Category: Forecasting

The Tournament Simulation Reference

Italian translation at settesei.it

Among the more popular features of Heavy Topspin are my tournament forecasts, based on draw simulations.  It’s about time that I summarize how these work.

Monte Carlo simulations

To generate tournament predictions, we first need a way to predict the outcome of individual matches.  For that, I use jrank, which I’ve written about elsewhere.  With numerical estimates of a player’s skill–not unlike ATP ranking points–we can calculate the probability that each player wins the match.

Once those matchup probabilities are calculated, it’s a matter of “playing” the tournament thousands upon thousands of times.  Here, computers come in awfully handy.

My code (a version of which is publicly available) uses a random-number generator (RNG) to determine the winner of each match.  For instance, at the top of the Rogers Cup draw this week, Novak Djokovic gets a bye, after which he’ll play the winner of Bernard Tomic‘s match with Michael Berrer.  My numbers give Tomic a 64% chance of beating Berrer.  To “play” that match in a simulated tournament, the RNG spits out a number between 0 and 1.  If the result is below .64, Tomic is the winner; if not, Berrer wins.

The winner advances to “play” Djokovic.  The code determines Djokovic’s probability of beating whoever advances to play him, then generates a new random number to pick the winner.  Repeat the process 47 times–one for each match–and you’ve simulated the entire tournament.

Each simulation, then, gives us a set of results.  Perhaps Tomic reaches the second round, losing to Djokovic, who then loses in the quarters to Juan Martin Del Potro, who goes on to win the tournament.   That’s one possibility–and it’s more likely than many alternatives–but it doesn’t tell the whole story.

That’s why we do it thousands (or even millions) of times.  Over that many simulations, Delpo occasionally wins, but somewhat more often, Djokovic wins that quarterfinal showdown.  Tomic usually reaches the second round, but sometimes it’s Berrer into the second round.  All of these “usually’s” and “sometimes’s” are converted into percentages based on just how often they occur.

Probability adjustments

For any given pair of players, we don’t always expect the same outcome.  Pablo Andujar is almost always the underdog on hardcourts, but we expect him to beat most mid-packers on clay.  Players perform (a bit) better in their home country.  Qualifiers do worse than equivalent players who didn’t have to qualify.

Thus, if we take last week’s Washington field and transplant it to the clay courts of Vina Del Mar, the numbers would change a great deal.  Americans and hard-court specialists would see their chances decrease, while Chileans and clay-courters would see theirs increase–just as conventional wisdom suggests would happen.

Simulation variations: Draw-independence

Some of the more interesting results come from messing around with the draw.  Every time a field is arranged into a bracket, there are winners and losers.  Whoever is drawn to face the top seed in the first round (or second, as Berrer and Tomic can attest) is probably unlucky, while somewhere else in the draw, a couple of lucky qualifiers get to play each other for a spot in the second round.

That’s one of the reasons I sometimes run draw-independent simulations (DIS).  If we want to know how much the draw helped or hurt a player, we need to know how successful he was likely to be before he was placed in the draw.  (DISs are also handy if you know the likely field, but the draw isn’t yet set.)

To run a draw-independent sim, we have to start one step earlier.  Instead of taking the draw as a given, we take the field as a given, including the seedings if we know them.  Then we use the same logic as tournament officials will use in constructing the draw.  The #1 seed goes at the top, #2 at the bottom.  #3 and #4 are randomly placed in the remaining quarters.  #5 through #8 are randomly placed in the remaining eighths, and so on.

(Update: I’ve published a python function, reseeder(), which generates random draws for any combination of number of seeds and field size that occurs on the ATP tour.)

Simulation variations: Seed-independence

We can take this even further to measure the beneficial effect of seeding.  Most of the time we take seeding for granted–we want the top two players in the world to clash only in the final, and so on.  But it can have a serious effect on a player’s chances of winning a tournament.  In Toronto this week, the top 16 seeds (along with, in all likelihood, a very lucky loser or two) get a bye straight into the second round.  That helps!

Even when there are no byes, seedings guarantee relatively easy matches for the first couple of rounds.  That may not make a huge difference for someone like Djokovic–he’ll cruise whether he draws a seeded Florian Mayer or an unseeded Jeremy Chardy.  But if you are Mayer, consider the benefits.  You’re barely better than some unseeded players, but you’re guaranteed to miss the big guns until the third round.

This is why we talk so much about getting into the top 32 in time for slams.  When the big points and big money are on the line, you want those easy opening matches even more than usual.  There isn’t much separating Kevin Anderson from Sam Querrey, but if the US Open draw were held today, Anderson would get a seed and Querrey wouldn’t.  Guess who we’d be more likely to see in the third round!

To run a seed-independent simulation: Instead of generating a logical draw, as we do with a DIS, generate a random draw, in which anyone can face anyone in the first round.

Measuring variations

If we compare forecasts based on the actual draw to draw-independent or seed-independent forecasts, we want to quantify the difference.  To do so, I’ve used two metrics: Expected Ranking Points (ERP) and Expected Prize Money (EPM).

Both reduce an entire tournament’s worth of forecasts to one number per player.  If Djokovic has a 30% chance of winning this week in Toronto, that’s the probability he’ll take home 1,000 points.  If those were the only points on offer, his ERP would be 30% of 1,000, or 300.

Of course, if Djokovic loses, he’ll still get some points.  To come up with his overall ERP, we consider his probability of losing the finals and the number of points awarded to the losing finalist, his probability of losing in the semis and the number of points awarded to semifinalists, and so on.  To calculate EPM, we use the same process, but with–you guessed it–prize money instead of ranking points.

Both numbers allow to see how much the draw helps or hurts a player.  For instance, before the French Open, I calculated that Richard Gasquet‘s EPM rose by approximately 25% thanks to a very lucky draw.

These numbers also help us analyze a player’s scheduling choices.  The very strong Olympics field and the much weaker Washington field last week created an odd situation: Lesser players were able to rack up far more points than their more accomplished colleagues. Even before the tournament, we could use the ERP/EPM approach to see that Mardy Fish could expect 177 points in Washington while the far superior David Ferrer could expect only 159 in London.

If you’ve read this far, you will probably enjoy the newest feature on TennisAbstract.com–live-ish forecast updates for all ATP events.  Find links on the TA.com homepage, or click straight to the Rogers Cup page.

2012 Olympics Round of 16 Forecasts

Here are my forecasts for the remaining 16 players in both Olympics singles draws.  Note that Djokovic has opened up a bigger gap over Federer.  Novak is aided by Berdych’s upset, while Federer is still likely to play the top seeds in his half.

On the women’s side, the third quarter is a crowded one, with Clijsters, Sharapova, and two dangerous floaters in Ivanovic and Lisicki.

For more background, you can see my initial forecasts, (almost) current rankings, and methodology.

Men:

Player                       QF     SF      F      W  
(1)Roger Federer          85.3%  64.5%  45.1%  25.7%  
Denis Istomin             14.7%   5.0%   1.5%   0.3%  
(10)John Isner            53.5%  16.9%   7.5%   2.4%  
(7)Janko Tipsarevic       46.5%  13.5%   5.6%   1.7%  
(4)David Ferrer           63.3%  36.3%  16.2%   6.7%  
(15)Kei Nishikori         36.7%  16.0%   5.2%   1.6%  
(12)Gilles Simon          32.3%  11.7%   3.3%   0.8%  
(8)Juan Martin Del Potro  67.7%  36.0%  15.5%   6.2%  

Player                       QF     SF      F      W  
Steve Darcis              39.5%   8.9%   1.5%   0.3%  
(11)Nicolas Almagro       60.5%  18.1%   4.2%   1.3%  
Marcos Baghdatis          22.7%  11.9%   2.7%   0.7%  
(3)Andy Murray            77.3%  61.1%  29.8%  16.4%  
(5)Jo-Wilfried Tsonga     67.5%  23.3%  12.0%   5.4%  
Feliciano Lopez           32.5%   6.9%   2.4%   0.7%  
(WC)Lleyton Hewitt         4.6%   0.6%   0.1%   0.0%  
(2)Novak Djokovic         95.4%  69.3%  47.3%  29.7%

Women:

Player                 QF     SF      F      W  
Victoria Azarenka   78.9%  53.3%  28.2%  18.0%  
Nadia Petrova       21.1%   7.9%   1.9%   0.6%  
Venus Williams      16.8%   2.5%   0.3%   0.1%  
Angelique Kerber    83.2%  36.3%  14.8%   7.6%  
Serena Williams     75.9%  56.2%  36.9%  26.2%  
Vera Zvonareva      24.1%  11.5%   4.4%   1.9%  
Daniela Hantuchova  36.2%   9.1%   2.9%   1.1%  
Caroline Wozniacki  63.8%  23.2%  10.6%   5.3%  

Player                 QF     SF      F      W  
Kim Clijsters       62.5%  33.2%  20.3%   8.9%  
Ana Ivanovic        37.5%  15.4%   7.4%   2.5%  
Sabine Lisicki      36.8%  15.7%   7.7%   2.5%  
Maria Sharapova     63.2%  35.6%  22.2%  10.0%  
Petra Kvitova       65.5%  45.7%  23.9%  10.2%  
Flavia Pennetta     34.5%  18.9%   7.0%   1.9%  
Maria Kirilenko     47.5%  16.2%   5.0%   1.2%  
Julia Goerges       52.5%  19.3%   6.6%   1.8%

2012 Olympics Women’s Projections

Forecasting the women’s singles event isn’t rocket science–it’s just a matter of how much you favor Serena Williams over everyone else.

My algorithm gives Serena a 22.7% chance of taking home the gold.  While the draw did her a favor, placing Kim Clijsters in the other half, it wasn’t perfect: Jelena Jankovic is a relatively difficult first round match.  With a randomized draw, Serena’s chances are nearly 25%.

Following the American is her very likely semifinal opponent, Victoria Azarenka, who I give a 18.4% chance of winning it all.  With an easier draw in the early rounds, Azarenka has a slightly better chance of making it to the semis (49.0% to 45.6%), but is less likely to come out of that showdown triumphant.

No one else has a double-digit chance of winning the tournament.  Williams and Azarenka are followed, in order, by Maria Sharapova, Agnieszka Radwanska, Petra Kvitova, and Clijsters.

Below, find the forecast for the entire field.  To see my current hard-court rankings, click here, and for some background on the system, click here.  I’ve also posted projections for the men’s singles event.

Player                         R32    R16     QF        W  
Victoria Azarenka            92.3%  79.6%  65.3%    18.4%  
Irina-Camelia Begu            7.7%   2.6%   0.8%     0.0%  
Maria Jose Martinez Sanchez  55.6%  10.6%   4.9%     0.1%  
Polona Hercog                44.4%   7.2%   3.0%     0.0%  
Anna Tatishvili              55.5%  12.3%   1.6%     0.0%  
Stephanie Vogt               44.5%   8.4%   0.9%     0.0%  
Jie Zheng                    49.9%  39.5%  11.6%     0.5%  
Nadia Petrova                50.1%  39.8%  11.8%     0.5%  
                                                           
Player                         R32    R16     QF        W  
Sara Errani                  62.9%  35.8%  13.2%     0.2%  
Venus Williams               37.1%  16.3%   4.4%     0.0%  
Marina Erakovic              45.6%  20.8%   6.1%     0.1%  
Aleksandra Wozniak           54.4%  27.1%   8.6%     0.1%  
Galina Voskoboeva            69.5%  23.6%  13.7%     0.4%  
Timea Babos                  30.5%   5.7%   2.2%     0.0%  
Petra Cetkovska              29.5%  17.0%  10.2%     0.3%  
Angelique Kerber             70.5%  53.6%  41.8%     4.9%  
                                                           
Player                         R32    R16     QF        W  
Serena Williams              83.9%  73.9%  60.2%    22.7%  
Jelena Jankovic              16.1%   9.6%   4.4%     0.2%  
Mona Barthel                 43.0%   6.3%   2.2%     0.0%  
Urszula Radwanska            57.0%  10.2%   4.2%     0.1%  
Francesca Schiavone          46.9%  18.8%   4.4%     0.2%  
Klara Zakopalova             53.1%  23.1%   6.0%     0.2%  
Sofia Arvidsson              28.1%  11.8%   2.3%     0.0%  
Vera Zvonareva               71.9%  46.3%  16.3%     1.6%  
                                                           
Player                         R32    R16     QF        W  
Na Li                        61.5%  41.9%  23.1%     2.3%  
Daniela Hantuchova           38.5%  22.0%   9.6%     0.5%  
Alize Cornet                 26.5%   5.5%   1.2%     0.0%  
Tamira Paszek                73.5%  30.6%  13.2%     0.6%  
Anabel Medina Garrigues      34.7%  10.3%   3.4%     0.0%  
Yanina Wickmayer             65.3%  27.8%  13.3%     0.7%  
Anne Keothavong              14.5%   3.9%   0.8%     0.0%  
Caroline Wozniacki           85.5%  58.0%  35.3%     4.1%  
                                                           
Player                         R32    R16     QF        W  
Samantha Stosur              81.9%  39.2%  23.9%     2.4%  
Carla Suarez Navarro         18.1%   3.3%   0.9%     0.0%  
Kim Clijsters                76.2%  48.7%  33.5%     5.6%  
Roberta Vinci                23.8%   8.8%   3.7%     0.1%  
Agnes Szavay                 21.8%   1.5%   0.1%     0.0%  
Elena Baltacha               78.2%  16.0%   2.7%     0.0%  
Christina McHale             43.9%  35.4%  13.9%     0.7%  
Ana Ivanovic                 56.1%  47.2%  21.3%     1.7%  
                                                           
Player                         R32    R16     QF        W  
Sabine Lisicki               95.1%  66.0%  31.5%     2.7%  
Ons Jabeur                    4.9%   0.5%   0.0%     0.0%  
Simona Halep                 61.6%  22.8%   7.6%     0.2%  
Yaroslava Shvedova           38.4%  10.7%   2.6%     0.0%  
Petra Martic                 37.2%   9.2%   3.2%     0.1%  
Lucie Safarova               62.8%  21.5%  10.1%     0.5%  
Shahar Peer                  18.4%   7.7%   2.6%     0.0%  
Maria Sharapova              81.6%  61.6%  42.3%     7.6%  
                                                           
Player                         R32    R16     QF        W  
Petra Kvitova                80.7%  61.8%  41.0%     6.5%  
Kateryna Bondarenko          19.3%   8.5%   2.8%     0.0%  
Su-Wei Hsieh                 42.9%  11.3%   3.8%     0.1%  
Shuai Peng                   57.1%  18.4%   7.5%     0.2%  
Sorana Cirstea               41.5%  16.9%   6.4%     0.2%  
Flavia Pennetta              58.5%  28.8%  13.2%     0.9%  
Tsvetana Pironkova           42.8%  21.5%   9.2%     0.5%  
Dominika Cibulkova           57.2%  32.8%  16.1%     1.3%  
                                                           
Player                         R32    R16     QF        W  
Maria Kirilenko              85.9%  60.6%  23.8%     1.0%  
Mariana Duque-Marino         14.1%   3.8%   0.4%     0.0%  
Silvia Soler-Espinosa        45.6%  15.3%   3.2%     0.0%  
Heather Watson               54.4%  20.3%   4.8%     0.0%  
Varvara Lepchenko            73.2%  13.1%   5.0%     0.0%  
Veronica Cepede Royg         26.8%   2.0%   0.4%     0.0%  
Julia Goerges                30.0%  23.0%  14.1%     0.7%  
Agnieszka Radwanska          70.0%  61.9%  48.2%     8.4%

2012 Olympics Men’s Projections

The draw is out.  Roger Federer is in one half, and everybody else is in the other.

Maybe that’s a harsh assessment of the 31 men who share the Olympic singles bracket with the world number one, but it’s a tough conclusion to avoid.  In the other half, Novak Djokovic is slated to meet Andy Murray in a semi, while Roger’s likely opponents are David Ferrer and Juan Martin Del Potro,  against whom he is on a combined 10-match winning streak.  Jo Wilfried Tsonga and Tomas Berdych—two men who I noted could derail Fed’s quest for the gold–are also in the bottom half, with Tsonga lined up against Djokovic and Berdych against Murray.

The only thing that could count against Federer are some past near-misses.  In the first round, he’ll face Alejandro Falla, and in the second, he could see Julien Benneteau.  Both men have taken him to five sets on the Wimbledon grass–in both cases, winning the first two sets.  In a best-of-three event, there isn’t quite so much wiggle room.  But even in the quarterfinals, Fed’s likely opponents are John Isner, David Nalbandian, and Janko Tipsarevic.  He couldn’t have drawn it up any better if they had let him.

This is a rare occasion where the draw does make a difference.  According to jrank, Djokovic still has a moderate edge over Federer on hard courts.  If the draw were randomized, Novak would have a 23.8% chance of winning the gold, while Roger would be a close second at 21.9%.  With the actual draw, the difference is more than halved.  Federer’s chances stay the same, with Novak’s dropping to 22.7%.

After the top two, Murray is the clear-cut choice for the bronze, with a 12.1% chance of winning the tournament outright.  Ferrer and Delpo follow, in position to take advantage of the weaker top half should Federer fall.

Below, find the forecast for the entire field.  To see my current hard-court rankings, click here, and for some background on the system, click here.  Women’s Olympic singles forecasts will be posted in a little while.

Player                      R32    R16     QF        W  
(1)Roger Federer          88.0%  69.8%  59.5%    21.9%  
Alejandro Falla           12.0%   4.1%   1.8%     0.0%  
Julien Benneteau          43.9%  10.5%   5.9%     0.3%  
Mikhail Youzhny           56.1%  15.6%   9.9%     0.9%  
(WC)Adrian Ungur          20.2%   2.9%   0.2%     0.0%  
Gilles Muller             79.8%  32.2%   6.2%     0.1%  
Denis Istomin             44.3%  27.5%   6.4%     0.2%  
(14)Fernando Verdasco     55.7%  37.5%  10.2%     0.6%  

Player                      R32    R16     QF        W  
(10)John Isner            72.9%  54.2%  31.4%     2.6%  
Olivier Rochus            27.1%  14.4%   5.1%     0.1%  
Yen-Hsun Lu               56.4%  19.1%   6.5%     0.1%  
(WC)Malek Jaziri          43.6%  12.4%   3.5%     0.0%  
Lukas Lacko               40.8%  13.7%   5.7%     0.1%  
Ivo Karlovic              59.2%  25.1%  12.6%     0.4%  
David Nalbandian          50.3%  30.8%  17.7%     1.2%  
(7)Janko Tipsarevic       49.7%  30.4%  17.5%     1.1%  

Player                      R32    R16     QF        W  
(4)David Ferrer           82.6%  59.4%  41.0%     6.8%  
(WC)Vasek Pospisil        17.4%   6.5%   2.1%     0.0%  
Philipp Kohlschreiber     75.7%  29.7%  15.4%     0.9%  
(WC)Blaz Kavcic           24.3%   4.5%   1.1%     0.0%  
Radek Stepanek            50.3%  21.5%   7.8%     0.3%  
Nikolay Davydenko         49.7%  20.9%   7.5%     0.2%  
Bernard Tomic             43.8%  23.6%   9.4%     0.5%  
(15)Kei Nishikori         56.2%  34.0%  15.7%     1.2%  

Player                      R32    R16     QF        W  
(12)Gilles Simon          62.9%  36.4%  16.3%     0.8%  
Mikhail Kukushkin         37.1%  16.7%   5.6%     0.1%  
Lukasz Kubot              48.1%  22.1%   8.1%     0.2%  
Grigor Dimitrov           51.9%  24.7%   9.5%     0.3%  
Andreas Seppi             56.2%  17.5%   8.2%     0.2%  
Donald Young              43.8%  11.6%   4.7%     0.1%  
Ivan Dodig                25.3%  13.5%   6.3%     0.1%  
(8)Juan Martin Del Potro  74.7%  57.3%  41.4%     5.9%  

Player                      R32    R16     QF        W  
(6)Tomas Berdych          70.7%  49.7%  33.6%     3.0%  
Steve Darcis              29.4%  14.6%   6.9%     0.1%  
Santiago Giraldo          44.9%  15.0%   6.6%     0.1%  
Ryan Harrison             55.1%  20.7%  10.2%     0.2%  
Alex Bogomolov Jr.        70.9%  27.3%   9.9%     0.1%  
Carlos Berlocq            29.1%   5.9%   1.2%     0.0%  
Viktor Troicki            45.0%  29.1%  13.0%     0.4%  
(11)Nicolas Almagro       55.0%  37.7%  18.5%     0.8%  

Player                      R32    R16     QF        W  
(16)Richard Gasquet       67.9%  39.9%  15.0%     0.9%  
Robin Haase               32.1%  12.9%   3.1%     0.0%  
Go Soeda                  33.8%  12.5%   2.9%     0.0%  
Marcos Baghdatis          66.2%  34.7%  12.1%     0.6%  
(WC)Somdev Devvarman      33.6%   4.8%   1.4%     0.0%  
Jarkko Nieminen           66.4%  16.1%   7.4%     0.2%  
Stanislas Wawrinka        26.2%  17.1%   9.6%     0.6%  
(3)Andy Murray            73.8%  62.1%  48.5%    12.1%  

Player                      R32    R16     QF        W  
(5)Jo-Wilfried Tsonga     78.7%  54.8%  38.2%     5.1%  
(WC)Thomaz Bellucci       21.3%   8.4%   3.2%     0.0%  
Tatsuma Ito               28.1%   6.5%   2.2%     0.0%  
Milos Raonic              71.9%  30.3%  16.8%     0.9%  
Dmitry Tursunov           36.6%  13.9%   4.3%     0.1%  
Feliciano Lopez           63.4%  32.6%  13.5%     0.6%  
David Goffin              40.0%  19.0%   6.6%     0.2%  
(9)Juan Monaco            60.0%  34.6%  15.2%     0.8%  

Player                      R32    R16     QF        W  
(13)Marin Cilic           56.2%  43.0%  13.1%     1.2%  
Jurgen Melzer             43.8%  31.4%   8.2%     0.5%  
(WC)Lleyton Hewitt        31.7%   5.2%   0.4%     0.0%  
(WC)Sergiy Stakhovsky     68.3%  20.3%   3.1%     0.1%  
Andy Roddick              78.0%  22.3%  13.6%     1.5%  
Martin Klizan             22.0%   2.6%   0.8%     0.0%  
Fabio Fognini              9.0%   2.7%   0.9%     0.0%  
(2)Novak Djokovic         91.0%  72.4%  59.9%    22.7%

2012 Wimbledon Men’s Projections

Here are my projections for this year’s Wimbledon men’s draw.  Djokovic is far and away the favorite now that we’ve moved away from clay.  Federer comes in a close third behind Nadal, helped in part by what is probably the easiest of the four quarters.

Intuitively, these numbers seem about right, especially for the top players.  But a few developments in the ATP recently have exposed some gaps in my ranking system.  Brian Baker’s quick ascendance has yet to do much for him in my system, in part because he hasn’t played very much top-level matches.  But after his performance in Nice, it seems wrong to give him less than a 35% chance against a journeyman like Rui Machado.

The other head-scratcher is Tommy Haas.  After winning Halle, my system isn’t giving him much credit, in large part because he’s 34. Since players start going downhill by age 26, a player’s rate of decline in his mid-30s would generally be staggering.   But, of course, most players are gone by then.  If someone like Haas is still playing (and winning), he probably isn’t subject to exactly the same laws.  Perhaps 34-year-olds on tour are rare enough that it isn’t all that important, but in this one case, it generates a forecast that doesn’t jibe with common sense.

If you’re interested in the rankings behind these forecasts, click here; for more background on the system, here.

Women’s odds were posted earlier today, and both forecasts will be updated throughout the tournament–I’ll post those links when I have them, probably mid-day Tuesday.

    Player                   R64    R32    R16        W  
1   Novak Djokovic         96.8%  81.3%  70.3%    26.2%  
    Juan Carlos Ferrero     3.2%   0.5%   0.1%     0.0%  
    Ryan Harrison          55.0%  10.7%   6.1%     0.3%  
    Yen-Hsun Lu            45.0%   7.6%   3.9%     0.1%  
    Benjamin Becker        53.2%  25.2%   4.8%     0.1%  
    James Blake            46.8%  20.5%   3.6%     0.0%  
    Sergiy Stakhovsky      54.4%  30.6%   6.7%     0.2%  
28  Radek Stepanek         45.6%  23.8%   4.7%     0.1%  

    Player                   R64    R32    R16        W  
24  Marcel Granollers      53.7%  42.9%  26.4%     1.0%  
    Viktor Troicki         46.3%  35.9%  20.9%     0.6%  
    Martin Klizan          65.0%  15.9%   5.4%     0.0%  
    Juan Ignacio Chela     35.0%   5.3%   1.1%     0.0%  
    Jeremy Chardy          88.5%  48.2%  22.9%     0.4%  
    Filippo Volandri       11.5%   1.8%   0.2%     0.0%  
    Leonardo Mayer         18.7%   4.7%   0.9%     0.0%  
15  Juan Monaco            81.3%  45.3%  22.1%     0.4%  

    Player                   R64    R32    R16        W  
12  Nicolas Almagro        60.2%  36.6%  18.6%     0.3%  
    Olivier Rochus         39.8%  20.3%   8.2%     0.0%  
    Guillaume Rufin        21.0%   4.4%   0.8%     0.0%  
    Steve Darcis           79.0%  38.8%  17.8%     0.2%  
    Carlos Berlocq         18.7%   2.6%   0.5%     0.0%  
    Ruben Bemelmans        81.3%  33.7%  16.7%     0.2%  
    Tobias Kamke           37.3%  21.0%  10.5%     0.1%  
18  Richard Gasquet        62.7%  42.7%  26.8%     1.0%  

    Player                   R64    R32    R16        W  
31  Florian Mayer          60.7%  38.2%  19.4%     0.8%  
    Dmitry Tursunov        39.3%  20.8%   8.3%     0.1%  
    Philipp Petzschner     54.8%  23.6%   9.6%     0.2%  
    Blaz Kavcic            45.2%  17.4%   6.2%     0.1%  
    Simone Bolelli         51.0%  17.4%   8.0%     0.1%  
    Jerzy Janowicz         49.0%  16.3%   7.2%     0.1%  
    Ernests Gulbis         36.3%  21.1%  11.4%     0.4%  
6   Tomas Berdych          63.7%  45.3%  29.9%     2.6%  

    Player                   R64    R32    R16        W  
3   Roger Federer          92.0%  73.7%  59.4%    10.4%  
    Albert Ramos            8.0%   2.1%   0.6%     0.0%  
    Fabio Fognini          36.9%   6.9%   3.0%     0.0%  
    Michael Llodra         63.1%  17.3%   9.6%     0.2%  
    A Menendez-Maceiras    31.5%   6.6%   0.8%     0.0%  
    Michael Russell        68.5%  25.3%   5.5%     0.0%  
    Gilles Muller          43.3%  28.2%   7.9%     0.1%  
29  Julien Benneteau       56.7%  39.9%  13.4%     0.3%  

    Player                   R64    R32    R16        W  
17  Fernando Verdasco      88.2%  53.1%  27.7%     0.8%  
    Jimmy Wang             11.8%   2.4%   0.3%     0.0%  
    Grega Zemlja           90.7%  43.6%  20.1%     0.3%  
    Josh Goodall            9.3%   0.9%   0.1%     0.0%  
    Xavier Malisse         51.6%  21.7%   9.8%     0.1%  
    Marinko Matosevic      48.4%  19.7%   8.6%     0.1%  
    Paul-Henri Mathieu     12.6%   2.5%   0.5%     0.0%  
13  Gilles Simon           87.4%  56.1%  32.8%     1.4%  

    Player                   R64    R32    R16        W  
11  John Isner             66.6%  46.0%  28.9%     1.2%  
    Alejandro Falla        33.4%  17.7%   8.2%     0.1%  
    Paolo Lorenzi          21.2%   3.4%   0.7%     0.0%  
    Nicolas Mahut          78.8%  32.9%  16.2%     0.2%  
    Igor Andreev           87.6%  37.3%  15.6%     0.1%  
    Oliver Golding         12.4%   1.2%   0.1%     0.0%  
    Denis Istomin          47.2%  28.3%  13.5%     0.2%  
23  Andreas Seppi          52.8%  33.2%  16.9%     0.4%  

    Player                   R64    R32    R16        W  
26  Mikhail Youzhny        50.8%  33.2%  16.3%     0.4%  
    Donald Young           49.2%  31.9%  15.3%     0.4%  
    Inigo Cervantes        20.2%   2.9%   0.4%     0.0%  
    Flavio Cipolla         79.8%  32.0%  12.5%     0.2%  
    Ryan Sweeting          79.1%  29.1%  13.8%     0.2%  
    Potito Starace         20.9%   2.8%   0.5%     0.0%  
    David Nalbandian       49.6%  33.7%  20.3%     0.9%  
8   Janko Tipsarevic       50.4%  34.4%  20.9%     1.0%  

    Player                   R64    R32    R16        W  
7   David Ferrer           70.4%  49.1%  32.6%     1.7%  
    Dustin Brown           29.6%  14.6%   6.7%     0.1%  
    Kenny De Schepper      40.5%  12.6%   5.3%     0.0%  
    Matthias Bachinger     59.5%  23.6%  11.8%     0.1%  
    Wayne Odesnik          30.0%   5.6%   1.0%     0.0%  
    Bjorn Phau             70.0%  24.3%   8.0%     0.0%  
    Jamie Baker            36.0%  22.5%   9.0%     0.1%  
30  Andy Roddick           64.0%  47.7%  25.5%     0.7%  

    Player                   R64    R32    R16        W  
19  Kei Nishikori          64.7%  52.4%  30.5%     1.9%  
    Mikhail Kukushkin      35.3%  24.7%  11.0%     0.2%  
    Andrey Kuznetsov       33.3%   5.1%   0.9%     0.0%  
    Florent Serra          66.7%  17.8%   5.3%     0.0%  
    Go Soeda               52.2%  16.7%   6.7%     0.0%  
    Igor Kunitsyn          47.8%  14.5%   5.4%     0.0%  
    Robin Haase            30.0%  16.5%   7.3%     0.1%  
9   J Del Potro            70.0%  52.3%  32.8%     2.4%  

    Player                   R64    R32    R16        W  
16  Marin Cilic            61.8%  42.7%  25.1%     1.5%  
    Cedrik-Marcel Stebe    38.2%  22.0%  10.3%     0.2%  
    Tatsuma Ito            50.0%  17.7%   6.8%     0.1%  
    Lukasz Kubot           50.0%  17.6%   6.9%     0.1%  
    Vasek Pospisil         38.9%  17.0%   7.5%     0.1%  
    Sam Querrey            61.1%  33.7%  18.5%     0.8%  
    Santiago Giraldo       42.8%  19.4%   8.9%     0.2%  
21  Milos Raonic           57.2%  30.0%  16.0%     0.5%  

    Player                   R64    R32    R16        W  
32  Kevin Anderson         53.2%  29.8%  12.7%     0.5%  
    Grigor Dimitrov        46.8%  24.9%   9.9%     0.3%  
    Albert Montanes        20.8%   4.5%   0.8%     0.0%  
    Marcos Baghdatis       79.2%  40.9%  17.6%     0.7%  
    Ivo Karlovic           39.3%   8.1%   2.5%     0.0%  
    Dudi Sela              60.7%  17.3%   7.1%     0.1%  
    Nikolay Davydenko      24.1%  13.7%   6.0%     0.1%  
4   Andy Murray            75.9%  61.0%  43.3%     7.0%  

    Player                   R64    R32    R16        W  
5   Jo-Wilfried Tsonga     93.2%  69.4%  47.0%     5.2%  
    Lleyton Hewitt          6.8%   1.2%   0.2%     0.0%  
    E Roger-Vasselin       44.5%  12.0%   4.7%     0.1%  
    G Garcia-Lopez         55.5%  17.4%   7.8%     0.1%  
    Lukas Lacko            82.2%  34.6%  12.5%     0.3%  
    Adrian Ungur           17.8%   2.4%   0.3%     0.0%  
    Jurgen Melzer          35.8%  19.6%   6.8%     0.1%  
25  Stanislas Wawrinka     64.2%  43.3%  20.8%     1.1%  

    Player                   R64    R32    R16        W  
20  Bernard Tomic          78.7%  51.6%  27.4%     1.0%  
    David Goffin           21.4%   7.3%   1.8%     0.0%  
    Jesse Levine           56.2%  24.4%  10.0%     0.1%  
    Karol Beck             43.8%  16.7%   5.9%     0.0%  
    James Ward             76.3%  28.0%  12.6%     0.1%  
    Pablo Andujar          23.7%   4.0%   0.9%     0.0%  
    R Ramirez Hidalgo       6.7%   1.1%   0.1%     0.0%  
10  Mardy Fish             93.3%  66.9%  41.3%     2.2%  

    Player                   R64    R32    R16        W  
14  Feliciano Lopez        58.5%  52.2%  28.3%     0.7%  
    Jarkko Nieminen        41.5%  35.4%  16.0%     0.2%  
    Brian Baker            33.8%   2.7%   0.2%     0.0%  
    Rui Machado            66.2%   9.8%   1.5%     0.0%  
    Matthew Ebden          58.7%  25.7%  13.2%     0.1%  
    Benoit Paire           41.3%  14.5%   6.3%     0.0%  
    Alex Bogomolov Jr.     39.8%  21.4%  11.0%     0.1%  
22  Alexandr Dolgopolov    60.2%  38.4%  23.4%     0.7%  

    Player                   R64    R32    R16        W  
27  Philipp Kohlschreiber  81.1%  52.3%  19.6%     0.9%  
    Tommy Haas             18.9%   5.9%   0.8%     0.0%  
    Jurgen Zopp            74.2%  35.2%  10.4%     0.2%  
    Malek Jaziri           25.8%   6.6%   0.9%     0.0%  
    Lukas Rosol            39.9%   9.2%   4.1%     0.1%  
    Ivan Dodig             60.1%  18.3%  10.0%     0.4%  
    Thomaz Bellucci        17.2%   7.5%   3.4%     0.1%  
2   Rafael Nadal           82.8%  64.9%  50.8%    12.0%

2012 Wimbledon Women’s Projections

Here are my forecasts for the Wimbledon women’s draw.  Despite Maria Sharapova’s performance at the French, my ranking system still has her third, behind both Serena and Azarenka.  Also, you might also be surprised by the significant chance I give Kim Clijsters.  While she hasn’t played much, she’s played well, and my system operates on the assumption that if someone takes the court, she is doing so fully healthy.  (Or, at least, as healthy as she’s been other times she took the court.)

If you’re interested in the rankings behind these forecasts, click here; for more background on the system, here.

I’ll post men’s odds later today, and the forecast will be updated throughout the tournament–I’ll post those links when I have them, probably mid-day Tuesday.

    Player                   R64    R32    R16        W  
1   Maria Sharapova        89.1%  68.7%  56.4%     8.7%  
    Anastasia Rodionova    10.9%   3.4%   1.2%     0.0%  
    Vesna Dolonc           21.8%   2.8%   0.9%     0.0%  
    Tsvetana Pironkova     78.2%  25.1%  15.9%     0.4%  
    Su-Wei Hsieh           51.5%  29.5%   8.0%     0.1%  
    Virginie Razzano       48.5%  27.0%   7.1%     0.1%  
    S Foretz Gacon         28.2%   7.8%   1.0%     0.0%  
29  Monica Niculescu       71.8%  35.6%   9.5%     0.1%  

    Player                   R64    R32    R16        W  
23  Petra Cetkovska        55.0%  38.3%  19.9%     0.3%  
    Vania King             45.0%  29.3%  13.8%     0.1%  
    Sloane Stephens        63.2%  23.1%   8.6%     0.0%  
    Karolina Pliskova      36.8%   9.2%   2.4%     0.0%  
    Bojana Jovanovski      58.0%  17.0%   6.8%     0.0%  
    Eleni Daniilidou       42.0%   9.9%   3.2%     0.0%  
    Petra Martic           32.6%  20.5%  10.2%     0.1%  
15  Sabine Lisicki         67.4%  52.6%  35.2%     1.2%  

    Player                   R64    R32    R16        W  
12  Vera Zvonareva         75.3%  64.2%  33.5%     2.3%  
    Mona Barthel           24.8%  16.3%   4.7%     0.0%  
    Edina Gallovits-Hall   37.5%   5.6%   0.8%     0.0%  
    Silvia Soler-Espinosa  62.5%  13.8%   3.0%     0.0%  
    Kai-Chen Chang         52.0%   7.6%   2.0%     0.0%  
    Andrea Hlavackova      48.0%   6.5%   1.5%     0.0%  
    Kim Clijsters          70.6%  63.1%  43.1%     5.4%  
18  Jelena Jankovic        29.4%  22.9%  11.4%     0.3%  

    Player                   R64    R32    R16        W  
28  Christina McHale       79.2%  64.0%  30.0%     0.7%  
    Johanna Konta          20.8%  11.0%   2.1%     0.0%  
    Lesia Tsurenko         59.4%  16.4%   3.4%     0.0%  
    Mathilde Johansson     40.6%   8.7%   1.3%     0.0%  
    Ekaterina Makarova     80.8%  38.2%  23.5%     0.6%  
    Alberta Brianti        19.2%   3.7%   1.1%     0.0%  
    Lucie Hradecka         19.1%   6.1%   2.3%     0.0%  
8   Angelique Kerber       80.9%  52.1%  36.1%     2.1%  

    Player                   R64    R32    R16        W  
3   Agnieszka Radwanska    88.4%  70.6%  50.7%     7.3%  
    Magdalena Rybarikova   11.6%   4.0%   1.1%     0.0%  
    Venus Williams         51.5%  13.3%   5.4%     0.1%  
    Elena Vesnina          48.5%  12.1%   4.8%     0.0%  
    Iveta Benesova         72.8%  35.1%  13.0%     0.3%  
    Heather Watson         27.2%   7.5%   1.4%     0.0%  
    Jamie Lee Hampton      20.8%   6.9%   1.3%     0.0%  
27  Daniela Hantuchova     79.2%  50.6%  22.3%     1.0%  

    Player                   R64    R32    R16        W  
20  Nadia Petrova          83.0%  56.0%  28.4%     0.4%  
    Maria Elena Camerin    17.0%   5.1%   1.0%     0.0%  
    Timea Babos            40.1%  13.3%   4.1%     0.0%  
    Melanie Oudin          59.9%  25.6%   9.9%     0.0%  
    Tamarine Tanasugarn    52.2%  11.9%   3.8%     0.0%  
    Anna Tatishvili        47.8%  10.1%   3.0%     0.0%  
    Camila Giorgi          18.9%  10.2%   3.6%     0.0%  
16  Flavia Pennetta        81.1%  67.9%  46.1%     1.7%  

    Player                   R64    R32    R16        W  
11  Na Li                  77.1%  60.0%  44.4%     3.8%  
    Ksenia Pervak          22.9%  11.8%   5.7%     0.0%  
    Sorana Cirstea         69.4%  22.5%  11.9%     0.1%  
    Pauline Parmentier     30.6%   5.6%   2.0%     0.0%  
    Naomi Broady           43.8%  10.4%   1.7%     0.0%  
    L Dominguez Lino       56.2%  16.1%   3.4%     0.0%  
    Alexandra Cadantu      15.1%   6.1%   0.9%     0.0%  
17  Maria Kirilenko        84.9%  67.4%  29.9%     0.6%  

    Player                   R64    R32    R16        W  
30  Shuai Peng             80.2%  54.1%  23.5%     0.4%  
    Sandra Zaniewska       19.8%   6.8%   1.3%     0.0%  
    Jarmila Gajdosova      59.4%  25.3%   7.9%     0.0%  
    Ayumi Morita           40.6%  13.9%   3.4%     0.0%  
    Arantxa Rus            52.1%  10.3%   3.7%     0.0%  
    Misaki Doi             47.9%   9.1%   3.1%     0.0%  
    Carla Suarez Navarro   17.6%   9.9%   4.0%     0.0%  
5   Samantha Stosur        82.4%  70.7%  53.1%     4.2%  

    Player                   R64    R32    R16        W  
6   Serena Williams        90.4%  80.9%  67.2%    16.1%  
    B Zahlavova Strycova    9.6%   4.6%   1.7%     0.0%  
    Johanna Larsson        43.5%   5.7%   2.0%     0.0%  
    Melinda Czink          56.5%   8.8%   3.6%     0.0%  
    Vera Dushevina         47.7%  19.1%   3.9%     0.0%  
    Aleksandra Wozniak     52.3%  22.2%   4.7%     0.0%  
    Stephanie Dubois       18.9%   5.7%   0.7%     0.0%  
25  Jie Zheng              81.1%  53.0%  16.2%     0.4%  

    Player                   R64    R32    R16        W  
19  Lucie Safarova         80.1%  57.6%  39.9%     0.8%  
    Kiki Bertens           19.9%   7.7%   2.7%     0.0%  
    Chanelle Scheepers     49.7%  17.2%   7.9%     0.0%  
    Yaroslava Shvedova     50.3%  17.6%   8.3%     0.0%  
    Laura Pous-Tio         35.9%   9.4%   2.2%     0.0%  
    Anne Keothavong        64.1%  24.9%   8.7%     0.0%  
    Coco Vandeweghe        33.8%  18.7%   6.6%     0.0%  
10  Sara Errani            66.2%  47.0%  23.7%     0.2%  

    Player                   R64    R32    R16        W  
13  Dominika Cibulkova     64.4%  53.7%  38.7%     1.5%  
    Klara Zakopalova       35.6%  26.2%  15.6%     0.1%  
    Olga Govortsova        50.6%  10.2%   3.6%     0.0%  
    Annika Beck            49.4%   9.9%   3.5%     0.0%  
    Polona Hercog          64.5%  28.1%  10.0%     0.0%  
    Kristyna Pliskova      35.5%  10.8%   2.7%     0.0%  
    Laura Robson           31.3%  15.2%   4.6%     0.0%  
24  Francesca Schiavone    68.7%  45.9%  21.3%     0.2%  

    Player                   R64    R32    R16        W  
31  A Pavlyuchenkova       64.0%  50.0%  18.4%     0.5%  
    Sofia Arvidsson        36.0%  24.0%   6.4%     0.0%  
    P Mayr-Achleitner      34.2%   6.2%   0.8%     0.0%  
    Varvara Lepchenko      65.8%  19.8%   3.9%     0.0%  
    Elena Baltacha         64.5%  10.0%   3.5%     0.0%  
    Karin Knapp            35.5%   3.5%   0.8%     0.0%  
    A Amanmuradova          9.4%   4.7%   1.4%     0.0%  
4   Petra Kvitova          90.6%  81.7%  64.8%     9.0%  

    Player                   R64    R32    R16        W  
7   Caroline Wozniacki     82.7%  71.2%  50.1%     5.0%  
    Tamira Paszek          17.3%   9.7%   3.3%     0.0%  
    Alize Cornet           55.1%  11.2%   3.3%     0.0%  
    Nina Bratchikova       44.9%   7.9%   2.0%     0.0%  
    Greta Arn              34.0%   9.8%   2.6%     0.0%  
    Galina Voskoboeva      66.0%  29.3%  11.6%     0.2%  
    Yanina Wickmayer       50.0%  30.4%  13.5%     0.3%  
32  Svetlana Kuznetsova    50.0%  30.5%  13.6%     0.3%  

    Player                   R64    R32    R16        W  
21  Roberta Vinci          81.4%  50.9%  22.1%     0.2%  
    Ashleigh Barty         18.6%   5.2%   0.9%     0.0%  
    Urszula Radwanska      48.3%  21.1%   7.0%     0.0%  
    Marina Erakovic        51.7%  22.9%   7.7%     0.0%  
    Mirjana Lucic          49.0%   8.2%   2.4%     0.0%  
    Alexandra Panova       51.0%   8.8%   2.6%     0.0%  
    Casey Dellacqua        18.1%  11.1%   4.4%     0.0%  
9   Marion Bartoli         81.9%  71.9%  53.0%     2.9%  

    Player                   R64    R32    R16        W  
14  Ana Ivanovic           67.6%  51.4%  34.2%     1.3%  
    M Martinez Sanchez     32.4%  19.7%   9.8%     0.1%  
    Kimiko Date-Krumm      31.7%   6.1%   1.8%     0.0%  
    Kateryna Bondarenko    68.3%  22.9%  10.5%     0.0%  
    Anastasiya Yakimova    49.0%  10.2%   2.2%     0.0%  
    Mandy Minella          51.0%  11.2%   2.5%     0.0%  
    Shahar Peer            37.1%  26.9%  11.1%     0.1%  
22  Julia Goerges          62.9%  51.7%  27.8%     0.6%  

    Player                   R64    R32    R16        W  
26  A Medina Garrigues     40.2%  27.6%   5.7%     0.0%  
    Simona Halep           59.8%  46.3%  12.4%     0.2%  
    Jana Cepelova          45.5%  11.2%   1.2%     0.0%  
    Kristina Mladenovic    54.5%  15.0%   1.8%     0.0%  
    Irina-Camelia Begu     34.9%   3.2%   1.0%     0.0%  
    Romina Oprandi         65.1%   9.6%   4.4%     0.0%  
    Irina Falconi           7.6%   3.4%   1.3%     0.0%  
2   Victoria Azarenka      92.4%  83.8%  72.1%    17.0%

Men’s and Women’s French Open Forecasts, Updating Live

Every match completed at Roland Garros has implications on the title chances of several players.  I’ve created two pages that update throughout the tournament to track each player’s odds of reaching each successive round:

For reference, you can check each player’s pre-tournament odds: men and women.

The Official JRank Reference

Italian translation at settesei.it

At HeavyTopspin, I frequently post references to “my rankings” which power my tournament projections.  (For instance, 2012 French Open men and women.)  My system is unofficially called “JRank”–in other words, it needs a new name.    The rankings it generates are superior to the ATP (and presumably WTA) rankings in the sense that they better predict the outcome of tour- and challenger-level matches.

The algorithm is complex but the ideas behind it are not.  The fundamental difference between JRank and the ATP system is how it values individual matches.

The ATP system awards points based on tournament and round.  (A first round win at Wimbledon is worth more than a first round win at Halle; a third round win at Roland Garros is worth more than a second round win.)  JRank, by contrast, awards points based on opponent and recency.  In my system, a win against Rafael Nadal is worth much more than a defeat of Igor Kunitsyn, even if both take place in the same round at the same tournament.  And a defeat of Kunitsyn is worth more if it took place last week than if it took place eight months ago.  A recent win tells you more about a player’s current ability level than an older one does.

The advantage of giving recent matches more weight is that it allows us to take into account matches more than one year old, without the veteran-favoring disadvantages of Nadal’s two-year plan.  JRank uses all matches from the last two years, but a match one year ago is worth only half as much as a match last week, while a match two years ago is worth only a quarter as much.  That way, we get the benefits of that much more data, but without unduly favoring vets.  There is the added benefit that JRank is “smoother” from week to week–none of the bizarre effects of a tournament “falling off” from last year–as if a player’s results 51 weeks ago are 100% more relevant than his results 54 weeks ago!

JRank’s value is even greater because it generates separate rankings for clay and hard surfaces.  Everyone knows that surface matters, but the ATP ranking system ignores it completely.  If you want to know who should be favored at the French, it seems silly to weight Bercy as heavily as Monte Carlo.  JRank gives more weight to a player’s clay record for his clay ranking, and so on.  Even further, beating a clay court specialist is worth more on clay than it is on a hard court.

Creating projections

Armed with rankings, it’s a few small steps to generating a forecast for any tournament.  For each match, the projection is based almost entirely on the rankings of the two players.  (The formula is a slightly more complicated version of A divided by A+B, where A is one player’s ranking point and B is the other’s.  It works–approximately–with ATP ranking points as well.)

There are a few tweaks, though.  First, my research has indicated that qualifiers, lucky losers, and wild cards all perform slightly below expectations.  It is unclear why, though with qualifiers I suspect it is due to fatigue–while their opponents rested, they played two or three tough matches to qualify.

Second, I’ve established that there is a slight home court advantage.  When surface is accounted for, home court advantage is minimal, but it is still there–the “home” player performs about 2% better than expected.  Perhaps it’s referee bias, home cooking, fan support, or some combination of the above.

A frequent suggestion is to incorporate head-to-head records into match projections.  It’s a tempting idea–so tempting that I’ve tried it.  However, it doesn’t seem to make much difference, at least for any broad cross-section of matches.  (Perhaps when a pair of players have, say, 10 or more head-to-head matches in the books, stronger patterns emerge.)  For the most part, it seems that if a ranking system represents a good approximation of each player’s ability level, head-to-head results are superfluous.

There may be other variables worth looking at, including the importance of the tournament, the player’s fatigue level or recent injury history, or each player’s experience at a particular event.  For now, those are among the influences I haven’t even tested.

2012 French Open Women’s Projections

For the Grand Slams, my ranking system takes aim at the WTA, too.  Here are pre-tournament odds for each player in the draw.

(Yes, it’s mid-day Monday and many first round matches are in the books.  I’ll post a link with automatically-updating odds soon; pre-tournament numbers on the record for comparison’s sake.)

    Player                      R64    R32    R16        W  
1   Victoria Azarenka         91.6%  85.8%  73.9%    14.3%  
    Alberta Brianti            8.4%   4.8%   1.8%     0.0%  
    Caroline Garcia           55.3%   5.6%   1.8%     0.0%  
    Dinah Pfizenmaier         44.7%   3.9%   1.1%     0.0%  
    Heidi El Tabakh           29.5%   9.0%   1.1%     0.0%  
    Aleksandra Wozniak        70.5%  36.2%   8.2%     0.1%  
    Alize Cornet              40.1%  19.5%   3.6%     0.0%  
31  Jie Zheng                 59.9%  35.3%   8.5%     0.1%  
                                                            
    Player                      R64    R32    R16        W  
20  Lucie Safarova            82.9%  57.2%  25.9%     0.5%  
    Anastasiya Yakimova       17.1%   5.6%   0.9%     0.0%  
    MJ Martinez Sanchez       74.6%  31.6%  10.5%     0.0%  
    Eva Birnerova             25.4%   5.6%   0.9%     0.0%  
    Vania King                57.6%  20.6%  10.7%     0.1%  
    Galina Voskoboeva         42.4%  12.5%   5.6%     0.0%  
    Kristina Mladenovic       12.7%   3.6%   1.0%     0.0%  
15  Dominika Cibulkova        87.3%  63.3%  44.5%     2.6%  
                                                            
    Player                      R64    R32    R16        W  
12  Sabine Lisicki            65.9%  35.2%  23.0%     0.5%  
    Bethanie Mattek-Sands     34.1%  12.7%   6.2%     0.0%  
    Ekaterina Makarova        69.5%  40.4%  27.3%     0.8%  
    Sloane Stephens           30.5%  11.7%   5.7%     0.0%  
    Mathilde Johansson        40.8%  10.9%   2.4%     0.0%  
    Anastasia Rodionova       59.2%  20.8%   6.2%     0.0%  
    Simona Halep              53.2%  37.1%  16.5%     0.2%  
24  Petra Cetkovska           46.8%  31.1%  12.7%     0.1%  
                                                            
    Player                      R64    R32    R16        W  
27  Nadia Petrova             55.7%  37.4%  15.3%     0.2%  
    Iveta Benesova            44.3%  27.4%   9.9%     0.1%  
    Laura Pous-Tio            37.5%  10.6%   2.4%     0.0%  
    Chanelle Scheepers        62.5%  24.7%   7.8%     0.0%  
    Irina Falconi             48.9%   8.4%   2.6%     0.0%  
    Edina Gallovits-Hall      51.1%   9.1%   2.9%     0.0%  
    Elena Baltacha            15.6%   8.8%   3.3%     0.0%  
6   Samantha Stosur           84.4%  73.7%  55.9%     4.4%  
                                                            
    Player                      R64    R32    R16        W  
3   Agnieszka Radwanska       86.1%  62.3%  47.5%     4.7%  
    Bojana Jovanovski         13.9%   4.4%   1.6%     0.0%  
    Venus Williams            78.7%  29.9%  18.4%     0.4%  
    Paula Ormaechea           21.3%   3.4%   1.1%     0.0%  
    Yung-Jan Chan             34.1%   8.6%   1.3%     0.0%  
    Kateryna Bondarenko       65.9%  25.3%   6.1%     0.0%  
    Mirjana Lucic             22.1%   9.6%   1.6%     0.0%  
26  Svetlana Kuznetsova       77.9%  56.5%  22.5%     0.5%  
                                                            
    Player                      R64    R32    R16        W  
21  Sara Errani               70.2%  48.9%  21.5%     0.3%  
    Casey Dellacqua           29.8%  14.8%   3.9%     0.0%  
    Melanie Oudin             40.7%  12.7%   3.0%     0.0%  
    Johanna Larsson           59.3%  23.6%   7.1%     0.0%  
    Stephanie Dubois          24.1%   4.3%   1.3%     0.0%  
    Shahar Peer               75.9%  28.7%  16.1%     0.1%  
    L Arruabarrena-Vecino     13.3%   4.1%   1.3%     0.0%  
13  Ana Ivanovic              86.7%  63.0%  45.9%     2.2%  
                                                            
    Player                      R64    R32    R16        W  
10  Angelique Kerber          88.3%  73.8%  56.2%     4.3%  
    Shuai Zhang               11.7%   4.7%   1.5%     0.0%  
    Romina Oprandi            46.5%   9.5%   3.7%     0.0%  
    Olga Govortsova           53.5%  11.9%   4.9%     0.0%  
    Anna Tatishvili           58.0%  18.0%   4.1%     0.0%  
    Alexa Glatch              42.0%  10.5%   1.9%     0.0%  
    Su-Wei Hsieh              31.8%  19.2%   5.3%     0.0%  
18  Flavia Pennetta           68.2%  52.2%  22.3%     0.4%  
                                                            
    Player                      R64    R32    R16        W  
29  A. Medina Garrigues       66.8%  48.5%  20.5%     0.1%  
    Laura Robson              33.2%  19.1%   5.4%     0.0%  
    Kai-Chen Chang            50.4%  16.4%   3.8%     0.0%  
    Irena Pavlovic            49.7%  16.0%   3.6%     0.0%  
    Petra Martic              58.2%  17.2%   8.9%     0.0%  
    Michaella Krajicek        41.8%   9.7%   4.3%     0.0%  
    Karolina Pliskova         15.4%   6.4%   2.5%     0.0%  
8   Marion Bartoli            84.6%  66.7%  51.1%     1.7%  
                                                            
    Player                      R64    R32    R16        W  
7   Na Li                     78.4%  71.0%  57.8%     8.4%  
    Sorana Cirstea            21.6%  15.6%   8.5%     0.1%  
    B Zahlavova Strycova      59.4%   8.9%   3.2%     0.0%  
    S Foretz Gacon            40.6%   4.5%   1.2%     0.0%  
    Christina McHale          75.3%  45.7%  15.4%     0.2%  
    Kiki Bertens              24.7%   8.5%   1.4%     0.0%  
    Lauren Davis              35.5%  13.0%   2.7%     0.0%  
30  Mona Barthel              64.5%  32.7%   9.7%     0.1%  
                                                            
    Player                      R64    R32    R16        W  
17  Roberta Vinci             50.3%  34.3%  22.7%     0.2%  
    Sofia Arvidsson           49.7%  33.7%  22.4%     0.2%  
    Yaroslava Shvedova        60.0%  21.3%  11.1%     0.0%  
    Mandy Minella             40.0%  10.7%   4.6%     0.0%  
    Tamarine Tanasugarn       25.3%   9.9%   2.4%     0.0%  
    Carla Suarez Navarro      74.7%  48.8%  23.3%     0.1%  
    Timea Babos               52.4%  22.3%   7.6%     0.0%  
    Sesil Karatantcheva       47.6%  19.0%   5.9%     0.0%  
                                                            
    Player                      R64    R32    R16        W  
14  Francesca Schiavone       81.6%  42.3%  25.8%     0.3%  
    Kimiko Date-Krumm         18.4%   3.7%   1.0%     0.0%  
    Tsvetana Pironkova        38.2%  18.1%   9.4%     0.1%  
    Yanina Wickmayer          61.8%  35.8%  22.5%     0.4%  
    Varvara Lepchenko         54.7%  23.0%   8.4%     0.0%  
    Ksenia Pervak             45.3%  17.3%   5.6%     0.0%  
    P Mayr-Achleitner         24.2%   9.4%   2.3%     0.0%  
19  Jelena Jankovic           75.8%  50.2%  25.1%     0.3%  
                                                            
    Player                      R64    R32    R16        W  
32  Monica Niculescu          64.8%  37.8%   8.0%     0.0%  
    Nina Bratchikova          35.2%  15.4%   2.1%     0.0%  
    Vera Dushevina            62.2%  31.9%   6.2%     0.0%  
    Claire Feuerstein         37.8%  14.9%   2.0%     0.0%  
    Pauline Parmentier        43.5%   6.1%   3.0%     0.0%  
    Urszula Radwanska         56.5%   9.7%   5.4%     0.0%  
    Ashleigh Barty             4.5%   1.1%   0.3%     0.0%  
4   Petra Kvitova             95.5%  83.0%  73.1%     8.5%  
                                                            
    Player                      R64    R32    R16        W  
5   Serena Williams           93.2%  87.6%  74.0%    23.3%  
    Virginie Razzano           6.8%   3.6%   1.1%     0.0%  
    Arantxa Rus               56.2%   5.4%   1.6%     0.0%  
    Jamie Hampton             43.8%   3.5%   0.9%     0.0%  
    Elena Vesnina             70.8%  29.7%   5.8%     0.1%  
    Heather Watson            29.2%   6.9%   0.7%     0.0%  
    Lucie Hradecka            32.2%  16.6%   2.9%     0.0%  
25  Julia Goerges             67.8%  46.7%  13.0%     0.6%  
                                                            
    Player                      R64    R32    R16        W  
23  Kaia Kanepi               75.3%  53.4%  22.4%     0.2%  
    Alexandra Panova          24.7%  11.0%   2.3%     0.0%  
    Irina-Camelia Begu        51.8%  18.8%   4.7%     0.0%  
    Aravane Rezai             48.2%  16.8%   3.9%     0.0%  
    Jarmila Gajdosova         56.8%  18.8%  10.2%     0.0%  
    Magdalena Rybarikova      43.2%  12.0%   5.8%     0.0%  
    Eleni Daniilidou          11.3%   3.1%   0.9%     0.0%  
9   Caroline Wozniacki        88.7%  66.1%  49.8%     2.3%  
                                                            
    Player                      R64    R32    R16        W  
16  Maria Kirilenko           75.9%  48.1%  24.8%     0.1%  
    Victoria Larriere         24.1%   8.7%   2.5%     0.0%  
    Klara Zakopalova          64.8%  31.2%  13.6%     0.0%  
    Lesia Tsurenko            35.2%  12.0%   3.8%     0.0%  
    Anne Keothavong           42.6%   9.6%   3.0%     0.0%  
    Melinda Czink             57.4%  15.7%   5.8%     0.0%  
    Greta Arn                 26.3%  15.5%   6.7%     0.0%  
22  Anastasia Pavlyuchenkova  73.7%  59.2%  39.9%     0.6%  
                                                            
    Player                      R64    R32    R16        W  
28  Shuai Peng                67.8%  44.7%  10.8%     0.1%  
    Tamira Paszek             32.2%  15.7%   2.3%     0.0%  
    Marina Erakovic           63.2%  28.0%   4.9%     0.0%  
    Lourdes Dominguez Lino    36.8%  11.6%   1.3%     0.0%  
    Polona Hercog             61.7%  11.2%   6.2%     0.0%  
    Ayumi Morita              38.3%   4.9%   2.2%     0.0%  
    Alexandra Cadantu          6.3%   2.1%   0.7%     0.0%  
2   Maria Sharapova           93.7%  81.9%  71.5%    14.8%