The Problem With “Unforced Errors”

Italian translation at settesei.it

In any sport, there are a handful of stats that are frequently cited, but are ultimately of limited use.  Often, these statistics tell you something, but are misunderstood to imply something more.  Simple examples are many “counting” stats — points scored in basketball, touchdowns thrown in football, RBI in baseball.  In all of those cases, they indicate something good, but don’t give you context — lots of field goal attempts, a great offensive line, or good hitters on base in front of you, to take those three cases.

The stat in tennis that aggravates me most is the unforced error.  Not only does it ignore some important context (as in the other-sport stats I just mentioned), but it relies on the judgment of a scorer.

Misjudgment

The second problem is the more problematic one.  How much does a number mean if two people watching the same match wouldn’t come up with the same result?  This was a hot-button issue during Wimbledon, when the scorers were assigning an unusually small number of UEs, especially on serve returns.

If you’re watching the match, you might not notice.  If the end-of-set stats show that Nadal had 8 UEs and Federer had 17, that does tell you something … Federer was making more obvious mistakes.  But if you want to compare that to a Nadal/Federer match three weeks ago, or last year, those numbers are all but useless.

I suspect that, at events like Wimbledon, someone from the ITF, or maybe IBM, is giving standardized instructions to scorers with general rules for categorizing errors.  That would be a good start, especially if it were implemented across all tournaments at all professional levels.

…but it doesn’t matter

I suspect that no matter how consistent scorers are, the distinction between “unforced” and “forced” errors will always be arbitrary.  Consider the case of service returns.  There are occasional points, especially on second serve returns, where the returning player misses an easy shot.  But more frequently, the returning player is immediately on defense.  When is an error “unforced” on the return of a 130 mile-per-hour shot?

Ultimately, we will probably have computerized systems that classify errors for us.  If you have all the necessary data and crunch the numbers, a 125-mph serve down the T in the ad court might be returned 60% of the time, meaning there is a 40% chance of an error or non-return.  With those numbers on every serve (and every other shot, eventually), we could set the line for an “unforced” error on a shot that the average top-100 player would make, say, 75% of the time.  Or we could have different classifications: “unforced errors,” “disastrous errors,” “mildly forced errors,” and so on, indicating different percentage ranges.

The problem we have now is that professionals are so good (and their equipment is so advanced), that almost every shot can be offensive, meaning that players are almost always–to some extent–on defense.  If you’re rallying with Nadal, you might hit some winners, but you’re always fighting the spin.  If you’re rallying with Federer, the spin isn’t so bad, but you’re always trying to keep the ball away from his forehand.  (If you’re rallying with Djokovic, you’re wishing you had hit a better serve.)  That perpetual semi-defensive posture means that nearly every error is, to some extent, forced.  And because players are so good, we expect them to return every reachable ball, suggesting that nearly every error is, to some extent, unforced.

Yikes!

The wisdom of baseball analysts

A very similar problem arises in baseball.  If a fielder makes a misplay (according to the official scorer), he is charged with an “error.”  Paradoxically, some of the best fielders end up with the highest error totals.  If, say, a shortstop has great range, he’ll reach a lot of groundballs, and have more chances to make bad throws, thus racking up the errors.

For decades, fans considered errors to be the standard measure of defensive prowess–a stat called “fielding percentage” measures the ratio of plays-successfully-made to chances.   (In other words, 1 minus “error rate.”)  But because of the paradox mentioned above, the highest fielding percentages do not necessarily belong to the best fielders.

The solution: Ignore errors, look only at plays made.  (This is an oversimplification, but not by much.)  If Shortstop A makes more plays than Shortstop B, it doesn’t matter whether A makes more errors.  The guy you want on your team is the one who makes more plays.

Essentially, baseball errors correspond to tennis unforced errors, and baseball plays-not-made (shortstop dives for the ball and can’t reach it) correspond to tennis forced errors.  The stat that ends up mattering to baseball analysts–“plays made”–corresponds to “shots successfully returned.”  The analogy is imperfect, but it illustrates the problem with separating one type of non-play from another.

Solutions

If we don’t distinguish between different types of errors, we’re left with “shots made” and “shots not made,” or–even less satisfactorily–“points won” and “points lost.”  Not exactly a step in the right direction, since we’re already counting points!

Still, I suspect it’s better to have no stat than to have a misleading stat.  Rally counts are a positive step, since we can look at outcomes for different types of points.  If you win a lot of 10-or-more-stroke rallies, that identifies you as a certain type of player (or playing a certain kind of match).  It doesn’t matter whether you lose that sort of point on an unforced error or your opponent’s winner–both outcomes might stem from the same tactical mistake three or four strokes sooner.

Either that, or we can wait until we can calculate real-time win probability and start categorizing errors with extreme precision.  “Unforced errors” aren’t going away any time soon, but as fans, we can be smarter about how much attention we grant to individual numbers.

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.

 

Stuttgart, De-Seeded

At the Mercedes Cup in Stuttgart this week, only two rounds have been completed, and all eight seeds are gone.  It isn’t even a particularly weak top of the field–five of the eight seeds are ranked in the top 20, and all eight are 37th or better.

Six of the eight lost their first-rounders, including #1 Gael Monfils (to Hanescu) and #2 Jurgen Melzer (to Giraldo).  The remaining two seeds–#3 Mikhail Youzhny and #8 Guillermo Garcia-Lopez–lost today.  Youzhny may be the only man in the draw without something to be ashamed of–he won a match, then lost to Juan Carlos Ferrero on clay.

The remaining draw almost makes Newport look good.  Of the eight unseeded players, we have two wild cards (Cedrik-Marcel Stebe and Lukasz Kubot) and two qualifiers (Pavol Cervenak and Federico Del Bonis).  The two qualifiers will play each other tomorrow, so at least one man from the qualifying draw will reach the final four.

It’s a project for another day, but it would be interesting to see which tournaments are most upset-prone.  The post-Wimbledon clay circuit seems like a prime contender, if only because of its awkwardness on the schedule.  And as friend-of-HT Tom Welsh pointed out, there seems to be a post-Davis Cup swoon, evident at Stuttgart with the losses to Mayer and Monfils.

Rik De Voest, Man on the Cusp

You don’t have to read much of this site to know that I am particularly interested in the second tier of pros.  Some of that is due to spending countless hours at the U.S. Open qualifying tournament; the rest may be attributable to a general tendency to root for the underdog.  So, I tend to be as familiar with guys in the 140s of the rankings as I am with the men in the 40s.

One of those men is South African Rik De Voest.  If you’ve followed the ATP for long, you’ve doubtless seen his name.  He’s a lock for a wild card at the Johannesburg event, he plays many events on the U.S. challenger circuits, and he occasionally qualifies for other top-level tourneys.  He’s a strong all-around player, though perhaps mentally weak–I’ve seen him play a handful of times, and while he’s rarely blown out, he’s prone to giving up the lead.

The impetus for this mini-post is my discovery that Rik De Voest has never cracked the singles top 100.  He broke into the top 200 almost nine years ago, has not fallen out of the top 300 in that time, and reached a peak of 110 in 2006.  He turned 31 last month, so while he currently sits at 130, moving into double-digits gets more difficult every day.

I suspect that De Voest’s record as a sub-top-100 player is very uncommon.  Each year, many players reach the top 100 with nothing more than a handful of solid showings at challenger events–two of the many current players to fit that mold are Steve Darcis (#95) and Matthias Bachinger (#93).  While the top 100 may be a mental hurdle, the difference between 110 (De Voest’s peak) and 99 is almost meaningless.  In the rankings right now, it’s 17 points–less than the difference between winning and losing in the quarterfinals of many challengers.

Right now, about 80 points stand between the South African and the top 100.  That’s a taller order, but still an achievable one for a player of De Voest’s caliber over the course of a few months.  Depending on which statistical oddity you prefer, you may or may not want to root for him.  If he reaches the top 100, he’ll be one of the oldest players ever to do so.  If he doesn’t, he may well end up with the record for most weeks inside the top 200 (or 150, or 250, or 300) without ascending to the slightly-more-rarefied first page of the ATP singles rankings.

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.

The Weak, Weak Newport Field

The ATP 250-level tournament in Newport this week is empty of the game’s best players.  The top seed is John Isner, ranked 46, and the 8th seed is Tobias Kamke, who is barely within the top 100.  This is no surprise.  Newport has one of the weakest ATP fields every year, situated as it is the week after Wimbledon, simultaneous with Davis Cup.

In a little study I did last year, I discovered that at least in 2009, Newport did have the weakest field of any ATP 250 event.  If you click the link, you’ll find a variety of metrics, but I think we can focus on just one: the median rank of main draw players.  By using median instead of average, the numbers aren’t skewed by a lowly-ranked wild card or qualifier.

In 2009, the players in the Newport draw had a median ranking of 125–that is, half the players in the main draw of an ATP event were ranked above 125.  Grand slams usually manage about 110 players below the 125 mark, but Newport only got 16–and most of those were closer to 125 than to 1.  Last year, the median fell to 129.5.  It may be a small consolation that Johannesburg’s field was equally weak.

A glance at this year’s draw can tell you that not much has changed.  Thanks to many late withdrawals, the cut fell to 218, which is considerably higher than the cut at some challengers.  For all that, the field quality has improved somewhat, to a median rank of 111.  That leaves Jo’burg in the dust; the South African event had a median rank of 118.5.

The non-challenger challengers

A few tour-level events–Newport, Jo’burg, and perhaps San Jose–obscure the line between the tour and challenger levels.  In the eyes of the ranking system, they are very different–Newport is worth 250 points to the winner, while no challenger is worth more than 125.  But for all intents and purposes, Newport and Jo’burg are challengers.

Last year, the May event in Bordeaux attracted a field with a median rank of 128–just above last year’s Newport and Jo’burg numbers.  This March, the odd 24-man field at Le Gosier had a median rank of 123.  Already in 2011, six challengers with 32-man fields had median ranks below 150, putting them in the same ballpark as the lowest rungs of the tour.

All of this is another strike against the ranking system, which treats Newport as if it were equivalent to, say, Sydney, where the last direct acceptance this year (#53 Benjamin Becker) was higher-ranked than Newport’s second seed (#60 Grigor Dimitrov).  Bad news for properly ordering second-tier pros, but good news for Isner, who can take advantage of this week’s cupcake draw to bounce back to as high as #36.

Bernard Tomic and the ATP Top 100: In Perspective

With his quarterfinal showing at Wimbledon, Bernard Tomic will break into the ATP top 100 for the first time on Monday.  He’ll do so with style, jumping from #158 to approximately #70.  (He will be considerably higher in my rankings–before the tournament, I had him just inside the top 50.)

As I’ve written before, a player’s chances of reaching the top of the men’s game have a lot to do with how early he cracks the top 100.  If you’re going to be a top-tenner, odds are you’re flashing some measure of those skills as a teenager.  In fact, to quote myself:

In the last 30 years, only one #1-ranked player (Pat Rafter) hadn’t reached the top 100 as a teenager, and he made it into the top 100 when he was 20.  Almost every eventual top-10 player had broken into the top 100 by age 21.

In that sense, Tomic is well ahead of the curve.  He doesn’t turn 19 until October, making him five months younger than Ryan Harrison, another teenager soon to break into the top 100.  Reaching #70 at such a young age isn’t a guarantee of future success, but it strongly points in that direction.  Again from my earlier post: 11% of players who cracked the top 100 at age 18 went on to become #1, and more than half (61%) eventually reached the top ten.

Tomic’s “comps”

Let’s take a narrower look and examine the 20 players who broke into the top 100 at ages closest to Tomic’s current age of 18.7 years.  It’s an impressive list, including Andy Roddick and Ivan Lendl, along with another 11 top-tenners.  Of these players the only “busts” were Andreas Vinciguerra (peak ranking: 33), Richard Fromberg (peak: 24), and Evgeny Korolev, who may yet improve on his peak ranking of 46.

In this group of 20 players, the average peak ranking is 11, and the median peak ranking is 8.  The average number of weeks in the top 100 is 362 (roughly eight years) and the median number of weeks is 410 (more than nine years).  Even 410 slightly understates a reasonable projection, since a few of these players (Roddick, Gael Monfils, Tommy Robredo, and Mikhail Youzhny) are guaranteed to add to their totals.

What may be most impressive about Tomic’s ranking at such a young age is that he has accomplished it the hard way.  He’s gotten plenty of wild cards–including at the Australian Open, where he reached the third round–but he qualified at Wimbledon, and a substantial chunk of his ranking points come from the challenger level, where he has reached four semifinals in 2011 alone.  His only “cheap” points are from Indian Wells, where he was wildcarded in, then beat Rohan Bopanna in the first round.

Now, Tomic’s ranking ensures that wild cards won’t be an issue, except at a few Masters 1000 tournaments.  If history is any guide, he’ll be a regular feature in the top echelon of the tour for most of this decade.

Live Wimbledon Odds

In conjunction with the work I’m doing for the Wall Street Journal’s Tennis Tracker, I’m generating a lot more data than they are able to show.  So, you can now see updated odds for each player in both the men’s and women’s singles draw, updated several times per hour.  Here are the links:

You can see the pre-tournament odds here and here.

Wimbledon Round 1: Qualifers and Other Underdogs

Some people watch the opening rounds of majors to see the top players drub lesser competition, perhaps gauging fitness by just how badly, say, Roger Federer beats Mikhail Kukushkin.  I get much more enjoyment out of the matches on Court 15, between players who are almost certainly not going to be around a week from now.

Last week’s qualifying rounds gave us a great group of contenders, plus another five lucky losers.  Wimbledon is also fairly unique in giving a handful of its eight wild cards to non-local players, giving a few free spots to players with good track records at the tournament (Arnaud Clement, Alejandro Falla) or guys on recent hot streaks (Dudi Sela).  Taken together, there are dozens of good early-round matches that can be enjoyed without the slightest reference to the thankfully-concluded Isner-Mahut first-rounder.

Let’s go to the bullet points:

  • Perhaps the biggest upset of the first round was Bernard Tomic’s straight-set win over Nikolay Davydenko.  Tomic is on the way up, and it’s ever more apparent that Davydenko is on the way out.  Tomic will next play Igor Andreev, who needed five sets to get past Teymuraz Gabashvili.
  • “Upset” may not be the right word, but I was somewhat surprised that Lleyton Hewitt was healthy enough to play today, let alone to beat Kei Nishikori.  The Aussie shouldn’t have much of a chance against Robin Soderling, but then again, Soderling’s performance was one of the weakest in the first round among the top seeds.
  • Grega Zemlja was one of two lucky losers to reach the second round; he beat Lucas Lacko to do so.  Lacko has been a bit of a mystery; he has posted a handful of solid wins in the last few years, but he hasn’t been able to stick in the top 100.  This was a big opportunity to get into a slam, and he let it go by.
  • The other very-lucky lucky loser was Ryan Harrison, who handled Ivan Dodig in straight sets.  Harrison bagelled the Croatian in the second, reeling off 25 of 33 points.  Depending on how some other lowly-ranked players do this week, the win might move Harrison into the ATP top 100.  His second-rounder against David Ferrer should be fun to watch, even if the conclusion is a given.
  • Frenchman Kenny De Schepper is ranked outside of the top 200, but he gave Olivier Rochus a real test today, pushing the Belgian to five sets.  My algorithm didn’t give De Schepper much credit, but apparently he didn’t check the numbers before heading out on court today.
  • Dudi Sela, in on a WC this year after stringing together some challenger titles this spring, had an easy first-rounder against Frederico Gil.  Gil always seems to be an easy match for somebody at a slam, yet he never leaves the top 100 for long.
  • Marinko Matosevic missed a big opportunity, falling to Juan Ignacio Chela without much of a fight.  Matosevic has a one-dimensional game, but when that dimension is a serve, a player still has a chance at the AEC.  Now the pressure is on Alex Bogomolov, another lower-ranked player who my algorithm favors over Chela.
For even more Wimbledon, check out the new Tennis Tracker at the Wall Street Journal website.  It gives real-time updates for about 20 top ATP and 20 top WTA players, including some win probabilities and a few stats, crunched by yours truly.

Wimbledon Women’s Draw Predictions

The women’s field is more tightly packed than the men’s, especially with Kim Clijsters out of action.  As such, my algorithm gives only Caroline Wozniacki and Victoria Azarenka better than a 10-to-1 shot of winning Wimbledon.  Serena and Venus Williams, of course, are wild cards–it’s easy to see Serena winning it all, or crashing out early from injury or rust.

Here is the full draw breakdown:

Player                         R64    R32    R16         W  
Caroline Wozniacki           94.0%  77.1%  65.9%    15.03%  
Arantxa Parra Santonja        6.0%   1.5%   0.5%     0.00%  
Sania Mirza                  26.0%   3.1%   1.2%     0.00%  
Virginie Razzano             74.0%  18.2%  11.3%     0.30%  
Anastasia Rodionova          58.4%  19.4%   3.0%     0.01%  
Andrea Hlavackova            41.6%  10.9%   1.3%     0.00%  
Alona Bondarenko             50.3%  35.2%   8.7%     0.11%  
Jarmila Gajdosova            49.7%  34.4%   8.3%     0.11%  
                                                            
Player                         R64    R32    R16         W  
Dominika Cibulkova           85.6%  64.5%  43.8%     1.98%  
Mirjana Lucic                14.4%   4.8%   1.4%     0.00%  
Polona Hercog                53.6%  17.0%   7.8%     0.03%  
Johanna Larsson              46.4%  13.6%   5.8%     0.01%  
Mathilde Johansson           39.1%   8.0%   1.5%     0.00%  
Heather Watson               60.9%  17.3%   4.4%     0.01%  
Anabel Medina Garrigues      26.3%  15.6%   4.6%     0.01%  
Julia Goerges                73.7%  59.0%  30.7%     0.66%  
                                                            
Player                         R64    R32    R16         W  
Samantha Stosur              81.6%  65.4%  38.3%     2.17%  
Melinda Czink                18.4%   8.8%   2.4%     0.00%  
Anastasiya Yakimova          48.5%  12.2%   3.5%     0.00%  
Sofia Arvidsson              51.5%  13.6%   4.0%     0.01%  
Elena Baltacha               64.2%  18.4%   6.6%     0.02%  
Mona Barthel                 35.8%   6.8%   1.6%     0.00%  
Kirsten Flipkens             21.2%  11.2%   3.8%     0.02%  
Shuai Peng                   78.9%  63.6%  39.9%     2.70%  
                                                            
Player                         R64    R32    R16         W  
Lucie Safarova               69.1%  42.3%  18.7%     0.44%  
Lucie Hradecka               30.9%  13.1%   3.7%     0.01%  
Klara Zakopalova             81.7%  41.1%  16.1%     0.23%  
Emily Webley-Smith           18.3%   3.5%   0.5%     0.00%  
Angelique Kerber             64.6%  15.7%   6.1%     0.02%  
Laura Robson                 35.4%   5.2%   1.4%     0.00%  
Anna Chakvetadze             25.1%  16.2%   7.8%     0.08%  
Maria Sharapova              74.9%  62.9%  45.7%     4.54%  
                                                            
Player                         R64    R32    R16         W  
Na Li                        84.1%  60.8%  46.2%     5.66%  
Alla Kudryavtseva            15.9%   5.2%   2.0%     0.00%  
Sabine Lisicki               54.1%  19.2%  10.9%     0.24%  
Anastasija Sevastova         45.9%  14.7%   7.7%     0.11%  
Jie Zheng                    86.6%  51.9%  18.9%     0.31%  
Zuzana Ondraskova            13.4%   2.8%   0.3%     0.00%  
Misaki Doi                   22.1%   5.5%   0.7%     0.00%  
Bethanie Mattek-Sands        77.9%  39.9%  13.3%     0.15%  
                                                            
Player                         R64    R32    R16         W  
Ana Ivanovic                 68.6%  55.8%  33.6%     1.87%  
Melanie Oudin                31.4%  20.8%   8.8%     0.07%  
Coco Vandeweghe              53.5%  13.1%   4.0%     0.01%  
Eleni Daniilidou             46.5%  10.3%   2.9%     0.00%  
Kristina Barrois             64.9%  17.2%   5.5%     0.01%  
Petra Cetkovska              35.1%   6.1%   1.3%     0.00%  
Olga Govortsova              20.2%  11.1%   3.4%     0.01%  
Agnieszka Radwanska          79.8%  65.7%  40.5%     2.34%  
                                                            
Player                         R64    R32    R16         W  
Marion Bartoli               88.5%  78.3%  47.8%     3.02%  
Kristyna Pliskova            11.5%   5.6%   1.1%     0.00%  
Lourdes Dominguez Lino       45.7%   6.9%   1.4%     0.00%  
Romina Oprandi               54.3%   9.2%   2.0%     0.00%  
Evgeniya Rodina              51.2%  11.3%   2.7%     0.00%  
Chanelle Scheepers           48.8%  10.1%   2.4%     0.00%  
Irina-Camelia Begu           14.5%   6.8%   1.5%     0.00%  
Flavia Pennetta              85.5%  71.8%  41.1%     2.36%  
                                                            
Player                         R64    R32    R16         W  
Maria Kirilenko              79.4%  57.5%  24.8%     0.61%  
Alberta Brianti              20.6%   8.4%   1.6%     0.00%  
Tamarine Tanasugarn          39.8%  11.5%   2.2%     0.00%  
Yaroslava Shvedova           60.2%  22.6%   6.0%     0.01%  
Simona Halep                 48.7%  11.6%   5.1%     0.02%  
Bojana Jovanovski            51.3%  12.7%   5.9%     0.04%  
Aravane Rezai                25.1%  14.9%   7.9%     0.09%  
Serena Williams              74.9%  60.8%  46.4%     5.54%  
                                                            
Player                         R64    R32    R16         W  
Francesca Schiavone          70.3%  49.3%  30.5%     0.96%  
Jelena Dokic                 29.7%  14.8%   6.1%     0.03%  
Barbora Zahlavova Strycova   57.8%  22.5%  10.0%     0.05%  
Aleksandra Wozniak           42.2%  13.4%   5.0%     0.01%  
Ayumi Morita                 44.0%  14.7%   5.2%     0.01%  
Tamira Paszek                56.0%  21.7%   9.0%     0.04%  
Christina McHale             31.1%  15.8%   6.2%     0.02%  
Ekaterina Makarova           68.9%  47.9%  27.9%     0.70%  
                                                            
Player                         R64    R32    R16         W  
Shahar Peer                  77.8%  58.9%  30.1%     1.15%  
Ksenia Pervak                22.2%  10.6%   2.7%     0.00%  
Sorana Cirstea               65.7%  22.9%   7.3%     0.03%  
Pauline Parmentier           34.3%   7.6%   1.5%     0.00%  
Irina Falconi                56.0%  10.1%   2.7%     0.00%  
Stephanie Dubois             44.0%   7.1%   1.8%     0.00%  
Stephanie Foretz Gacon       11.8%   5.7%   1.5%     0.00%  
Andrea Petkovic              88.2%  77.2%  52.4%     4.11%  
                                                            
Player                         R64    R32    R16         W  
Anastasia Pavlyuchenkova     86.2%  59.1%  38.5%     2.28%  
Lesia Tsurenko               13.8%   3.8%   0.9%     0.00%  
Vesna Dolonts                26.3%   6.0%   1.7%     0.00%  
Nadia Petrova                73.7%  31.1%  16.2%     0.32%  
Kateryna Bondarenko          53.7%  24.2%   9.5%     0.12%  
Alize Cornet                 46.3%  19.3%   7.2%     0.07%  
Sara Errani                  35.3%  16.6%   5.9%     0.05%  
Kaia Kanepi                  64.7%  40.0%  20.1%     0.62%  
                                                            
Player                         R64    R32    R16         W  
Daniela Hantuchova           86.5%  70.1%  28.5%     1.40%  
Vitalia Diatchenko           13.5%   5.4%   0.6%     0.00%  
Kai-Chen Chang               56.0%  14.7%   2.6%     0.01%  
Marina Erakovic              44.0%   9.8%   1.4%     0.00%  
Sandra Zahlavova             26.6%   2.8%   0.7%     0.00%  
Iveta Benesova               73.4%  17.3%   7.9%     0.10%  
Magdalena Rybarikova         16.6%   9.0%   3.9%     0.04%  
Victoria Azarenka            83.4%  70.8%  54.5%    10.87%  
                                                            
Player                         R64    R32    R16         W  
Petra Kvitova                89.6%  79.6%  63.3%     7.16%  
Alexa Glatch                 10.4%   5.0%   1.6%     0.00%  
Naomi Broady                 38.9%   4.8%   1.3%     0.00%  
Anne Keothavong              61.1%  10.6%   3.9%     0.01%  
Rebecca Marino               66.9%  22.5%   5.2%     0.01%  
Patricia Mayr-Achleitner     33.1%   6.6%   0.9%     0.00%  
Vera Dushevina               47.6%  33.4%  10.8%     0.11%  
Roberta Vinci                52.4%  37.5%  12.9%     0.17%  
                                                            
Player                         R64    R32    R16         W  
Yanina Wickmayer             80.9%  66.9%  34.8%     1.28%  
Varvara Lepchenko            19.1%  10.1%   2.4%     0.00%  
Anastasia Pivovarova         49.0%  10.9%   2.3%     0.00%  
Anna Tatishvili              51.0%  12.0%   2.6%     0.00%  
Jill Craybas                 27.7%   4.4%   1.1%     0.00%  
Alexandra Dulgheru           72.3%  21.4%   8.9%     0.05%  
Shuai Zhang                  14.7%   6.2%   1.9%     0.00%  
Svetlana Kuznetsova          85.3%  68.0%  46.1%     3.25%  
                                                            
Player                         R64    R32    R16         W  
Jelena Jankovic              58.7%  44.3%  24.0%     0.97%  
Maria Jose Martinez Sanchez  41.3%  28.3%  13.0%     0.27%  
Monica Niculescu             48.4%  12.9%   3.7%     0.01%  
Sybille Bammer               51.6%  14.6%   4.5%     0.01%  
Katie O'Brien                26.3%   3.8%   0.7%     0.00%  
Kimiko Date-Krumm            73.7%  22.1%   8.4%     0.04%  
Akgul Amanmuradova           14.9%   6.4%   1.6%     0.00%  
Venus Williams               85.1%  67.7%  44.0%     2.94%  
                                                            
Player                         R64    R32    R16         W  
Tsvetana Pironkova           75.0%  41.3%  10.3%     0.08%  
Camila Giorgi                25.0%   7.4%   0.8%     0.00%  
Vania King                   54.9%  29.4%   6.6%     0.02%  
Petra Martic                 45.1%  22.0%   4.3%     0.01%  
Elena Vesnina                84.3%  26.9%  18.2%     0.48%  
Laura Pous-Tio               15.7%   1.5%   0.4%     0.00%  
Alison Riske                 10.4%   3.1%   1.3%     0.00%  
Vera Zvonareva               89.6%  68.4%  58.0%     9.23%