Quantitatively measuring WTA players’ recent form

There’s a lot of talk in tennis about which players are in form—who looks ready to make a breakthrough, who has peaked, and who is due for a collapse. Some of the talk is based on actual match results (which count), and some is based on how a player’s game looks and sounds on court (which doesn’t count unless it produces match results). I developed a mathematical way to measure player’s recent form.

The mathematically inclined can see the formula I use at the bottom of this post. For everyone else, here’s the basic idea: I take into account the ranking points a player has scored over the previous 15 weeks, giving more weight to the most recent results. I divide this by the number of points available in the weeks the player was active (again weighting the more recent weeks more heavily). Then I divide the result by the player’s current total ranking points, because the idea is to pick out which players have been playing better or worse than their present ranking would lead you to expect. Finally, I scale the results so that the average player scores a 5. Players with a score over 5 have been playing well, and can be expected to move up the rankings if that form continues. Players scoring less than 5 can be expected to slide down the rankings unless they improve their play.

Now, let’s take a look at some of the WTA players with exceptionally high scores based on their results since last summer. I’ve divided these into some broad categories to help explain the players’ scores, some of which might seem surprising at first glance:

Players to Watch in the New Year

My picks, based both on the numbers and on qualitative impressions:

Player Total Points Form Score
Flipkens 1096 13.3
Robson 1131 10.6
Watson 1161 9.2
Mladenovic 697 8.9
Petrova 3040 8.0
Williams, S 9400 7.7
Hsieh 1636 7.1

Kirsten Flipkens spent years as a frequently injured journeywoman, but her health and confidence in her all-court game seems to have turned the corner with her run to the semifinals in ‘s-Hertogenbosch, where she beat Sam Stosur and Roberta Vinci. Since then she’s compiled a 34-6 match record, won Quebec City, and beaten Dominika Cibulkova, Ana Ivanovic, and Sabine Lisicki.

Laura Robson, Heather Watson, and Kristina Mladenovic are all young players who have shown new confidence that they can compete against established stars. Robson’s defeats of Kim Clijsters and Li Na at the US Open attracted the most attention, and she probably has the most potential of the three. But Watson was the first to win a WTA title, in Osaka, which propelled her past Robson in the rankings. Mladenovic’s late season run was impressive too, beating Erakovic and Pavlyuchenkova in straight sets at the US Open, making the semifinals of Quebec City, and winning the late-season WTA-125 tournament in Taipei.

I’ve been skeptical of Nadia Petrova for a long time. For years she was plagued by mental demons and over-reliant on an unreliable serve. But she made me a believer this year on her way to titles in Tokyo and Sofia. She seems to have real chemistry with new coach Ricardo Sanchez and is applying her doubles skills to round out her singles game.

Since her first-round loss to Virginie Razzano at Roland Garros, Serena Williams has completely dominated the big tournaments, and no one doubts her ability to continue such dominance as long as she retains the necessary health and motivation. Then again, she’s gone through enough periods in her career where her health or motivation were lacking to give pause to any unqualified predictions of her future success.

At age 26, Hsieh Su-Wei won the first and second WTA titles of her career in 2012, in Pattaya and Guangzhou. Her results in Sofia show that she can still be overpowered by most of the top 20, and caused some commentators to write off her prospects for next year. But her crafty all-court game, constructed of unexpected changes in spin, will continue to frustrate most opponents. I think she’ll back up her breakout season.

Sometimes the Numbers Only Tell Part of the Story

Players with impressive recent results I’m taking with a grain of salt:

Player Total Points Form Score
Begu 1140 13.0
Hampton 884 10.0
Chang 737 9.7
Beck 810 9.3
Hradecka 1224 7.7
Puchkova 636 7.4
Vekic 620 7.4
Wozniacki 3765 7.2

Irina Begu has a solid, power-grinding game, and had a strong late-season run sparked by her upset of Caroline Wozniacki at the US Open. But she had a similar run in 2010 and then faded for a year and a half. Jamie Hampton is not without weapons, but profited from some luck, her biggest result of the season being a victory over an injured Kanepi in Tokyo. Chang Kai-Chen’s run to the final in Osaka, where she lost to Watson in a third-set tiebreak after beating Casey Dellacqua, Robson, and Stosur can’t be ignored. But it’s too soon to say whether she just had a great week or will be a consistent threat. Annika Beck is a young player who has put together an impressively consistent run of results, but so far they’re mostly in ITF tournaments against relatively weak opponents. Lucie Hradecka is a very powerful player whose confidence and singles game has benefited from her doubles success, but whose ability to hit her groundstrokes inside the lines from one week to the next remains in question. Olga Puchkova is another big hitter and has had something of a comeback year, but her commitment to the tour has wavered in the past and it remains to be seen if she can put it all together. Donna Vekic looked like the next teenage sensation in Tashkent, but her results since then have been disappointing.

Finally, after a mostly dismal season, Wozniacki put together a strong series of results late in the year and seemed to regain some of her lost confidence. The rankings of top-10 players don’t leave a lot of room for improvement, so above-average form scores are a real achievement for them, and Caro and Serena are the only ones holding that honor at the moment. On the other hand, Wozniacki was at her best in 2009 and 2010 when she was thinking on the court, breaking up the rhythm of rallies with unexpected tactics to keep her opponents from dictating points. After enduring two years of criticism by those who said she wasn’t “a real number one” player, I think she started to believe the common misconception that her game consists only of running down every ball and getting it back in court. Until she breaks free of the stifling influence of her father, and hires on her own a new coach who can break her out of her routine and convince her to add more initiative and risk-taking to her game, I am afraid her full potential as a star player will go unrealized.

Late Surgers

Players who racked up results in ITF tournaments when most of the tour was already on vacation:

Player Total Points Form Score
Doi 711 13.9
Date-Krumm 685 11.6
Voegele 712 8.5
Putintseva 638 8.2

Misaki Doi and Yulia Putintseva are young players whose recent ITF results may indicate they’re ready to become threats at the WTA level, or might not. At age 42 and for the second year in a row, Kimiko Date-Krumm has used a run through the late-season ITF tournaments to boost her ranking high enough for direct entry into the Australian Open after struggling to win matches against WTA Tour competition for most of the year. Stefanie Voegele is a hard-fighting journeywoman and I hope her ITF results herald a breakthrough for her, but I don’t really expect it.


Quality players returning from injury or playing limited schedules:

Player Total Points Form Score
Mattek-Sands 385 16.3
Williams, V 1650 14.5
Petkovic 556 9.6
Kanepi 1905 8.1

Bethanie Mattek-Sands and especially Kaia Kanepi have shown enormous ability during fleeting moments when they have been healthy, but are reaching stages of their careers where it’s unrealistic to hope those moments will ever be anything but fleeting. Hopefully Andrea Petkovic’s growing list of past injuries reflects only bad luck, because she has the game to stake out a lasting position in the top 15. At age 32, Venus Williams has proved she has the determination and talent to win matches against quality opponents despite her struggles with Sjögren’s Syndrome. But the autoimmune disorder causes intermittent fatigue that will likely prevent her from making deep runs into the biggest tournaments.

Insufficient Data

Outliers with scores based on only one tournament:

Player Total Points Form Score
Baltacha 377 23.3
Zvonareva 697 21.7
Dulgheru 242 8.5

All of these players were injured or ill for most of the season. Their scores reflect their present low rankings and a decent result for each in just one tournament. All of them should move far up the rankings in the new year if they are healthy. However, I don’t see any of them returning to her career-high ranking (#2 for Vera Zvonareva, #26 for Alexandra Dulgheru, and #49 for Elena Baltacha).

Players with Poor Scores

The vast majority of the players earning the lowest form scores are those whose seasons ended with a mixture of absences and first-round losses caused by injuries and illnesses. It just seems cruel to list all their names alongside their embarrassing numbers. But I will mention two well-known players for whom some commentators are predicting big success in the new year:

Player Total Points Form Score
Kvitova 5085 1.9
Lisicki 1424 1.4

I like both of these players. They have appealing personalities, and on the court they have massive weapons with which they can beat anyone on a good day. Petra Kvitova was sick for the last several weeks of the season, and Lisicki suffered minor back and abdominal injuries. Kvitova showed new tenaciousness in 2012, fighting her way to enough wins to stay comfortably in the top 10 even though her fitness declined and her game seldom approached the level that won the Wimbledon and Tour Championships titles the previous year. Lisicki had a great run to the 2012 Wimbledon quarterfinals, finally beating Maria Sharapova on the big stage, and then went 1-6 on hard courts after the Olympic Games. The bottom line is that neither of these players has proven she knows how to beat quality opponents on days where the timing is off on her big shots. Until they do, I won’t be among those predicting that Kvitova will again contend for the #1 ranking, or that Lisicki will break into the top-10.

A Final Caveat

Although these scores provide some useful objective hints about how well players have been playing, that’s not always a reliable indicator of how well they will play as the new season starts. During the offseason, players are free from the demands of defending points and fulfilling tournament obligations every week. They use the time to try to develop new skills and correct deficiencies in their games and physiques. Some of these attempts are more successful than others. Some players are more motivated than others to do the necessary work. Some players have new coaches. Some will be inspired by new advice that unlocks their previously hidden potential. Some will be confused and frustrated by new advice that they absorb incompletely or that interferes with their natural strengths. No matter how well informed we are as fans, some players will surprise us as the 2013 season starts. That’s why the beginning of a new season is so exciting.

The Formula

For the curious, here’s how my form scores are calculated:
Form Formula
a is a scaling factor: 75,000 for the WTA
k is a weight factor: 0.8
t represents the current week
Pscored is the ranking points scored by a player in a given week
Ppossible is the maximum number of points available in any tournament in a given week
Ptotal is a player’s current total number of ranking points

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