of Dodig, Michael Russell, and Vasek Pospisil.

As it turns out, Anderson’s victory was the 14th-biggest upset win of the ATP season.  (I took out retirements and “comeback players,” like Fernando Gonzalez and Tommy Haas, whose rankings aren’t very predictive.)  That’s 14 out of nearly 1,700.

But, as you might guess, 14th-best of the season isn’t enough to be 1st with Murray on the losing end.  The Murray loss to Young in March is the biggest upset of the year–Donald entered the match with an 8.6% chance of winning.  The Bogomolov match comes in 4th overall; the American had a 10.1% chance before play began.

Edit: This is what I get for writing a draft the night before!  Dodig’s upset victory comes in tied for #10 on the season, pushing Murray/Anderson down one more spot on the list.  Nadal will go home having suffered the biggest upset of the Rogers Cup, though he played far and away better than Murray did to achieve the same outcome.

The biggest upsets of the year

I couldn’t possibly give you those numbers without following through with a complete table.  Here are the 36 matches where the winner entered the match with less than a 20% chance of winning.  This list is through last week’s matches, so it doesn’t yet show Murray’s latest meltdown and Dodig’s shocker.

(This site doesn’t show wide tables very well; click here for a clearer version.)

P(UPSET)  WINNER                 LOSER               TOURNEY          SCORE
 8.6%     Donald Young           Andy Murray         Indian Wells     7-6(4) 6-3
 9.4%     Bernard Tomic          Robin Soderling     Wimbledon        6-1 6-4 7-5
 9.7%     Jimmy Wang             Igor Kunitsyn       Newport          4-6 7-5 6-2
10.1%     Alex Bogomolov         Andy Murray         Miami            6-1 7-5
11.6%     Stephane Robert        Tomas Berdych       French Open      3-6 3-6 6-2 6-2 9-7
13.1%     Milos Raonic           Mikhail Youzhny     Australian Open  6-4 7-5 4-6 6-4
13.8%     Denis Kudla            Grigor Dimitrov     Newport          6-1 6-4
14.0%     James Ward             Stanislas Wawrinka  Queen's Club     7-6(3) 6-3
14.1%     Federico del Bonis     Florian Mayer       Stuttgart        6-2 6-3
14.4%     Jo-Wilfried Tsonga     Rafael Nadal        Queen's Club     6-7(3) 6-4 6-1               

P(UPSET)  WINNER                 LOSER               TOURNEY          SCORE
15.0%     Jan Hernych            Thomaz Bellucci     Australian Open  6-2 6-7(11) 6-4 6-7(3) 8-6
15.2%     Nikolay Davydenko      Rafael Nadal        Doha             6-3 6-2
15.6%     Andrey Kuznetsov       Marcos Baghdatis    Casablanca       6-4 4-6 6-4
16.4%     Flavio Cipolla         Andy Roddick        Madrid Masters   6-4 6-7(7) 6-3
16.6%     Lukas Rosol            Jurgen Melzer       French Open      6-7(4) 6-4 4-6 7-6(3) 6-4
16.8%     Antonio Veic           Nikolay Davydenko   French Open      3-6 6-2 7-5 3-6 6-1
17.0%     Sergei Bubka Jr.       Daniel Gimeno       Doha             6-0 6-3
17.1%     Leonardo Mayer         Marcos Baghdatis    French Open      7-5 6-4 7-6(6)
17.6%     Ivan Dodig             Robin Soderling     Barcelona        6-2 6-4
17.6%     Michael Yani           Dudi Sela           Newport          7-6(5) 6-3                   

P(UPSET)  WINNER                 LOSER               TOURNEY          SCORE
17.7%     Frank Dancevic         Feliciano Lopez     Johannesburg     6-7(5) 6-2 7-6(8)
17.8%     Alexander Dolgopolov   Robin Soderling     Australian Open  1-6 6-3 6-1 4-6 6-2
17.9%     James Ward             Samuel Querrey      Queen's Club     3-6 6-3 6-4
17.9%     Jan Hernych            Sergey Stakhovsky   Halle            6-3 6-7(5) 7-6(8)
18.2%     Jan Hernych            Denis Istomin       Australian Open  6-3 6-4 3-6 6-2
18.3%     Jo-Wilfried Tsonga     Roger Federer       Wimbledon        3-6 6-7(3) 6-4 6-4 6-4
19.0%     Milos Raonic           Fernando Verdasco   San Jose         7-6(6) 7-6(5)
19.0%     Lukasz Kubot           Gael Monfils        Wimbledon        6-3 3-6 6-3 6-3
19.2%     Federico del Bonis     Sergey Stakhovsky   Stuttgart        6-4 6-3
19.3%     Lukasz Kubot           Nicolas Almagro     French Open      3-6 2-6 7-6(3) 7-6(5) 6-4    

P(UPSET)  WINNER                 LOSER               TOURNEY          SCORE
19.3%     Bernard Tomic          Feliciano Lopez     Australian Open  7-6(4) 7-6(3) 6-3
19.7%     Thomaz Bellucci        Andy Murray         Madrid Masters   6-4 6-2
19.7%     Pavol Cervenak         Victor Hanescu      Stuttgart        6-3 7-6(6)
19.7%     Richard Gasquet        Roger Federer       Rome Masters     4-6 7-6(2) 7-6(4)
19.9%     Rajeev Ram             Grigor Dimitrov     Atlanta          6-4 6-4
20.0%     Philipp Kohlschreiber  Robin Soderling     Indian Wells     7-6(8) 6-4

Do Points Get Shorter as the Match Progresses?

On Friday, some interesting ideas were batted around in the comments to my post on the 61-shot rally.  One of the simpler ones boils down to the question that titles today’s post: Do points get shorter as the match progresses?

Two forces seem to work in opposite directions:

  • As players get used to each other’s games (and specifically their serves), more balls get returned.  Before looking at the numbers, I would’ve bet that this was the case, meaning that aces and service winners decline as you go deeper into a match.
  • The longer the match, the more tired the players.  Tired (or even slightly injured) players take more risks and probably have shorter rallies.

To answer the question, I looked at rally lengths shown in Pointstream at the last three grand slams.  That gives us close to 250 men’s matches, all best-of-five sets.

The short, unsatisfying conclusion is: The results are mixed.  At Wimbledon and Roland Garros, rally length increased later in matches–as much as 10% in London and 20% in Paris.  At the Australian Open, the result was the exact opposite, with rally length decreasing substantially.  Perhaps rally length increases in most cases, except when it is extremely hot or the players are not yet in top shape.  The blistering heat in Melbourne is certainly a plausible reason for a decrease in rally length.

As we’ll see when we move into more specific findings, the results get even more jumbled.  It seems that points generally get longer as a match progresses, but not necessarily because players read and return serves better.  While rally lengths increase, the number of one-stroke points (aces, service winners, service return errors) often increases, as well.

Follow the jump for my methodology and full results.

Continue reading Do Points Get Shorter as the Match Progresses?

The Simon/Monfils 61-Shot Rally: In Perspective

A couple of weeks ago, Gael Monfils and Gilles Simon made the unorthodox decision of extending their warm-up into the first game of the match.  Or somthing.  At 40-40 in the opening game, they counterpunched each other into oblivion, needing sixty-one shots before Monfils finally sent a slice long to end the point.

If you haven’t seen it, or you suffer from insomnia, click the link here.

What might be most remarkable about the rally is that, when Monfils made his error, there was no sign of the point drawing to a close — it isn’t hard to imagine those two hitting another 61 shots like that.  But even at 61, it’s an awfully long point.

So (asks the statistician) … how long was it?  Rally length is not widely available for ATP matches.  But thanks to IBM Pointstream, I do have rally length for each point on a Hawkeye court from the French Open.  (I’ve played around a bit with those numbers.)

From the French Open, we have roughly 20,000 men’s points to look at, which doesn’t count double faults.  About 35% of those points lasted only one stroke: an ace, a service winner, or an error of some sort on the return.  Only 15% of the points went 8 strokes or longer, and fewer than 10% reached 10 strokes.

In the entire tournament, only 12 rallies hit the 30-shot mark–only halfway to the Simon/Monfils level.  You won’t be surprised at most of the names involved in those dozen extreme points:

Mardy Fish    Gilles Simon       38  
Andy Murray   Viktor Troicki     37  
Gilles Simon  Robin Soderling    36  
David Ferrer  Sergiy Stakhovsky  33  
Andy Murray   Viktor Troicki     33  
David Ferrer  Gael Monfils       33  
Rafael Nadal  Pablo Andujar      32  
Tobias Kamke  Viktor Troicki     31  
David Ferrer  Sergiy Stakhovsky  31  
Rafael Nadal  Andy Murray        31  
Rafael Nadal  Pablo Andujar      30  
Andy Murray   Viktor Troicki     30

Both Simon and Monfils make an appearance, with Ferrer, Murray, and Nadal showing up multiple times.  What surprises me a bit are some of the guys who hung in there with the counterpunchers, especially Fish and Troicki.

In any event, 61 shots still stands out as a once-in-a-blue-moon accomplishment.

WTA rally length

Incidentally, you might suspect (as I did) that some WTA players would slug it out even longer.  Again using Pointstream data from the Hawkeye courts at the French, it turns out that ladies only reached the 30-shot threshold twice.  First, Marion Bartoli went to 33 against Olga Govortsova, and Na Li got to 32 shots against Silvia Soler-Espinosa.  The tongue-tying Wozniacki-Wozniak matchup comes in third, with a 28-stroke rally.

Wimbledon rallies

While we’re at it, let’s check the Wimbledon data.  Surprise, surprise–tied for the longest rally of the tournament is a 31-stroke exchange between Juan Martin del Potro and … Gilles Simon.  In fact, that match featured four of the 20 longest rallies of the tournament.

Also notable is Novak Djokovic, who reached 31, 30, and 29 against Bernard Tomic, and 25 (twice) and 24 against Marcos Baghdatis.

The true oddity in the top ten is John Isner and Nicolas Mahut, who somehow took a break from aces and errant groundstrokes to go 25-deep.  It was the  only point of the match that went longer than 12 shots.

 

Doubly Lopsided Matches

Italian translation at settesei.it

On Sunday, Novak Djokovic beat Rafael Nadal by a somewhat unusual score: 6-4 6-1 1-6 6-3.  A four-setter in the final doesn’t raise any eyebrows, but a 1-6 set … that’s a bit of a head-scratcher, especially on a fast surface.  Wimbledon is better known for server domination, which means 6-4’s, 7-5’s, tiebreaks, and the occasional 70-68.

The Djokovic-Nadal score got me curious about two questions:

  1. How often does a player lose a set 1-6 (or even 0-6) yet still win the match?
  2. How often does a player both win and lose a lopsided (6-1 or 6-0 ) set?

(Note: Yes, sometimes a 6-1 set includes only two breaks, in which case it is similar to a 6-2 set.  Yet 6-1/1-6’s are far less frequent that 6-2/2-6’s.  It would be nice to distinguish “two-break” 6-1’s from “three-break” 6-1’s, but for now, all we can do is enjoy the trivia and accept the limitations.)

Bi-directional bagels

First things first.  As we might guess, scores such as these are extremely rare at Wimbledon.  This year, the final was one of only two such matches.  The other was Xavier Malisse’s second-round win over Florian Mayer, which went in the books as 1-6 6-3 6-2 6-2.  Last year, only one Wimbledon match qualified: a first-rounder between Victor Hanescu and Andrey Kuznetsov.  Oddly enough, Hanescu dropped the third set 1-6 after splitting two tiebreaks.  In neither of these matches did the winner take his own lopsided set, as Djokovic did.

In this department, Wimbledon remains unique among the majors–it isn’t just a matter of “clay” and “everything else.”  At this year’s Australian Open, there were eight matches with 1-6 or 0-6 scores; last year there were 11.  At the 2010 US Open, there were six.  These scores are more common at the slams, because the five-set format makes it more likely that the loser of an early set (by any score) can come back to win the match.

The numbers

Last year, there were roughly 2600 tour-level matches that were played to their conclusion.  (That is, neither player retired.)   Of those, about two-thirds were straight-set victories, leaving us with 871 matches that went three sets (or five, at the slams).

Of those 871, only 94 matches contained a 1-6 or 0-6 set, and only 30 included a “lopsided” set in favor of both players, as in the Nadal-Djokovic final.  Both have been somewhat less frequent so far this year; in 1546 matches, 48 saw the winner lose a lopsided set, and 11 saw both players lose a lopsided set.  Combining the two years of data, the likelihood that any given match will include a 6-1 (or 6-0) and a 1-6 (or 0-6) is almost exactly 1 in 100.  Again, the five-set format of the slams increases the probability a bit, while the fast courts at Wimbledon have the reverse effect.

The offenders

Which players find themselves in these roller-coaster matches?  To answer that question, we have to stick with the less-specific filter of matches that include a 1-6 or 0-6 set.  If we also require a 6-1/6-0 from the winner, there isn’t enough data to make things interesting.

One might guess that the strongest servers would be far down the list, while counterpunchers populate the top.  That isn’t the case.  The players who are known for mental lapses–regardless of their serving and returning skills–seem to dominate the upper tier.

Looking at all tour-level matches from 2007 through last week, we find that Andy Murray takes the cake.  He has played in 18 of these matches, dropping a lopsided set in 10 of his victories, while winning a lopsided set in 8 of his losses.  Murray is in a class by himself–number two on the list is Guillermo Garcia-Lopez, at 13.  In third place is Djokovic, with 12 (he is 8-4 in such matches), though the Wimbledon final was the only occurence so far in 2011.

Twelve men are clustered at 10 and 11 of these matches, and the list features a lot of Frenchmen, and several other players known for questionable mental strength:

  • 11: Julian Benneteau, David Ferrer, Fabio Fognini, Fernando Verdasco
  • 10: Thomaz Bellucci, Mardy Fish, Richard Gasquet, Paul-Henri Mathieu, Phillipp Petzschner, Tommy Robredo, Radek Stepanek, Jo-Wilfried Tsonga

Of these, Fognini (9-2) and Tsonga (8-2) have the dubious honor of winning the most matches–that is, they are on the list because they drop lopsided sets in matches that they win.  Mathieu (2-8) is at the other extreme, dominating sets in the middle of losses.

The Wimbledon final was a rarity for Nadal–it was only the fourth time he’d been involved in a match with this sort of score, and it was only the second time he won a lopsided set in the middle of a loss.  Roger Federer has only played in three such matches.

We probably can’t read too much into these numbers, but it is interesting to see so many of the same types of players show up at the top of a list.  At the very least, we’ve learned that the 1-6 set in Sunday’s final was quite rare, and the 6-1 1-6 sequence was even rarer.