Measuring Return Aggression

In the last couple of years, I’ve gotten a lot of mileage out of a metric called Aggression Score (AS), first outlined here by Lowell West. The stat is so useful due to its simplicity. The more aggressive a player is, the more she’ll rack up both winners and unforced errors. AS, then, is essentially the rate at which a player hits winners and unforced errors.

Yet one limitation lies in Aggression Score’s simplicity. It works best when winners and unforced errors move together, and when they are roughly similar. If someone is having a really bad day, her unforced errors might skyrocket, resulting in a higher AS, even if the root cause of the errors is poor play, not aggression. On the flip side, a locked-in player will see her AS increase by hitting more winners, even if those winners are more a reflection of good form than a high-risk tactic.

I’ve long wanted to extend the idea behind Aggression Score to return tactics, but when we narrow our view to the second shot of the rally, the simplicity of the metric becomes a handicap. On the return, the vast majority of “aggressive” shots are errors, so the results will be swamped by error rate, minimizing the role of return winners, which are a more reliable indicator. Using Match Charting Project data from 2010-present women’s tennis, returns result in errors 18% of the time, while they turn into winners (or they induce forced errors) less than one-third as often, 5.5% of the time. The appealingly simple Aggression Score formula, narrowed to consider only returns of serve, won’t do the job here.

Return aggression score

Let’s walk through a formula to measure return aggression, using last month’s Miami final between Sloane Stephens and Jelena Ostapenko as an example. Tallying up return points (excluding aces and service winners), along with return errors* and return winners** for both players from the match chart, we get the following:

Returner          RetPts  RetErr  RetWin  RetE%  RetW%  
Sloane Stephens       64       9       1  14.1%   1.6%  
Jelena Ostapenko      63      11       6  17.5%   9.5%

* “errors” are a combination of forced and unforced, because most return errors are scored as forced errors, and because the distinction between the two is so unreliable as to be meaningless. Some forced error returns are nearly impossible to make, so they don’t really belong in this analysis, but with the state of available data, it’ll have to do.

** throughout this post, I’ll use “winners” as short-hand for “winners plus induced forced errors” — that is, shots that were good enough to end the point.

These numbers make clear which of the two players is the aggressive one, and they confirm the obvious: Ostapenko plays much higher-risk tennis than Stephens does. In this case, Ostapenko’s rates are nearly equal to or above the tour averages of 17.8% and 5.5%, while both of Stephens’s are well below them.

The next step is to normalize the error and winner rates so that we can more easily see how they relate to each other. To do that, I simply divide each number by the tour average:

Returner          RetE%  RetW%  RetE+  RetW+  
Sloane Stephens   14.1%   1.6%   0.79   0.28  
Jelena Ostapenko  17.5%   9.5%   0.98   1.73

The last two columns show the normalized figures, which reflect how each rate compares to tour average, where 1.0 is average, greater than 1 means more aggressive, and less than 1 means less aggressive.

We’re not quite done yet, because, as Ostapenko and Stephens illustrate, return winner rates are much noisier than return error rates. That’s largely a function of how few there are. The gap between the two players’ normalized rates, 0.28 and 1.73, looks huge, but represents a difference of only five winners. If we leave return winner rates untouched, we’ll end up with a metric that varies largely due to movement in winner rates–the opposite problem from where we started.

To put winners and errors on a more equal footing, we can express both in terms of standard deviations. The standard deviation of the adjusted error ratio is 0.404, while the standard deviation of the adjusted winner ratio is 0.768, so when we divide the ratios by the standard deviations, we’re essentially reducing the variance in the winner number by half. The resulting numbers tell us how many standard deviations a certain statistic is above or below the mean, and these final results give us winner and error rates that are finally comparable to each other:

Returner          RetE+  RetW+  RetE-SD  RetW-SD  
Sloane Stephens    0.79   0.28    -0.52    -0.93  
Jelena Ostapenko   0.98   1.73    -0.05     0.95

(Math-oriented readers might notice that the last two steps don’t need to be separate; we could just as easily think of these last two numbers as standard deviations above or below the mean of the original winner and error rates. I included the intermediate step to–I hope–make the process a bit more intuitive.)

Our final stat, Return Aggression Score (RAS) is simply the average of those two rates measured in standard deviations:

Returner          RetE-SD  RetW-SD    RAS  
Sloane Stephens     -0.52    -0.93  -0.73  
Jelena Ostapenko    -0.05     0.95   0.45

Positive numbers represent more aggression than tour average; negative numbers less aggression. Ostapenko’s +0.45 figure is higher than about 75% of player-matches among the nearly 4,000 in the Match Charting Project dataset, though as we’ll see, it is far more conservative than her typical strategy. Stephens’s -0.73 mark is at the opposite position on the spectrum, higher than only one-quarter of player-matches. It is also lower than her own average, though it is higher than the -0.97 RAS she posted in the US Open final last fall.

The extremes

The first test of any new metric is whether the results actually make sense, and we need look no further than the top ten most aggressive player-matches for confirmation. Five of the top ten most aggressive single-match return performances belong to Serena Williams, and the overall most aggressive match is Serena’s 2013 Roland Garros semifinal against Sara Errani, which rates at 3.63–well over three standard deviations above the mean. The other players represented in the top ten are Ostapenko, Oceane Dodin, Petra Kvitova, Madison Keys, and Julia Goerges–a who’s who of high-risk returning in women’s tennis.

The opposite end of the spectrum includes another group of predictable names, such as Simona Halep, Agnieszka Radwanska, Caroline Wozniacki, Annika Beck, and Errani. Two of Halep’s early matches are lowest and third-lowest, including the 2012 Brussels final against Radwanska, in which her return aggression was 1.6 standard deviations below the mean. It’s not as extreme a mark as Serena’s performances, but that’s the nature of the metric: Halep returned 46 of 48 non-ace serves, and none of the 46 returns went for winners. It’s tough to be less aggressive than that.

The leaderboard

The Match Charting Project has shot-by-shot data on at least ten matches each for over 100 WTA players. Of those, here are the top ten, as ranked by RAS:

Player                    Matches  RetPts   RAS  
Oceane Dodin                   11     665  1.18  
Aryna Sabalenka                11     816  1.12  
Camila Giorgi                  19    1155  1.07  
Mirjana Lucic                  11     707  1.05  
Julia Goerges                  27    1715  0.94  
Petra Kvitova                  65    4142  0.90  
Serena Williams                91    5593  0.90  
Jelena Ostapenko               35    2522  0.88  
Anastasia Pavlyuchenkova       21    1180  0.78  
Lucie Safarova                 34    2294  0.77

We’ve already seen some of these names, in our discussion of the highest single-match marks. When we average across contests, a few more players turn up with RAS marks over one full standard deviation above the mean: Aryna Sabalenka, Camila Giorgi, and Mirjana Lucic-Baroni.

Again, the more conservative players don’t look as extreme: Only Madison Brengle has a RAS more than one standard deviation below the mean. I’ve included the top 20 on this list because so many notable names (Wozniacki, Radwanska, Kerber) are between 11 and 20:

Player                Matches  RetPts     RAS  
Madison Brengle            11     702   -1.06  
Monica Niculescu           32    2099   -0.93  
Stefanie Voegele           12     855   -0.85  
Annika Beck                16    1181   -0.78  
Lara Arruabarrena          10     627   -0.72  
Johanna Larsson            14     873   -0.65  
Barbora Strycova           20    1275   -0.63  
Sara Errani                25    1546   -0.60  
Carla Suarez Navarro       36    2585   -0.55  
Svetlana Kuznetsova        27    2271   -0.55 

Player                Matches  RetPts     RAS  
Viktorija Golubic          16    1272   -0.53  
Agnieszka Radwanska        96    6239   -0.51  
Yulia Putintseva           22    1552   -0.51  
Caroline Wozniacki         80    5165   -0.50  
Christina McHale           11     763   -0.48  
Angelique Kerber           93    6611   -0.46  
Louisa Chirico             13     806   -0.44  
Darya Kasatkina            26    1586   -0.43  
Magdalena Rybarikova       12     725   -0.41  
Anastasija Sevastova       30    1952   -0.40

A few more notable names: Halep, Stephens and Elina Svitolina all count among the next ten lowest, with RAS figures between -0.30 and -0.36. The most “average” player among game’s best is Victoria Azarenka, who rates at -0.08. Venus Williams, Johanna Konta, and Garbine Muguruza make up a notable group of aggressive-but-not-really-aggressive women between +0.15 and +0.20, just outside of the game’s top third, while Maria Sharapova, at +0.63, misses our first list by only a few places.

Unsurprisingly, these results track quite closely to overall Aggression Score figures, as players who adopt a high-risk strategy overall are probably doing the same when facing the serve. This metric, however, allows to identify players–or even single matches–for which the two strategies don’t move in concert. Further, the approach I’ve taken here, to separate and normalize winners and errors, rather than treat them as an undifferentiated mass, could be applied to Aggression Score itself, or to other more targeted versions of the metric, such as a third-shot AS, or a backhand-specific AS.

As always, the more data we have, the more we can learn from it. Analyses like these are only possible with the work of the volunteers who have contributed to the Match Charting Project. Please help us continue to expand our coverage and give analysts the opportunity to look at shot-by-shot data, instead of just the basics published by tennis’s official federations.

Feast, Famine, and Sloane Stephens

Italian translation at settesei.it

Last week, Sloane Stephens reeled off an impressive series of victories, defeating Garbine Muguruza, Angelique Kerber, Victoria Azarenka, and Jelena Ostapenko to secure the title at the WTA Premier Mandatory event in Miami.  The trophy isn’t quite as life-changing as the one she claimed at the US Open last September, but it’s a close second, and the competition she faced along the way was every bit as good.

The Miami title comes with 1,000 WTA ranking points, and by adding those to her previous tally, Stephens moved into the top ten, reaching a career high No. 9 on Monday. With two high-profile championships to her name, not to mention semifinal showings last summer in Toronto and Cincinnati, there’s little doubt she deserves it. Elo isn’t quite convinced, but its more sophisticated algorithm (and its disregard for the magnitude of the US Open and Miami titles) puts her within spitting distance of the top ten as well.

What makes Stephens’s rise to the top ten so remarkable is her efficiency in converting wins to ranking points. Since her return from injury at Wimbledon last year, she has played only 38 matches, winning 24 of them. She has suffered six first-round losses, plus two more defeats at last year’s Zhuhai Elite Trophy round-robin and another pair in the Fed Cup final against Belarus. All told, in the last nine months, she has won matches at only six different events. Her unusual record illustrates some of the quirks in the ranking system, and how a player who peaks at the right times can exploit them.

24 wins is almost never enough for a spot in the vaunted top ten. From 1990 to 2017, a player has finished a season with a top-ten ranking only seven times while winning fewer than 30 matches. Only two of those involved fewer wins than Sloane’s 24: Monica Seles‘s 1993 and 1995, the timespans leading up to her tragic on-court stabbing and following her eventual comeback. Here are the top-ten seasons with the fewest victories, including the last 52 weeks of a few players currently near the top of the WTA table:

Year  Player              YE Rk   W   L  W-L %  
1995  Monica Seles*           1  11   1    92%  
1993  Monica Seles            8  17   2    89%  
2018  Sloane Stephens**       9  24  14    63%  
2010  Serena Williams         4  25   4    86%  
1993  Jennifer Capriati       9  28  10    74%  
2015  Flavia Pennetta         8  28  20    58%  
2000  Mary Pierce             7  29  11    73%  
2004  Jennifer Capriati      10  29  12    71%  
1993  Mary Joe Fernandez      7  31  12    72%  
1995  Iva Majoli              9  31  13    70%  
2018  Venus Williams**        8  31  14    69%  
1995  Mary Joe Fernandez      8  31  15    67%  
2015  Lucie Safarova          9  32  21    60%  
2008  Maria Sharapova         9  33   6    85%  
1998  Steffi Graf             9  33   9    79%  
2018  Petra Kvitova**        10  33  14    70%

* ranking frozen after her assault

** rankings as of April 2, 2018; wins and losses based on previous 52 weeks

What almost all of these seasons have in common is exceptional performances at grand slams. Sloane won the US Open; Seles won the 1993 Australian; Serena Williams won a pair of majors in 2010; Flavia Pennetta capped an otherwise anonymous 2015 campaign with a title in New York. The slams are where the rankings points are.

Even within this group of slam successes, Sloane stands out. Of the 16 players on that list, only two–Pennetta and Lucie Safarova–won matches at a lower rate than Stephens has since her comeback. In other words, most women who are this efficient with their victories don’t lose quite so early or often at lesser events.

That 63% won-loss record is even more extreme than the above list makes it look. Of the nearly 300 year-end top-tenners since 1990, only eight finished the season with a lower win rate. Here’s that list, expanded to the top 11 to include another noteworthy recent season:

Year  Player              YE Rk   W   L  W-L %  
2014  Dominika Cibulkova     10  33  24    58%  
2000  Nathalie Tauziat       10  36  26    58%  
2015  Flavia Pennetta         8  28  20    58%  
1999  Nathalie Tauziat        7  37  25    60%  
2007  Marion Bartoli         10  47  31    60%  
2015  Lucie Safarova          9  32  21    60%  
2000  Anna Kournikova         8  47  29    62%  
2010  Jelena Jankovic         8  38  23    62%  
2018  Sloane Stephens*        9  24  14    63%  
2004  Elena Dementieva        6  40  23    63%  
2016  Garbine Muguruza        7  35  20    64%

* ranking as of April 2, 2018; wins and losses based on previous 52 weeks

There’s not much overlap between these lists; the first group generally missed some time, then made up for it by scoring big at slams, while the second group slogged through a long season and leveled up with a strong finish or two at a major. The typical player with a 63% winning percentage doesn’t end up in the top ten: She wraps up the season, on average, in the mid-twenties. At least that’s better than the average 24-win season: Those result in year-end finishes near No. 40.

Stephens has always been a big-match player: She made an early splash at the 2013 Australian Open, reaching the semifinals and upsetting Serena as a 19-year-old, and her overall career record at majors (66%) is nearly ten percentage points higher than her record at other tour events (57%). For all that, she will probably not conclude 2018 with such a extreme set of won-loss numbers. To do so, she’d probably need to win a major to replace her 2017 US Open points while losing early at most other events. Recovered from injury, Stephens may maintain her feast-or-famine ways to some degree, but it’s unlikely she’ll continue to display such extreme peaks and valleys.

Should Serena Be Seeded?

Italian translation at settesei.it

Serena Williams returned to professional tennis this month after more than a year of pregnancy, childbirth, and recovery. She took wild cards into both Indian Wells and Miami, competing as an unseeded player for the first time since August 2011. In her initial effort in California, she reached the third round before falling to sister Venus, and this week in Miami, she drew Indian Wells champ Naomi Osaka in her opening match and went home early, losing 6-3 6-2.

Seeing Serena without a number next to her name feels wrong. She left the tour for maternity leave just after winning last year’s Australian Open, a title that moved her back into the No. 1 ranking position. While she is clearly rusty–as she has been after previous absences–there’s little doubt she’ll quickly resume competing at a top-32 level (the threshold for an Indian Wells or Miami seed), if not considerably higher.

The brutal Miami draw and Serena’s ensuing early exit prompted all sorts of commentary, much of it calling for a rule change, some castigating the WTA for its lack of a maternity leave policy. The latter is not quite true: The WTA rulebook addresses absences for childbirth and treats returning players almost exactly as it handles women coming back from injury. Nevertheless, edge cases–like the greatest player in women’s tennis rejoining the tour without a single ranking point to her name–tend to put rules to the test.

Seedings are not just a convenient way to identify the top players on a printed bracket. They have an effect on the outcome of the tournament. In the March tournaments, seeded players get free passes to the second round. At every event, the seeding system keeps top players away from each other until the final rounds. Even minor differences, like the one between the fourth and fifth seeds, can have a major effect on two players’ potential routes to the title. This is all to say: Seedings matter, not just to returning players like Serena, but also to everyone else in the draw. While granting a seed to Williams right now may be the right thing to do, it would also push another seeded player into the unseeded pool, affecting that competitor’s chances at late-round ranking points and prize money. It’s important to acknowledge how the rules affect the entire field.

In a moment, I’ll outline various approaches the WTA could take to deal with future maternity leaves. I don’t have a strong opinion; there’s merit in each of them, as I’ll try to explain. What is most important to me, as a fan, is that any rules adopted are designed for the benefit of the whole tour, not just patches to handle once-in-a-generation superstars. Serena deserves a fair shake from the WTA, and her peers are entitled to the same.

1. Minor tweaks to the existing rule. The most likely outcome is almost always the status quo, and Osaka notwithstanding, the status quo is not that bad. The WTA rules allow for returning players (whether from injury or motherhood) to use a “Special Ranking” (SR) in eight events, including two slams.  The SR is the player’s ranking at the time she left the tour, and it determines whether she qualifies to enter tournaments upon her return. While Serena used wild cards for her two events thus far (more on that later), she could have used her SR for either or both.

In other words, new mothers are already allowed to pick up where they left off … with the important exception of seeding. Serena’s SR will allow her to enter, say, the French Open as if she were the No. 1 ranked player, but unless Roland Garros invokes their right to tweak seedings (like Wimbledon does), her seed will be determined by her actual ranking at that time. Since it’s only two months away, it’s very possible she’ll be unseeded there as well, making possible another nasty first-round matchup in the vein of the Simona HalepMaria Sharapova opener at last year’s US Open.

The debate over seeding boils down to “respect” versus “practicality.” Serena’s achievements and her probable quick return to greatness suggest that she “deserves” to be seeded as such. On the other hand, many players (including Sharapova, different as her situation is) have had a hard time returning to their previous level. The post-comeback results of Sharapova or, more recently, Novak Djokovic, indicates that a star’s ranking 12 months ago might not tell you much about how she’ll play now. Seedings exist partly to induce top players to compete, but also to increase the likelihood that the best women will face each other in the final rounds. By the latter criterion, it’s not clear that Serena (or any returning player) should immediately reclaim a top seed.

If the WTA does stick with this basic principle, I would suggest offering a few more SR entries–perhaps 12 instead of 8, and 3 slams instead of 2. Maternity leave necessitates more time on the sidelines than the six-month injury break required to qualify for the SR rule, and it may require still more time to return to form. The WTA might also convince the ITF to offer an additional few SR entries to lower-level events. Kei Nishikori came back from injury by playing a couple of Challengers; women might prefer to get their feet wet with a few ITF $100Ks before using their SR entries on top-tier events.

2. Link seeding to Special Rankings. The second option is essentially what fans wanted when they realized Serena might not make it to the Miami second round. Instead of using current ranking to determine seeding, tournaments could use SR for players who used them to enter the event.

There is a precedent for this: Monica Seles was given a top seeding when she returned from injuries sustained during her 1993 on-court stabbing. More than two years later, she came back as the top seed in Canada and the second seed at the 1995 US Open, where she lived up to that draw placement, winning 11 matches in a row before falling to Steffi Graf in the New York final.

The pros and cons of this route are the opposite of the first proposal. Giving players their pre-break seeding would show respect for their accomplishments, but since most players don’t come back from any length time off court the way Seles did, it’s possible the seedings would appear overly optimistic. (And yes, I realize the irony of saying so during the 2018 Miami tournament, when the top two seeded women won only one match between them.)

3. Devise a time-off-court algorithm. Players usually need some time to resume their former level, but their skill upon return has some relationship to how they played before. When I wrote about Sharapova’s return from her drugs ban last year, I showed that elite players who missed a year or more (for whatever reason), tended to play much worse than their pre-break level for their first five or so matches, and then a moderately lower level for the next 50. I measured it in Elo points: a 200 point drop at first, then a 100 point drop.

I don’t expect the WTA to adopt Elo anytime soon, but an algorithm of this sort could be based on any ranking system, and it represents a reasonable compromise between the first two positions. For someone as dominant as Serena, it would fulfill most of her fans’ wishes: A 200-point drop from her pre-break level would still leave her roughly even with Halep, meaning that a system of this sort would’ve made her the first or second seed in this month’s draws.

A better illustration of how the algorithm would work requires a player who didn’t so overwhelmingly outclass the rest of the field: If Wozniacki (current Elo: 2156) were to miss the next year, her seeding upon return would use an Elo 200 points lower, of 1956, dropping her to about 30th (assuming all the top players were competing). After the first five matches, when players usually start getting their groove back, her seedings would rise to around 15th. Several months in, her ranking would rise, and her seeding would no longer need to be adjusted.

The obvious flaw here is the level of complexity. My algorithm is approximate at best and would need to be improved for such an important role. The advantage, though, is that if an acceptable formula could be found, it would allow the WTA to offer a perfect compromise between the needs of returning mothers and the rights of the rest of the field.

And about those wild cards… 

I’ve mentioned that Serena used wild cards to enter both Indian Wells and Miami, even though she could have used her Special Ranking. Just about every WTA event would happily hand her a wild card, as they should. So in Serena’s case, the SR rule is largely irrelevant–if it didn’t exist, she could immediately resume a full schedule.

I also wrote that, as a fan, what matters to me is that all tour players are treated equally. Tournament entries are opportunities to gain ranking points, which in turn determine entries and seeding, which affects the likelihood of racking up wins and titles. Wild cards are often thought of as gifts, but we rarely acknowledge the effect that those gifts have on the players who rarely get them. Because tournaments understandably tend to hand out free passes to home-country players (like Donald Young) and marquee personalities (like Eugenie Bouchard), the wild card system introduces systemic bias into rankings and results. Wild cards can’t make a journeyman into a superstar, but they can boost a player from the top 200 to the top 100, or from No. 70 to No. 50. For some tour players, these differences really matter.

Thus, when a superstar or media darling–or just a player from a country that happens to host a lot of tournaments, like the United States–returns from maternity leave, injury, or a suspension, the regular rules don’t apply. Maria Sharapova was wild carded into most of the tournaments she wanted to play last year, while Sara Errani has spent the last six months playing ITFs, $125Ks, and qualifying. Sharapova gets to play matches with 100 ranking points at stake while Errani contests entire tournaments with less on the line.

Wildly different as their cases are, Serena’s situation with regard to wild cards is the same as Sharapova’s. Her allotment of SR entries doesn’t matter. But imagine if, say, Anastasija Sevastova or Magdalena Rybarikova took time off to have a child. They might get a few free entries into European international-level events, or maybe a wild card into a tournament they’ve previously won. But for the most part, a Sevastova or a Rybarikova–despite taking her hypothetical absence while a top-20 player–would be jealously protecting her eight SRs. She would need them.

Just to be clear, I’m not trying to say that Serena doesn’t “deserve” all the wild cards she’s going to get. Her achievements make it obvious that she does. On a tour where events can award draw places at their discretion, no one deserves them more. However, the very existence of those discretionary spots means that maternity leave means something very different for Serena than it would for the more anonymous players near the top of the WTA rankings.

How about this proposal, then: For players coming back from maternity leave, expand the number of SR entries from 8 to 12, and tack on another four free entries to ITFs, so that returning players can have a child knowing that they’ll be able to compete at the top level for nearly a season once they come back. But–they may accept no wild cards during that time. If they take a wild card, they lose their SRs. That proposal would put all players on an even keel: Close to a year of tournament entries at their pre-break ranking. It would give the next Serena-level superstar plenty of time to regain her lost status, and best of all, it would do the same for her lesser-known peers.

Is Jelena Ostapenko More Than the Next Iva Majoli?

Italian translation at settesei.it

Winning a Grand Slam as a teenager–or, in the case of this year’s French Open champion Jelena Ostapenko, a just-barely 20-year-old–is an impressive feat. But it isn’t always a guarantee of future greatness. Plenty of all-time greats launched their careers with Slam titles at age 20 or later, but three of the players who won their debut major at ages closest to Ostapenko’s serve as cautionary tales in the opposite direction: Iva Majoli, Mary Pierce, and Gabriela Sabatini. Each of these women was within three months of her 20th birthday when she won her first title, and of the three, only Pierce ever won another.

However, simply comparing her age to that of previous champions understates the Latvian’s achievement. Women’s tennis has gotten older over the last two decades: The average age of a women’s singles entrant in Paris this year was 25.6, a few days short of the record established at Roland Garros and Wimbledon last year. That’s two years older than the average player 15 years ago, and four years older than the typical entrant three decades ago. Headed into the French Open this year, there were only five teenagers ranked in the top 100; at the end of 2004, the year of Maria Sharapova’s and Svetlana Kuznetsova’s first major victories, there were nearly three times as many.

Thus, it doesn’t seem quite right to group Ostapenko with previous 19- and 20-year-old first-time winners. Instead, we might consider the Latvian’s “relative age”—the difference between her and the average player in the draw—of 5.68 years younger than the field. When I introduced the concept of relative age last week, it was in the context of Slam semifinalists, and in every era, there have been some very young players reaching the final four who burned out just as quickly. The same isn’t true of women who went on to win major titles.

In the last thirty years, only two players have won a major with a greater relative age than Ostapenko: Sharapova, who was 6.66 years younger than the 2004 US Open field, and Martina Hingis, who won three-quarters of the Grand Slam in 1997 at age 16, between 6.3 and 6.6 years younger than each tournament’s average entrant. The rest of the top five emphasizes Ostapenko’s elite company, including Monica Seles (5.29, at the 1990 French Open) and Serena Williams (5.26, at the 1999 US Open).

Each of those four women went on to reach the No. 1 ranking and win at least five majors–an outrageously optimistic forecast for Ostapenko, who, even after winning Roland Garros, is ranked outside the top ten. By relative age, Majoli, Pierce, and Sabatini are poor comparisons for Saturday’s champion–Majoli and Pierce were only three years younger than the fields they overcame, and Sabatini was only two years younger than the average entrant. By comparison, Garbine Muguruza, who won last year’s French Open at age 22, was two and a half years younger than the field.

Which is it, then? Unfortunately I don’t have the answer to that, and we probably won’t have a better idea for several more years. For most of the Open Era, until about ten years ago, the average age on the women’s tour fluctuated between 21 and 23. Thus, for the overall population of first-time major champions, actual age and relative age are very highly correlated. It’s only with the last decade’s worth of debut winners that the numbers meaningfully diverge. For Ostapenko and Muguruza–and perhaps Victoria Azarenka and Petra Kvitova–we have yet to see what their entire career trajectory will look like. To build a bigger sample to test the hypothesis, we’ll need a few more young first-time Slam winners, something we may finally see with Sharapova and Williams out of the way.

For more post-French Open analysis, here’s my Economist piece on Ostapenko and projecting major winners in the long term. Also at the Game Theory blog, I wrote about Rafael Nadal and his abssurd dominance on clay in a fast-court-friendly era.

Finally, check out Carl Bialik’s and my extra-long podcast, recorded Monday, with tons of thoughts and the winners and the fields in general.

First Meetings in Grand Slam Finals

Italian translation at settesei.it

The 2017 Roland Garros final is crammed with firsts for 20-year-old Latvian Jelena Ostapenko. Playing in only her eighth major, she had never before reached the round of 16, let alone the final two. Her opponent, Simona Halep, has been here before–she lost the 2014 French Open final to Maria Sharapova–but the two women have one first in common: Halep and Ostapenko have never played each other.

Slam finals are usually reserved for an elite group, and that select few tends to play each other quite a bit. Since 1980, women’s major finalists have had an average of 12 previous meetings. The veteran Australian Open finalists this year, Serena Williams and Venus Williams, had faced off 27 times before their clash in Melbourne.

That makes the Halep-Ostapenko debut meeting an unusual one, but the situation is not unheard of. The 2012 Roland Garros final was the first match between Sharapova and Sara Errani (they’ve since played five more). Overall, there have been five first meetings in women’s major finals in the last 35 years:

Slam     Winner           Finalist               
2012 RG  Maria Sharapova  Sara Errani         
2009 US  Kim Clijsters    Caroline Wozniacki  
2007 W   Venus Williams   Marion Bartoli      
1988 RG  Steffi Graf      Natalia Zvereva

(There were probably a few more before that, but my database is missing a lot of matches from the mid-1970s, so I don’t know for sure.)

In all of these cases, the established star defeated the upstart, which bodes well for Halep. On the other hand, the Romanian doesn’t quite measure up to the previous four winners, all of whom had won a Grand Slam title before their final on this list.

First meetings in Grand Slam finals are a bit more common in the men’s game, though it’s been nearly a decade since the last one. We’ll probably wait quite a bit longer, too. Rafael Nadal and Stanislas Wawrinka will play for the 19th time on Sunday, and of the 45 possible pairings in the current top ten, only Kei Nishikori and Alexander Zverev have yet to face off. The next highest-ranked pair without a head-to-head is Andy Murray and Jack Sock which, come to think of it, would make for an interesting Wimbledon final next month.

The last debut clash on such a big stage was the 2008 Australian Open, between Novak Djokovic and Jo Wilfried Tsonga. It was the eighth in the last 35 years:

Slam     Winner            Finalist                
2008 AO  Novak Djokovic    Jo Wilfried Tsonga   
2003 US  Andy Roddick      Juan Carlos Ferrero  
1997 RG  Gustavo Kuerten   Sergi Bruguera       
1997 AO  Pete Sampras      Carlos Moya          
1996 W   Richard Krajicek  Malivai Washington   
1986 RG  Ivan Lendl        Mikael Pernfors      
1985 W   Boris Becker      Kevin Curren         
1984 AO  Mats Wilander     Kevin Curren

Before 1982, most first-meeting finals took place at the Australian Open, which at that time usually featured a weaker draw than the other Slams. For instance, the 1979 final was played by Guillermo Vilas and John Sadri. While Vilas is among the all-time greats, Sadri never advanced beyond the fourth round of any other major–where he might have encountered Vilas more often.

One thing seems certain: It won’t be the last meeting for Halep and Ostapenko. All of the pairs I’ve listed played at least once after their Slam final, and with the exception of Wilander-Curren, each one played at least twice more. Halep is only 25, so if she remains near the top of the game and Ostapenko continues climbing the ranks, the pair could aim to match Graf and Zvereva, who met 20 more times after the 1988 French Open final. The loser of today’s match will want to avoid Zvereva’s fate, though: In those 20 matches, the Belarussian won only once.

Simona Halep and Recoveries From Match Point Down

Italian translation at settesei.it

In yesterday’s French Open quarterfinals, Elina Svitolina held a commanding lead over Simona Halep, up a set and 5-1. Depending on what numbers you plug into the formula, Svitolina’s chance of winning the match at that stage was somewhere between 97% and 99%. Halep fought back to 5-5, and in the second-set tiebreak, Svitolina earned a match point at 6-5. Halep recovered again, won the breaker, and then cruised to a 6-0 victory in the third set.

It’s easy to fit a narrative to that sequence of events: After losing two leads, Svitolina was dispirited, and Halep was all but guaranteed a third-set victory. Maybe. It’s impossible to test that sort of thing on the evidence of a single match, but this is hardly the first time a player has failed to convert match point and needed to start fresh in a new set.

Even without a match point saved, the player who wins the second set has a small advantage going into the decider. In the last six-plus years of women’s Slam matches, the player who won the second set went on to win 51.3% of third sets. On the other hand, if the second set was a tiebreak, the winner of the second set won the decider only 43.7% of the time. Though it sounds contradictory at first, consider what we know about such sets. The second-set winner just barely claimed her set (in the tiebreak), while usually, her opponent took the first set more decisively. Momentum helps a little, but it can’t overcome much of a difference in skill level.

Let’s dig into the specific cases of second-set match points saved. Thanks to the data behind IBM’s Pointstream on Grand Slam websites, we have the point-by-point sequence for most Slam singles matches going back to 2011. (The missing matches are usually those on non-Hawkeye courts and a few small courts at Roland Garros.) That’s over 2,600 women’s singles matches. In just over 1,700 of them, one of the two players earned a match point in the second set. Over 97% of the time, that player converted–needing an average of 1.7 match points to do so–and avoiding playing a third set.

That leaves 45 matches in which one player held a match point in the second set, failed to finish the job, and was forced to play a third set. It’s a limited sample, and it doesn’t wholeheartedly support the third-set-collapse narrative suggested above. 60% of the time–27 of the 45 matches–the player who failed to convert match point in the second set, like Svitolina did, went on to lose the third set. The third set was often lopsided: 5 of the 27 were bagels (including yesterday’s match), and the average score was 6-2. None of the third sets went beyond 6-4.

The other 18 matches–the 40% of the time in which the player with the second-set match point bounced back to win the third set–featured rather one-way deciders, as well. In those, the third-set loser managed an average of only 2.3 games, also never doing better than 6-4.

This is a small sample, so it’s unwise to conclude that this 60/40 margin is anything close to an iron law of tennis. That said, it does provide some evidence that players don’t necessarily collapse after failing to convert a straight-sets win at match point. What happened to Svitolina yesterday is far from certain to happen next time.

Jelena Ostapenko and Teenage Slam Breakthroughs

Italian translation at settesei.it

Jelena Ostepenko is looking ahead to a big day on Thursday: She’ll celebrate her 20th birthday by playing her first Grand Slam semifinal.

A generation or two ago, a breakthrough accomplishment at age 20 would barely merit acknowledgement. In the late 1990s, women’s tennis was dominated by teens a recent teens: Serena Williams and Martina Hingis both won majors before their 20th birthday, and Venus Williams won her first Slam only a few days into her third decade. That youth brigade wasn’t just a couple of once-in-a-generation talents, either: 19-year-old Iva Majoli won a major, and Mirjana Lucic, Jelena Dokic, and Anna Kournikova all reached semifinals before their 18th birthdays.

Times have changed. The last teenage Slam champion was Maria Sharapova in 2006, and we haven’t had a teenager in a major final since Caroline Wozniacki in 2009. Since then, only four players–Ostapenko, Sloane Stephens, Eugenie Bouchard, and Madison Keys–have reached Grand Slam semifinals before their 20th birthdays. (To simplify matters, I’m defining tournament age as age at the beginning of the event, so Ostapenko is a 19-year-old for the purpose of this discussion.)

By just about any measure you can dream up, the sport is getting older. In 1990, the average age of the women in the French Open main draw was 21.8 years. In 2000, it was 23.5. This year, the average age at the start of the tournament was 25.6, just a tiny bit short of last year’s record–set at Roland Garros and Wimbledon–of 25.7. Veterans are sticking around longer, and it takes longer for young players to develop tour-ready games.

Accordingly, we need to revise our notion of what constitutes a big breakthrough. 20 years ago, the semifinal debut of a 19-year-old was a nice achievement for the player herself, but nothing earth-shaking. Today, it’s a once-in-two-years event, and immediately puts the debutante in elite company. While Stephens and Bouchard have stumbled since their own breakthroughs, they (along with Keys) are still among the most promising young players in the game.

To quantify Ostapenko’s achievement, let’s consider her age relative to the average of all main draw players–just the raw difference between those two numbers. Ostapenko is 5.68 years younger than the average woman at Roland Garros this year, making her the 7th youngest (relative to the field) semifinalist at a major since 2000:

Slam     Youngest SF         Age  Avg Age  Diff  
2004 W   Maria Sharapova   17.17    24.17  7.00  
2006 FO  Nicole Vaidisova  17.10    23.63  6.53  
2000 W   Jelena Dokic      17.21    23.69  6.48  
2005 W   Maria Sharapova   18.17    24.45  6.28  
2005 AO  Maria Sharapova   17.75    23.99  6.24  
2007 AO  Nicole Vaidisova  17.73    23.48  5.75  
2017 FO  Jelena Ostapenko  19.97    25.65  5.68  
2001 FO  Kim Clijsters     17.97    23.62  5.65  
2005 US  Maria Sharapova   18.36    23.78  5.42  
2015 AO  Madison Keys      19.92    25.33  5.41

Only three players–Sharapova, Dokic, and Nicole Vaidisova–have reached a Slam semifinal this century at such a young age compared to the rest of the draw.

Of course, names like Dokic and Vaidisova aren’t the most encouraging comparisons for an emerging star. Both players peaked in the top ten, but neither ever reached a major final. The WTA’s past is littered with teenage rising stars who ultimately fizzled.

Yet if we are to see one historically great player come from among today’s young players, she should start building her trophy collection now. It’s tough to put together a Hall of Fame-caliber career without winning some big titles by one’s early 20s. Madison Keys has put herself in that conversation, and this week, Ostapenko has done so as well.

Smaller Swings In Big Moments

Italian translation at settesei.it

Despite the name, unforced errors aren’t necessarily bad. Sometimes, the right tactic is to play more aggressively, and in order to hit more winners, most players will commit more errors as well. Against some opponents, increasing the unforced error count–as long as there is a parallel improvement in winners or other positive point-ending shots–might be the only way to win.

Last week, I showed that one of the causes of Angelique Kerber’s first-round loss was her disproportionate number of errors in big moments. But as my podcasting partner Carl Bialik pointed out, that isn’t the whole story. If Kerber played more aggressively on the most important points–one possible cause of more errors–it might be the case that her winner rate was higher, as well. Since the 6-2 6-2 scoreline was so heavily tilted against her, it was a safe bet that Kerber recorded more high-leverage errors than winners. Still, Carl makes a valid point, and one worth testing.

To do so, let’s revisit the data: 500 women’s singles matches from the last four majors and the first four rounds of this year’s French Open. By measuring the importance of each point, we can determine the average leverage (LEV) of every point in each match, along with the average leverage of points which ended with a player hitting an unforced error, or a winner. Last week, we found that Kerber’s UEs in her first-round loss had an average LEV of 5.5%, compared to a LEV of 3.8% on all other points. For today’s purposes, let’s use match averages as a reference point: Her average UE LEV of 5.5% also compares unfavorably to the overall match average LEV of 4.1%.

What about winners? Kerber’s 15 winners came on points with an average LEV of 3.9%, below the match average. Case closed: On more important points, Kerber was more likely to commit an error, and less likely to hit a winner.

Across the whole population, players hit more errors and fewer winners in crucial moments, but only slightly. Points ending in errors are about one percent more important than average (percent, not percentage point, so 4.14% instead of 4.1%), and points ending in winners are about two percent less important than average. In bigger moments, players increase their winner rate about 39% of the time, and they improve their W-UE ratio about 45% of the time. Point being, there are tour-wide effects on more important points, but they are quite small.

Of course, Kerber’s first-round upset isn’t indicative of how she has played at Slams in general. In my article last week, I mentioned the four players who did the best job of reducing errors at big moments: Kerber, Agnieszka Radwanska, Timea Bacsinszky, and Kiki Bertens. Kerber and Radwanska both hit fewer winners on big points as well, but Bacsinszky and Bertens manage a perfect combination, hitting slightly more winners as the pressure cranks up. Among players with more than 10 Slam matches since last year’s French, Bacsinszky is the only one to hit winners on more important points than her unforced errors over 75% of the time.

Compared to her peers, Kerber’s big-moment tactics are remarkably passive. The following table shows the 21 women for whom I have data on at least 13 matches. “UE Rt.” (“UE Ratio”) is similar to the metric I used last week, comparing the average importance of points ending in errors to average points; “W Ratio” is the same, but for points ending in winners, and “W+UE Ratio” is–you guessed it–a (weighted) combination of the two. The combined measure serves as an rough approximation of aggression on big points, where ratios below 1 are more passive than the player’s typical tactics and ratios above 1 are more aggressive.

Player                     M  UE Rt.  W Rt.  W+UE Rt.  
Angelique Kerber          20    0.92   0.85      0.88  
Alize Cornet              13    0.92   0.87      0.94  
Agnieszka Radwanska       17    0.91   0.95      0.95  
Simona Halep              19    0.93   0.94      0.95  
Samantha Stosur           13    0.95   0.98      0.96  
Timea Bacsinszky          14    0.89   1.02      0.97  
Elina Svitolina           15    1.02   0.95      0.97  
Karolina Pliskova         18    0.97   0.98      0.97  
Caroline Wozniacki        14    0.93   1.00      0.97  
Johanna Konta             13    1.00   0.97      0.98  
Caroline Garcia           14    0.94   1.02      0.98  
Svetlana Kuznetsova       17    0.96   0.98      0.99  
Garbine Muguruza          20    1.02   0.94      0.99  
Venus Williams            25    1.00   0.97      0.99  
Elena Vesnina             13    0.96   1.03      0.99  
Anastasia Pavlyuchenkova  15    1.03   0.99      0.99  
Coco Vandeweghe           13    1.08   0.95      1.01  
Madison Keys              13    1.01   1.02      1.01  
Serena Williams           27    0.99   1.05      1.02  
Carla Suarez Navarro      14    1.00   1.14      1.05  
Dominika Cibulkova        14    1.11   1.03      1.07

Kerber’s combined measure stands out from the pack. Her point-ending shots–both winners and errors, but especially winners–occur disproportionately on less important points, and the overall effect is double that of the next most passive big-moment player, Alize Cornet. Every other player is close enough to neutral that I would hesitate before making any conclusions about their pressure-point tactics.

Even when Kerber wins, she does so with effective defense at key points. In only two of her last 20 matches at majors did her winners occur on particularly important points. (Incidentally, one of those two was last year’s US Open final.) In general, her brand of passivity works–she won 16 of those matches. But defensive play doesn’t leave very much room for error–figuratively or literally. The tactics were familiar and proven, but against Makarova, they were poorly executed.

Angelique Kerber’s Unclutch Unforced Errors

Italian translation at settesei.it

It’s been a rough year for Angelique Kerber. Despite her No. 1 WTA ranking and place at the top of the French Open draw, she lost her opening match on Sunday against the unseeded Ekaterina Makarova. Adding insult to injury, the loss goes down in the record books as a lopsided-looking 6-2 6-2.

Andrea Petkovic chimed in with her diagnosis of Kerber’s woes:

She’s simply playing without confidence right now. It was tight, even though the scoreline was 2 and 2 but everyone who knows a thing about tennis knew that Angie made errors whenever it mattered because she’s playing without any confidence right now – errors she didn’t make last year.

This is one version of a common analysis: A player lost because she crumbled on the big points. While that probably doesn’t cover all of Kerber’s issues on Sunday–Makarova won 72 points to her 55–it is true that big points have a disproportionate effect on the end result. For every player who squanders a dozen break points yet still wins the match, there are others who falter at crucial moments and ultimately lose.

This family of theories–that a player over- or under-performed at big moments–is testable. For instance, I showed last summer that Roger Federer’s Wimbledon loss to Milos Raonic was due in part to his weaker performance on more important points. We can do the same with Kerber’s early exit.

Here’s how it works. Once we calculate each player’s probability of winning the match before each point, we can assign each point a measure of importance–I prefer to call it leverage, or LEV–that quantifies how much the single point could effect the outcome of the match. At 3-0, 40-0, it’s almost zero. At 3-3, 40-AD in the deciding set, it might be over 10%. Across an entire tournament’s worth of matches, the average LEV is around 5% to 6%.

If Petko is right, we’ll find that the average LEV of Kerber’s unforced errors was higher than on other points. (I’ve excluded points that ended with the serve, since neither player had a chance to commit an unforced error.) Sure enough, Kerber’s 13 groundstroke UEs (that is, excluding double faults) had an average LEV of 5.5%, compared to 3.8% on points that ended some other way. Her UE points were 45% more important than non-UE points.

Let’s put that number in perspective. Among the 86 women for whom I have point-by-point UE data for their first-round matches this week*, ten timed their errors even worse than Kerber did. Magdalena Rybarikova was the most extreme: Her eight UEs against Coco Vandeweghe were more than twice as important, on average, as the rest of the points in that match. Seven of the ten women with bad timing lost their matches, and two others–Agnieszka Radwanska and Marketa Vondrousova–committed so few errors (3 and 4, respectively), that it didn’t really matter. Only Dominika Cibulkova, whose 15 errors were about as badly timed as Kerber’s, suffered from unclutch UEs yet managed to advance.

* This data comes from the Roland Garros website. I aggregate it after each major and make it available here.

Another important reference point: Unforced errors are evenly distributed across all leverage levels. Our instincts might tell us otherwise–we might disproportionately recall UEs that came under pressure—-but the numbers don’t bear it out. Thus, Kerber’s badly timed errors are just as badly timed when we compare her to tour average.

They are also poorly timed when compared to her other recent performances at majors. Petkovic implied as much when she said her compatriot was making “errors she didn’t make last year.” Across her 19 matches at the previous four Slams, her UEs occurred on points that were 11% less important than non-UE points. Her errors caused her to lose relatively more important points in only 5 of the 19 matches, and even in those matches, the ratio of UE leverage to non-UE leverage never exceeded 31%, her ratio in Melbourne this year against Tsurenko. That’s still better than her performance on Sunday.

Across so many matches, a difference of 11% is substantial. Of the 30 players with point-by-point UE data for at least eight matches at the previous four majors, only three did a better job timing their unforced errors. Radwanska heads the list, at 16%, followed by Timea Bacsinszky at 14% and Kiki Bertens at 12%. The other 26 players committed their unforced errors at more important moments than Kerber did.

As is so often the case in tennis, it’s difficult to establish if a stat like this is indicative of a longer-trend trend, or if it is mostly noise. We don’t have point-by-point data for most of Kerber’s matches, so we can’t take the obvious next step of checking the rest of her 2017 matches for similarly unclutch performances. Instead, we’ll have to keep tabs on how well she limits UEs at big moments on those occasions where we have the data necessary to do so.

Bouncing Back From a Marathon Third Set

Italian translation at settesei.it

In this year’s edition of the French Open, we’ve already seen two women’s matches charge past the 6-6 mark in the third set. On Sunday, Madison Brengle outlasted Julia Goerges 13-11 in the decider, and yesterday, Kristina Mladenovic overcame Jennifer Brady 9-7 in the final set. Marathon three-setters aren’t as gut-busting as the five-set equivalent on the men’s tour, yet they still require players to go beyond the usual limit of a tour match.

Do marathon three-setters affect the fortunes of those players that move on to the next round? Back in 2012, I published a study showing that men who win marathon five-setters (that is, matches that go to 8-6 or longer) win fewer than 30% of their following matches, a rate far worse than what we would expect, given the quality of their next opponents. It seems likely that long three-setters wouldn’t have the same effect, especially since many top women are willing to play five-setters themselves.

The numbers bear out the intuition. From 2001 to the 2017 Australian Open, there have been 185 marathon three-setters in Grand Slam main draws, and the winners of those matches have gone on to win 42.2% of their next contests. That’s more than the equivalent number for men, and it’s even better than it sounds.

Players who need to go deep into a third set to vanquish an early-round opponent are, on average, weaker than those who win in straight sets, so many of the marathon women would already be considered underdogs in their next matches. Using sElo–surface-specific Elo, which I recently introduced–we see that these 185 marathon women would have been expected to win only 44.0% of their following matches. There may be a real effect here, but it is a minor one, especially compared to the fortunes of players who struggle through marathon five-setters.

I ran the same algorithm for women’s Slam matches that ended at 7-6, 7-5, and 6-4 or 6-3 in the final set. Since only the US Open uses the third-set tiebreak format, the available sample for that score is limited, which may explain a slightly wacky result. For the other scores, we see numbers that are roughly similar to the marathon findings. Winners tend to be underdogs against their next opponents, but there is little, if any, hangover effect:

3rd Set Score  Sample  Next W%  Next ExpW%  
Marathons         185    42.2%       44.0%  
7-6                56    48.2%       42.2%  
7-5               232    43.1%       42.7%  
6-4 / 6-3         421    41.6%       43.2%

In short: A long match often tells us something about the winner’s chances against her next foe, but it’s something that we already knew. The tight three-setter itself–marathon or otherwise–has little effect on her chances later on. That’s good news for Mladenovic, who will be back on court tomorrow against Sara Errani, an opponent likely to give her another grueling workout.