Slow Conditions Might Just Flip the Outcome of Federer-Nadal XL

Italian translation at settesei.it

Roger Federer likes his courts fast. Rafael Nadal likes them slow. With eight Wimbledon titles to his name, Federer is the superior grass court player, but the conditions at the All England Club have been unusually slow this year, closer to those of a medium-speed hard court.

On Friday, Federer and Nadal will face off for the 40th time, their first encounter at Wimbledon since the Spaniard triumped in their historical 2008 title-match battle. Rafa leads the head-to-head 24-15, including a straight-set victory at his favorite slam, Roland Garros, several weeks ago. But before that, Roger had won five in a row–all on hard courts–the last three without dropping a set.

Because of the contrast in styles and surface preferences, the speed of the conditions–a catch-all term for surface, balls, weather, and so on–is particularly important. Nadal is 14-2 against his rival on clay, with Federer holding a 13-10 edge on hard and grass. Another way of splitting up the results is by my surface speed metric, Simple Speed Rating (SSR). 22 of the matches have been been on a court that is slower than tour average, with the other 17 at or above tour average speed:

Matches     Avg SSR  RN - RF  Unret%  <= 3 shots  Avg Rally  
SSR < 0.92     0.74     17-5   21.2%       49.5%        4.7  
SSR >= 1.0     1.14     7-10   27.0%       56.9%        4.3

At faster events–all of which are on hard or grass–fewer serves come back, more points end by the third shot, and the overall rally length is shorter. Fed has the edge, with 10 wins in 17 tries, while on slower surfaces–all of the clay matches, plus a handful of more stately hard courts–Rafa cleans up.

Rafa broke Elo

According to my surface-weighted Elo ratings, Federer is the big semi-final favorite. He leads Nadal by 300 points in the grass-only Elo ratings, which gives him a 75% chance of advancing to the final. The betting market strongly disagrees, believing that Rafa is the favorite, with a 57% chance of winning.

The collective wisdom of the punters is onto something. Elo has systematically underwhelmed when it comes to forecasting the 39 previous Fedal matches. Federer has more often been the higher-rated player, and if Roger and Rafa behaved like the algorithm expected them to, the Swiss would be narrowly leading the head-to-head, 21-18. We might reasonably conclude that, going into Friday’s semi-final, Elo is once again underestimating the King of Clay.

How big of Fedal-specific adjustment is necessary? I fit a logit model to the previous 39 matches, using only the surface-weighted Elo forecast. The model makes a rough adjustment to account for Elo’s limitations, and reduces Roger’s chances of winning the semi-final from 74.8% all the way down to 48.5%.

Now, about those conditions

The updated 48.5% forecast takes the surface into account–that’s part of my Elo algorithm. But it doesn’t distinguish between slow grass and fast grass.

To fix that, I added SSR, my surface speed metric, to the logit model. The model’s prediction accuracy improved from 64% to 72%, its Brier score dropped slightly (a lower Brier score indicates better forecasts), and the revised model gives us a way of making surface-speed-specific forecasts for this matchup. Here are the forecasts for Federer at several surface speed ratings, from tour average (1.0) to the fastest ratings seen on the circuit:

SSR  p(Fed Wins)  
1.0        49.3%  
1.1        51.4%  
1.2        53.4%  
1.3        55.5%  
1.4        57.5%  
1.5        59.5% 

In the fifteen years since Rafa and Roger began their rivalry, the Wimbledon surface has averaged around 1.20, 20% quicker than tour average. In 2006, when they first met at SW19, it was 1.24, and in 2008, it was 1.15. Three times in the last decade it has topped 1.30, 30% faster than the average ATP surface. This year, it has dropped almost all the way to average, at 1.00, when both men’s and women’s results are taken into account.

As the table shows, such a dramatic difference in conditions has the potential to influence the outcome. On a faster surface, which we’ve seen as recently as 2014, Federer has the edge. At this year’s apparent level, the model narrowly favors Nadal. Rafa has said that the surface itself is unchanged, but that the balls have been heavier due to humidity. He should hope for another muggy day on Friday–the end result could depend on it.

The Grass Dies, But the Speed Lives On

Italian translation at settesei.it

Earlier this week, I trotted out some stats showing that the Wimbledon grass is playing slower this year, the latest tick in a years-long trend. Many fans suspect that by the second week, the conditions are even slower still, with huge brown spots around each baseline where the players have worn away the grass. Assuming that the dying-grass effect is similar each year, this is something we can test.

I ran my surface speed algorithm for several subsets of Wimbledon men’s singles matches: week 1, week 2, each round from 1 to 4, and the final 8. For a single year, the “week 2,” “round 4,” and “final 8” samples are too small to give us any reliable indicators. But over the course of two decades, the differences between weeks and rounds–the effect we’re interested in today–should become clear.

(Quick refresher on my surface speed method: It uses ace rate as a proxy for speed–not perfect, but functional, using a stat that is universally available–and takes into account the server and returner in each match. An average court speed is 1.0, and ratings typically range from about 0.5 for a venue like Monte Carlo to 1.5 for the fastest grass and indoor hard courts.)

For example, here are the week-by-week and round-by-round speed ratings for the 2018 Wimbledon men’s draw:

  • Week 1: 1.16
  • Week 2: 1.16
  • Round 1: 1.02
  • Round 2: 1.29
  • Round 3: 1.33
  • Round 4: 1.25
  • Last 8: 1.08

I promised noise, and there it is. Each week is equally speedy, but the first round and last few rounds are oddly slower than the rest. I don’t have a good explanation for the first round (and there might not be one–it could be random), but the last 8 often features fewer aces, even when adjusting for the players involved. We’ll come back to that in a bit.

Wimbledon, 2000-18

Here are the same numbers, averaged over the last 19 Wimbledons:

  • Week 1: 1.20
  • Week 2: 1.21
  • Round 1: 1.19
  • Round 2: 1.20
  • Round 3: 1.21
  • Round 4: 1.25
  • Last 8: 1.16

The sample of the last 8 still deviates from the rest, but with more data, the difference is much smaller. The gap between 1.20 and 1.16 is just an ace or two per match. That’s not enough to reverse the outcome of any but the very closest matches.

As usual, I must acknowledge that an ace-based metric isn’t definitive. There’s more to court speed than what aces can tell us. It’s possible that the surface behaves differently as the grass is worn away, even if it doesn’t show up in serve stats. Since net approaches are increasingly rare, the service-box grass lasts longer than the baseline grass, meaning that the speed at which serves move through the court would be relatively unchanged. On the other hand, the biggest brown spots on court are behind the baseline, so most groundstrokes also bounce on green grass, not on brown dirt.

The best versus the best

Even the small difference between the last 8 and the rest of the tournament may not have anything to do with the decaying of the surface. Since 2000, the US Open has exhibited the same trend: 1.07 for week 1, 1.06 for round 4, and 0.97 for the final 8. (The Australian Open numbers are much noisier than the other slams, perhaps due to frequent use of the roof, so I’m hesitant to use them.)

It seems safe to assume that the hard courts in Flushing don’t suddenly get slower starting on Tuesday or Wednesday of the second week. Instead, I think the answer is in the mix of players–or more precisely, how those players interact with each other. By this ace-based metric, the Tour Finals have often been rated as one of the slowest indoor hard court events–even though the official Court Pace Index (CPI) ratings disagree.

In other words, aces tend to go down when the best play the best. Maybe the elites serve more tactically when facing tough opponents? Perhaps they focus more consistently on return, rarely allowing cheap aces? Maybe the best players know each other’s games so well that they anticipate even better than usual? This seems like an interesting line of research, even if it’s not something I’m going to resolve today.

The bottom line is that partly-brown Wimbledon courts play just about as fast as totally-green Wimbledon courts do. There might be a very minor slowdown toward the end of the fortnight, but even there, we should remain skeptical. The conditions are slow this year, but at least they won’t get much slower.

Introducing Elo Ratings for Mixed Doubles

Scroll down for Wimbledon updates, including a forecast for the title match.

With Andy Murray and Serena Williams pairing up in this year’s Wimbledon mixed doubles event, more eyes than ever are on tournament’s only mixed-gender draw. Mixed doubles is played just four times a year (plus the Olympics, the occasional exhibition, and the late Hopman Cup), so most partnerships are temporary, and it’s tough to get a sense of who is particularly good in the dual-gender format.

That’s where math comes into play. Over the last few years, I’ve deployed a variation of the Elo rating algorithm for men’s doubles. It treats each team as the average of the two members, and after every match, it adjusts each player’s rating based on the result and the quality of the opponent. Doubles Elo–D-Lo–is even better suited for mixed than for single-gender formats, because players rarely stick with the same partner. The main drawback of D-Lo for men’s or women’s doubles is that it doesn’t help us tease out the individual contributions of long-time teams such as Bob and Mike Bryan. By contrast, mixed doubles draws often look like a game of musical chairs from one major to the next.

The rating game

Let’s jump right in. The Wimbledon mixed doubles draw consists of 56 teams. Here are the 10 highest-rated of those 112 players, as of the start of the fortnight:

Rank  Player                 XD-Lo  
1     Venus Williams          1855  
2     Serena Williams         1847  
3     Bethanie Mattek-Sands   1834  
4     Jamie Murray            1809  
5     Ivan Dodig              1793  
6     Latisha Chan            1785  
7     Bruno Soares            1776  
8     Leander Paes            1771  
9     Heather Watson          1770  
10    Gabriela Dabrowski      1760

Serena and Venus Williams require a bit of an asterisk, since both are playing mixed for the first time after a long break. Venus last played at the 2016 Olympics, and Serena last competed in mixed at the 2012 French Open. Maybe they’re rusty. My XD-Lo algorithm doesn’t include any kind of adjustment for injuries or other layoffs, so it’s possible that we should expect them to perform at a lower level. On the other hand, they are among the greatest doubles players of all time, and players tend to age gracefully in doubles. Venus lost her opening match, but perhaps we should blame that on Francis Tiafoe (XD-Lo: 1,494). The sisters will probably trade places at the top of the list once Wimbledon results are incorporated.

Murray’s rating is a decent but more pedestrian 1,648, so Murray/Williams is not the best team in the field. But they’re close. The strongest pair is Jamie Murray and Bethanie Mattek Sands–3rd and 4th on the list above–followed by Ivan Dodig and Latisha Chan, 5th and 6th on the individual list. Due to the vagaries of ATP and WTA doubles rankings and the resulting seedings, Dodig/Chan entered the event as the narrow favorites, because they got a first-round bye and Murray/Mattek-Sands did not.

Here are the top ten teams in the draw:

Rank  Team                                XD-Lo  
1     Bethanie Mattek-Sands/Jamie Murray   1822  
2     Ivan Dodig/Latisha Chan              1789  
3     Bruno Soares/Nicole Melichar         1762  
4     Serena Williams/Andy Murray          1748  
5     Gabriela Dabrowski/Mate Pavic        1734  
6     Leander Paes/Samantha Stosur         1731  
7     Heather Watson/Henri Kontinen        1708  
8     Venus Williams/Frances Tiafoe        1674  
9     Abigail Spears/Marcelo Demoliner     1653  
10    Neal Skupski/Chan Hao-ching          1634

The top five have survived (though Murray/Mattek-Sands and Pavic/Dabrowski will complete their second-round match this afternoon, leaving only four), and of the last 18 teams standing, only one other one–John Peers and Shuai Zhang–is rated above 1,600.

Forecasting SerAndy

Using my ratings, Murray/Williams entered the tournament with a 9.8% chance of winning. That made them fourth favorite, behind Dodig/Chan (17.1%), Murray/Mattek-Sands (16.3%), and the big-serving duo of Bruno Soares and Nicole Melichar (14.5%). I’ll update the forecast this evening, when the second round is finally complete.

Murray/Williams’s second-round match is against Fabrice Martin and Racquel Atawo. They are both excellent doubles players, though neither has excelled in mixed. Atawo, especially, has struggled. Her XD-Lo is 1,304, the third-lowest of anyone who has entered a mixed draw since 2012. (Shuai Peng is rated 1,268, and Marc Lopez owns last place with 1,252.) A player with no results at all enters the system with 1,500 points, so falling to 1,300 requires a lot of losing. The combined ratings translate into a 89% chance of a Murray/Williams victory.

The challenge comes in the third round. Soares/Melichar are the top seed, and they have already advanced to the round of 16, awaiting the winner of Murray/Williams and Martin/Atawo. Thus two of of the top four teams will likely play for a place in the quarter-finals, with Soares/Melichar holding a narrow, 52% edge.

Historical peaks

Generating these current ratings required amassing a lot of data, so it would be a waste to ignore the history of the mixed doubles format. Here are the top 25 female mixed doubles players, ranked by their peak XD-Lo ratings:

Rank  Player                   Peak  
1     Billie Jean King         2043  
2     Greer Stevens            2035  
3     Margaret Court           2015  
4     Rosie Casals             2000  
5     Martina Navratilova      1998  
6     Helena Sukova            1991  
7     Anne Smith               1989  
8     Betty Stove              1985  
9     Jana Novotna             1977  
10    Martina Hingis           1964  
11    Wendy Turnbull           1956  
12    Kathy Jordan             1948  
13    Elizabeth Smylie         1947  
14    Arantxa Sanchez Vicario  1946  
15    Serena Williams          1942  
16    Venus Williams           1937  
17    Francoise Durr           1934  
18    Jo Durie                 1929  
19    Kristina Mladenovic      1922  
20    Zina Garrison            1901  
21    Samantha Stosur          1898  
22    Larisa Neiland           1891  
23    Lindsay Davenport        1888  
24    Victoria Azarenka        1887  
25    Natasha Zvereva          1886 

Venus really can’t catch a break. She’s one of the best players of all time, and Serena is always just a little bit better.

And the top 25 men:

Rank  Player               Peak XD-Lo  
1     Owen Davidson              2043  
2     Bob Hewitt                 2042  
3     Marty Riessen              2016  
4     Todd Woodbridge            2000  
5     Frew McMillan              1999  
6     Kevin Curren               1997  
7     Jim Pugh                   1995  
8     Ilie Nastase               1975  
9     Tony Roche                 1962  
10    Bob Bryan                  1949  
11    Rick Leach                 1938  
12    Mahesh Bhupathi            1933  
13    Mark Woodforde             1929  
14    Justin Gimelstob           1929  
15    Max Mirnyi                 1926  
16    John Lloyd                 1922  
17    Emilio Sanchez             1918  
18    Ken Flach                  1909  
19    Jeremy Bates               1908  
20    John Fitzgerald            1906  
21    Cyril Suk                  1902  
22    Wayne Black                1889  
23    Dick Stockton              1881  
24    Jean-Claude Barclay        1879  
25    Mike Bryan                 1875

Owen Davidson won eight mixed slams with Billie Jean King, plus three more with other partners. Bob Hewitt won six, spanning 18 years from 1961 to 1979. (We can’t erase his accomplishments from the history books, but any mention of Hewitt comes with the caveat that he is a convicted rapist who has since been expelled from the International Tennis Hall of Fame.)

It is interesting to see two famous pairs represented on the men’s list. Bob Bryan ranks 10th to Mike’s 25th, and Todd Woodbridge comes in 4th to Mark Woodforde’s 13th. We probably can’t conclude from mixed doubles results that one member of the team was a superior men’s doubles player, but it is one of the few data points that allows us to compare these partners.

The ignominious Spaniards

Finally, I can’t spend this much time with mixed doubles ratings without revisiting the case of David Marrero. You may recall the 2016 Australian Open, when Marrero’s first-round match with Lara Arruabarrena triggered “suspicious betting patterns.” As I wrote at the time, the most suspicious thing about it was that Marrero–who was terrible at mixed doubles and admitted that he played differently with a woman across the net–could still find a partner.

He entered that match with an XD-Lo rating of 1,349–the worst of any man in the draw, though Anastasia Pavlyuchenkova was a few points lower–and left it at 1,342. He played his last mixed doubles match at Wimbledon that year, and–surprise!–he lost. One hopes he’ll stick to men’s doubles for the remainder of his career, sticking with an XD-Lo rating of 1,326.

Marrero’s only saving grace is that he’s better than his compatriot Marc Lopez. Lopez has been active in mixed doubles more recently, entering the US Open last year with Arruabarrena. After that loss, he fell to his current rating of 1,252, the lowest mark recorded in the Open Era.

Fortunately for us, this year’s Wimbledon draw includes both Williams sisters, both Murray brothers, a healthy Mattek-Sands … and very few players as helpless in the mixed doubles format as Marrero or Lopez.

Update: Murray/Williams won their second-rounder, setting up the final 16. Mixed doubles isn’t the top scheduling priority, so it didn’t exactly work that way–by the time Muzzerena advanced, two other teams had already secured places in the quarter-finals. Ignoring those for the moment, here is the last-16 forecast:

Team                      QF     SF      F      W  
Soares/Melichar        52.5%  44.5%  33.2%  18.8%  
Murray/Williams        47.5%  39.7%  29.0%  15.8%  
Middelkoop/Yang        55.5%   9.5%   3.6%   0.8%  
Daniell/Brady          44.5%   6.3%   2.1%   0.4%  
Peers/Zhang            61.6%  36.9%  13.8%   5.2%  
Lindstedt/Ostapenko    38.4%  18.7%   5.2%   1.5%  
Skugor/Olaru           56.2%  26.3%   8.3%   2.6%  
Mektic/Rosolska        43.8%  18.0%   4.8%   1.3%  
                                                   
Player                    QF     SF      F      W  
Koolhof/Peschke        42.6%  10.1%   2.4%   0.6%  
Qureshi/Kichenok       57.4%  16.7%   4.9%   1.5%  
Sitak/Siegemund        27.4%  16.0%   5.3%   1.8%  
Pavic/Dabrowski        72.6%  57.2%  30.8%  17.5%  
Dodig/Chan             75.9%  64.6%  44.1%  28.1%  
Roger-Vasselin/Klepac  24.1%  15.5%   6.6%   2.5%  
Hoyt/Silva             54.1%  11.3%   3.5%   1.0%  
Vliegen/Zheng          45.9%   8.6%   2.5%   0.6% 

The two teams already in the quarters are Skugor/Olaru and Hoyt/Silva. Since both of their matches were close to 50/50, you can roughly double their odds, and the odds of the other teams are only a tiny bit less. The remaining six third-round matches are scheduled for Wednesday, and I’ll try to update again when those are in the books.

Update 2: Murray/Williams are out, so the number of people interested in mixed doubles has fallen from double digits back to the typical level of single digits. The departure of the singles stars also leaves one clear favorite in each half. Here is the updated forecast:

Team                    SF      F      W  
Soares/Melichar      83.4%  64.3%  36.4%  
Middelkoop/Yang      16.6%   6.7%   1.5%  
Lindstedt/Ostapenko  46.0%  12.6%   3.7%  
Skugor/Olaru         54.0%  16.4%   5.2%  
Koolhof/Peschke      37.5%   7.3%   1.8%  
Sitak/Siegemund      62.5%  17.2%   6.0%  
Dodig/Chan           84.4%  68.3%  43.3%  
Hoyt/Silva           15.6%   7.2%   2.0%

All four quarter-finals are scheduled for Thursday, so I’ll post another update tomorrow evening.

Update 3: We’re down to four teams. Of the Elo favorites in the quarter-finals, only Dodig/Chan survived, leaving them as the overwhelming pick to take the title. Here’s the full forecast:

Team                     F      W  
Middelkoop/Yang      42.3%   8.2%  
Lindstedt/Ostapenko  57.7%  14.1%  
Koolhof/Peschke      14.1%   6.3%  
Dodig/Chan           85.9%  71.4% 

Update 4: Both favorites won in Friday’s semi-finals, so we’ve got a final between Lindstedt/Ostapenko and Dodig/Chan. The first team didn’t get an opening-round bye, so they won one more match to get here. They also have a better story, since Ostapenko keeps hitting her partner in the head. Dodig/Chan entered as the 8th seeds, despite being the second-best team according to XD-Lo.

Consequently, Dodig/Chan get the edge here, with an 81% of winning the 2019 Wimbledon Mixed Doubles title.

Yep, Wimbledon is Playing Slower This Year

Italian translation at settesei.it

The players are right. Wimbledon’s surface–or balls, or atmosphere, or aura–has slowed down in comparison with recent years. We’ve heard comments to that effect from Roger Federer, Milos Raonic, Boris Becker, Rafael Nadal, and many others. Raonic attributes the change to the grass, and Nadal to the balls. Regardless of the reason, the numbers back up their perceptions.

Here is an overview of several surface-speed indicators for the first three rounds of singles matches at Wimbledon, 2017-19:

                     2017   2018   2019  
Aces (Men)           8.9%  10.0%   8.5%  
Aces (Women)         4.1%   4.2%   4.1%  
                                         
Unret (Men)         36.0%  36.6%  33.3%  
Unret (Women)       25.9%  27.6%  25.2%  
                                         
<= 3 Shots (Men)    65.2%  65.6%  61.9%  
<= 3 Shots (Women)  55.3%  57.9%  55.0%  
                                         
Avg Rally (Men)       3.4    3.5    3.7  
Avg Rally (Women)     4.0    3.8    4.1

The second set of rows, "Unret," is the percent of unreturned serves. The next set, "<=3 Shots," is the percent of points that ended in three shots or less. For all four of the stats shown, including aces and average rally length, men's numbers point to slower conditions. The women's numbers are less clear, but to the extent that they point in either direction, they concur.

Not just 2019

Aggregate numbers such as these usually give us an idea of what's going on. But we can do better. The numbers above do not control for the mix of players or the length of their matches. For instance, 2019's rates would be different if John Isner, instead of Mikhail Kukushkin, had played a third-round match. The surface speed might have affected that result, but if we're going to compare ace rate from one year to the next, we shouldn't compare Isner's ace rate with Kukushkin's ace rate.

That's where my surface speed metric comes in. For each tournament, I control for the mix of servers and returners (yes, returners affect ace rate, too) to boil down each event to one number, representing how the tournament's ace rate compares to tour average. While there's more to surface speed than ace rate, aces are a good proxy for many of those other indicators, and more importantly, aces are one of the few stats that are available for every match.

The resulting score usually ranges between 0.5--50% fewer aces than average, usually on a slow clay court like Monte Carlo--and 1.5--50% more aces than average, on a fast grass or indoor hard court, like Antalya or Metz. Over the last decade, Wimbledon's conditions have drifted from the high end of that range to the middle:

Year      Men    Women  Average  
2011     1.26     1.37     1.31  
2012     1.27     1.06     1.17  
2013     1.29     1.04     1.17  
2014     1.35     1.19     1.27  
2015     1.20     1.16     1.18  
2016     1.06     1.03     1.04  
2017     1.03     1.07     1.05  
2018     1.14     0.98     1.06  
2019     1.04     0.96     1.00 

The men's numbers are usually more reliable measurements, because they are based on many more aces, which means that the ace rate for any given match is less fluky. Ideally, we'd see the men's and women's speed ratings move in lockstep, but there is some noise in the calculation, and the ratings are also relative to that year's tour average, which depends in turn on the changing speeds of dozens of other surfaces.

Caveats aside, the direction of the trend is clear. There isn't a substantial difference between 2019 and the last few years, but the gap between the first and second half of the decade is dramatic.

What is less clear--and will require considerable further research--is how much it matters. In 2014, Nick Kyrgios upset Nadal in four sets, while last week, the result was reversed. How much of that can we attribute to the surface? Would faster conditions have allowed Isner to outlast Kukushkin? Kevin Anderson to hold off Guido Pella? Jelena Ostapenko to withstand Su Wei Hsieh?

For now, those questions remain in the speculation-only file. Now that we can conclude that the grass really has gotten slower, we can focus that speculation on the fates of several grass court savants, including Federer, Raonic, and Karolina Pliskova. By the end of the fortnight, they--like Kyrgios--might be wishing it was 2014 again.

Podcast Episode 69: Middle Sunday Check-Ins on Gauff, Nadal, Murray, Serena, Barty, and the Draw

Episode 69 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, recaps the first week of Wimbledon, with a focus on the oustanding debut of 15-year-old Cori Gauff. (I also wrote about her earlier this week at the Economist, and this morning at the blog.)

We also talk Kyrgios-Nadal, Andy Murray the doubles player and his partnership with Serena Williams, the possibly slower grass this year, and some surprisingly decent returning from Milos Raonic. We also offer forecasts for each of the 16 fourth-round matches, along with Elo- and market-based predictions for each one.

Thanks for listening!

(Note: this week’s episode is about 61 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

How Good is Cori Gauff Right Now?

Italian translation at settesei.it

15-year-old sensation Cori Gauff holds a WTA ranking of No. 313. She has played only a limited number of events that are considered by the WTA’s system, so even before her impressive run began, we could’ve predicted that her ranking was an understatement. But by how much?

Gauff doesn’t show up yet on my Elo ratings list because, before Wimbledon qualies, she hadn’t played at least 20 matches at the ITF $50K level or higher in the last year. However, she still had a rating: 1,488, good for 194th place among those who had met the playing time minimum. A rating in that range translates to about a 3% chance of upsetting current top-ranked player Ashleigh Barty, and a 10% chance of beating someone around 20th, such as Donna Vekic. Given how little data we had to work with at that point, that seemed like a reasonable assessment.

Since she arrived in London, she has won six matches: Three in qualifying and three in the main draw, with wins over Venus Williams, Magdalena Rybarikova, and Polona Hercog. Not bad for a teenager who had previous won only one slam qualifying match and one tour-level main draw match in her young career!

194th place doesn’t seem like such a fair judgment anymore. Any player who comes through qualifying and reaches the fourth round at a major deserves some reassessment, and that’s even more applicable to a player about whom we knew so little two weeks ago. The tricky part is figuring out how much to adjust. Is Gauff now a top-100 player? Top 50? Top 20?

Revising with Elo

The Elo algorithm does a good job of approximating how humans make those reassessments: The more data we already have about a player, the less we will adjust her rating after a win or loss. The previous player to defeat Hercog was Simona Halep, at Eastbourne. We already have years’ worth of match results for Halep, and she was heavily favored to win the match. Thus, the fact that she recorded the victory alters our opinion of her by only a small amount. In Elo terms, it was an increase from 2,100 points to 2,102–basically nothing.

Gauff is a different story. Entering her third-round clash with Hercog, not only did we know very little about her skill level, it wasn’t even clear if she was the favorite. The result caused Elo to make a considerably larger adjustment, increasing her rating from 1,713 to 1,755, a rise 21 times greater than what Halep received after beating the same opponent. The 42-point jump caused her to leapfrog 16 players in the rankings.

Here is Gauff’s Elo progression, from the moment she arrived at Wimbledon to middle Sunday. After each match, I show her overall Elo (the numbers I’ve been discussing so far), her grass-specific Elo, and her grass-weighted Elo, a 50/50 blend of overall and grass-specific that is used for forecasting. For each of the three ratings, I also show her ranking among WTA players with at least 20 matches in the last 52 weeks.

Match          Overall   Rk  Grass   Rk  Weighted   Rk  
Pre-Wimbledon     1488  194   1350  163      1419  187  
d. Bolsova        1540  171   1405  132      1473  155  
d. Ivakhnenko     1566  157   1447  107      1507  131  
d. Minnen         1614  132   1514   57      1564   95  
d. Venus          1670  108   1578   40      1624   73  
d. Rybarikova     1713   83   1650   21      1682   41  
d. Hercog         1755   67   1686   17      1721   31

Over the course of only six matches, Gauff has jumped from 194th in the overall Elo rankings to 67th. For forecasting purposes, her grass court rating has soared from 187th to 31st. Her current weighted rating of 1,721 is better than that of three other women in the round of 16: Karolina Muchova, Carla Suarez Navarro, and Shuai Zhang. She trails another surviving player, Elise Mertens, by only 20 points.

So you’re telling me there’s a chance

Unfortunately, none of those relatively weak grass-court players are Gauff’s next opponent. Instead, the 15-year-old will face Halep, the third-best remaining player (behind Barty and Karolina Pliskova), and a three-time quarter-finalist at the All England Club. Halep’s weighted Elo rating is 229 points higher than Gauff’s, implying that the veteran has a 79% chance of winning on Monday. The betting market concurs, suggesting that the probability of a Halep victory is about 80%.

It doesn’t usually have much of an effect on forecasts to update Elo ratings throughout a tournament. While anyone reaching the 4th round has a higher rating than they did before the event, the differences are typically small. And since forecasts are based on the difference between the ratings of two players, the forecast isn’t affected if both players’ ratings have increased by roughly the same amount.

As a teenager with such limited match experience, Gauff breaks the mold. Her pre-Wimbledon 1,488 Elo rating is only two weeks old, and it is already completely unrepresentative of what we know of her skill level. She’ll have ample time to prove us right or wrong in the upcoming years, but for now, we have good reason to estimate that she belongs–even more than some of the older players who have reached the second week at Wimbledon.

Forecasting Andy Murray, Doubles Specialist

We are three weeks into the mostly-triumphant doubles comeback of Andy Murray. In his first week back, he raced to the Queen’s Club title with Feliciano Lopez. A week later, he paired Marcelo Melo and lost in the first round. At Wimbledon, he is partnering Pierre-Hugues Herbert, with whom he has already defeated the only-at-a-slam duo of Marius Copil and Ugo Humbert.

Today in the second round, Herbert/Murray face a sterner test: sixth-seeded team Nikola Mektic and Franco Skugor. The betting markets heavily favored Herbert/Murray going into the contest, but we have to assume that punters (including an unusually high number of casual ones) are probably overrating the familiar name on his home turf.

D-Lo to the rescue

Let’s see what D-Lo (Elo for doubles!) says about today’s match. D-Lo treats each team as a 50/50 mix of the two players, and adjusts each player’s rating after every match, depending on the quality of the opponent. It also very slightly regresses both partners to the team average after each match, because it’s impossible to know how much each player contributed to the result.

Herbert is D-Lo’s top doubles player in the world on hard and clay courts, though he falls to 6th in the 50/50 blend of overall and grass-specific ratings used for forecasting. Murray, thanks to his run at Queen’s, is up to 54th in the blend, though that’s really more like 40th among players in the draw, since several injured and recently-retired players are clinging to high D-Lo ratings.

Mektic and Skugor are credible specialists, as indicated by their ATP ranking. They are 24th and 26th in the D-Lo, respectively. Combined, the two teams’ ratings are quite close: 1773 for Herbert/Murray to 1763 for Mektic/Skugor. In a best-of-three match, a difference of 10 points translates to a 51.4% edge for the favorites. In best-of-five, the better team is always more likely to come out on top, though with such a small margin it barely matters. Here, the best-of-five number is 51.6%.

Versus the pack

How does a team rating of 1773 compare to the rest of the remaining field? Entering Saturday’s play, 22 men’s doubles pairs were still in the draw. As I write this, Lopez and Pablo Carreno Busta are the only additional team to have been eliminated, reducing the field to 21.

Here are the combined D-Lo ratings of these teams. The rank shown for each player is based on the 50/50 blend of overall and grass rating used for forecasting.

Team D-Lo  Rank  Player             Rank  Player             
1873       2     Mike Bryan         3     Bob Bryan          
1858       4     Lukasz Kubot       7     Marcelo Melo       
1836       9     Raven Klaasen      10    Michael Venus      
1817       8     John Peers         17    Henri Kontinen     
1802       12    Nicolas Mahut      22    E Roger-Vasselin   
1788       18    J S Cabal          19    Robert Farah       
1773       6     P H Herbert        54    Andy Murray        
1764       15    Oliver Marach      36    Jurgen Melzer      
1763       24    Nikola Mektic      26    Franco Skugor      
1757       20    Rajeev Ram         33    Joe Salisbury      
1747       23    Horia Tecau        41    Jean Julien Rojer  
1709       42    Maximo Gonzalez    46    Horacio Zeballos   
1695       29    Ivan Dodig         88    Filip Polasek      
1681       58    Marcus Daniell     62    Wesley Koolhof     
1677       50    Frederik Nielsen   77    Robin Haase        
1644       81    Marcelo Demoliner  90    Divij Sharan       
1637       84    A Ul Haq Qureshi   99    Santiago Gonzalez  
1596       106   Philipp Oswald     123   Roman Jebavy       
1575       101   Mischa Zverev      184   Nicholas Monroe    
1533             Jaume Munar        216   Cameron Norrie     
1517       177   Marcelo Arevalo    214   M Reyes Varela

Herbert/Murray rank 7th among the surviving pairs. The combined rating of 1773 makes them competitive against anyone. The 100-point difference separating them and the Bryans gives them a 33% chance of pulling off a best-of-five upset, while the 29-point gap between them and Nicolas Mahut/Edouard Roger Vasselin translates to a 45/55 proposition.

Fortunately for the French-British pair, they won’t have to play a higher-rated team for some time. If they win today, they’ll face the winner of Dodig/Polasek vs Zverev/Monroe. The first of those teams is rated 80 points lower than Herbert/Murray (64% odds for the favorites), and the second is 200 points lower (81% for the faves). The three teams that could advance to become the quarter-final opponent for Herbert/Murray are all rated lower than Dodig/Polasek.

The draw certainly favored Sir Andrew. Yes, the 1859-rated Pavic/Soares duo crashed out in their section, but even before that, three of the best teams–Bryan/Bryan, Kubot/Melo, and Mahut/Roger-Vasselin–were stuck together in another quarter. While no men’s doubles match is a sure thing, the path is clear for Herbert/Murray to reach the final four.

Beyond Wimbledon

Does Murray have what it takes to become a full-time doubles specialist? Taking his Queen’s Club title into account, his overall D-Lo is already up to 36th best on tour, just ahead of Skugor, and several places better than Roland Garros co-champ Kevin Krawietz. Jurgen Melzer, another excellent singles player making of a go of it on the doubles circuit, is ranked 20 places lower, with a D-Lo 40 points less than Murray’s.

The short answer, then, is yes. It must be noted, though, that he isn’t the best choice among the big four to have a successful post-singles career as part of a team. That honor goes overwhelmingly to Rafael Nadal. Nadal’s career peak D-Lo is 100 points higher than Murray’s, and even his grass-court rating–based, admittedly, on some old results–is 70 points higher. Aside from the injured doubles wizard Jack Sock, Nadal is the best active player absent from the Wimbledon draw.

So, Murray/Nadal, Wimbledon 2021 champions? Sounds good to me–as long as Herbert relinquishes his new partner and finally commits to focusing on singles.

Let Bernie Keep His Money

Italian translation at settesei.it

On Tuesday, Bernard Tomic lost his first-round match at Wimbledon to Jo-Wilfried Tsonga. No surprise there: My forecast gave Tsonga a 64% chance of advancing, and that didn’t even take into account Tomic’s shaky health, which has caused him to retire from matches twice in the last six weeks.

Tomic-Tsonga immediately made the news, and for the wrong reasons. The Australian lost, winning only seven games. Ignominiously, the match lasted only 58 minutes, the shortest at Wimbledon since Roger Federer needed only 54 minutes to thump Alejandro Falla back in 2004.

The All England Club responded this morning, announcing that Tomic would lose his prize money. Officially, he “did not perform to the required professional standard.”

Fast and insufficiently furious

I don’t know whether Tomic performed to the required professional standard, because there’s no exact definition of “professional standard.” I suspect it’s some combination of the following:

  • The player lost badly
  • The player has a reputation for tanking
  • The match got a lot of attention so we have to be seen doing something about it

What I do know is that Wimbledon officials are looking at the wrong number. Yes, 58 minutes is an extremely fast three-set match. But Tomic–even when he’s fully engaged and playing his best–is probably the quickest player on tour, often serving as soon as a ballkid gets him the ball. Tsonga also plays fast. Neither player is a good returner, and the Frenchman is a devastating server on a fast surface, so the points were always going to be short.

The more appropriate metric, then, is points played. Tomic and Tsonga contested 125, which is considerably less headline-grabbing than the time on the clock.

Fines all around!

Suddenly, Tomic-Tsonga doesn’t stand out as much. Since 2000, there have been 77 other men’s grand slam matches that required 125 points or less. That’s almost exactly one per slam. The list includes two quarter-finals, three semi-finals, and the 2003 Australian Open title match, in which Andre Agassi dispatched Rainer Schuettler in 76 minutes, needing only 123 points. If we expand our view to matches with fewer than 130 points, we’re looking at another 45 matches, including both of this year’s Australian Open semi-finals.

Simply put: It is not unusual for a men’s slam match to be decided with 125 points. Really good players sometimes lose that fast. It just doesn’t usually attract so much attention, because on average, 125 points takes an hour and 21 minutes to play.

Of course, there are plenty of one-sided contests in the women’s draw, as well. 125 points is about 42 per set, so the “Tomic line” is at 83 or 84 points for a best-of-three match. Since 2003, there have been 235 women’s singles matches of 83 points or less, including five at this year’s French Open alone. (Ironically, Anna Tatishvili’s loss to Maria Sakkari, which triggered its own unprecedented fine, lasted 93 points and 28 minutes per set.)

Reactionary

All of this isn’t to say that Tomic tried his hardest on Tuesday, or that he “deserves” £45,000 in an ethical sense. If tournament referees made it a practice to review video of every first-round match and dock the prize money of the one player who competed most lackadaisically, then sure, the Australian is probably that guy at Wimbledon this year.

But that’s not how it works. The “professional standard” clause is almost never invoked. Had Tomic frittered away more time between points in order to push this match over the one-hour mark, or the offender had been a player with a less checkered past, we wouldn’t be talking about it now.

If the All England Club were focused on the right metric–the amount of tennis played, not how long it took–Bernie’s speedy, casual style of play wouldn’t be in the headlines. After all, there’s another casual, mercurial Australian with a poor return game who deserves more of our attention today.

Visualizing Trends in Net Play Across Five Decades of Grass Court Tennis

Earlier this week, I wrote about one aspect of the long-term decline in net play: the widespread belief that approaching the net is more difficult now because fewer players have a weaker side. I presented evidence indicating that most players still have a weaker side, which suggests that all groundstrokes–on both strong and weak sides–have gotten stronger, making net play a riskier proposition.

If that is true, it is reasonable to assume that passing shot winners are more frequent (relative to the number of net approaches), and perhaps that volleys are more aggressive, resulting in more first-volley winners and first-volley errors. More powerful and precise strokes should, on balance, make net points shorter than they used to be.

We can begin to test these theories using the extensive shot-by-shot records assembled by the Match Charting Project (MCP). MCP data includes every men’s Wimbledon final and semi-final back to 1990, as well as many elite-level grass court matches from the 1970s and 80s. For the purposes of today’s study, I will use only Wimbledon semi-finals and finals, plus a handful of other grass court matches from 1970-89 to complement the sparser Wimbledon data. This way, we know we’re comparing the elites of various generations to one another.

Contemporary net approaches

Let’s start by looking at what happens in a 2010s Wimbledon’s men’s final or semi-final when a player approaches the net. I’m excluding serve-and-volley points, and will do so throughout. I’m also excluding approach shot winners, which are often little more than gestures in the direction of the net following a big shot. (Even when they’re not, it can be difficult for charters to distinguish between approach and non-approach winners.) Thus, we’re looking at about 1,250 net approaches in which the other player got his racket on the ball.

The ball came back almost 73% of the time, and on slightly more than half the points, the approaching player put his first volley (or smash, or whatever shot he needed to hit) in play. 19% of the points saw a second passing shot attempt put in play, and nearly 12% had a second net shot keep the point going. About 1 in 30 approach-shot points continued even longer, forcing the the netman to contend with a third pass attempt.

The following visualization is a Sankey diagram showing how these net points developed. “App” stands for approach, “Unret” for “unreturned,” “Pass1” for “first passing shot,” “V1” for “first volley,” and so on. Mouse over any region of the diagram for a brief summary of what it represents.

2010s Wimbledon Net ApproachesApps → Pass1 In: 72.6%Pass1 In → V1 In: 51.2%V1 In → Unret V1: 32.1%Unret V1 → App’er Wins: 32.1%Apps → Unret App: 27.4%Unret App → App’er Wins: 27.4%Pass1 In → Unret Pass1: 21.4%Unret Pass1 → App’er Loses: 21.4%V1 In → Pass2 In: 19.1%Pass2 In → V2 In: 11.6%V2 In → Unret V2: 8.4%Unret V2 → App’er Wins: 8.4%Pass2 In → Unret Pass2: 7.5%Unret Pass2 → App’er Loses: 7.5%V2 In → Rally Continues: 3.2%Rally Continues → App’er Loses: 1.9%Rally Continues → App’er Wins: 1.3%Apps: 100%Apps: 100%Unret App: 27.4%Unret App: 27.4%Pass1 In: 72.6%Pass1 In: 72.6%V1 In: 51.2%V1 In: 51.2%Unret Pass1: 21.4%Unret Pass1: 21.4%Unret V1: 32.1%Unret V1: 32.1%Pass2 In: 19.1%Pass2 In: 19.1%V2 In: 11.6%V2 In: 11.6%Unret Pass2: 7.5%Unret Pass2: 7.5%Unret V2: 8.4%Unret V2: 8.4%Rally Continues: 3.2%Rally Continues: 3.2%App’er Wins: 69.2%App’er Wins: 69.2%App’er Loses: 30.8%App’er Loses: 30.8%

There’s a lot of information in the graphic, and it may not be entirely intuitive, especially hindered by my clunky design. Each region is sized based on what fraction of points developed in a certain way. As the regions move toward the right side of the diagram, they as classified by whether the approaching player won the point. As we can see, in the 2010s sample, these approach shots resulted in points won about 69% of the time.

The golden era

To compare eras, we need more than just one decade’s worth of data. I separated the approach shots by decade (grouping together the 70s and 80s), and the most distinctive era turned out to be the 1990s, when Pete Sampras ruled the roost and many of his challengers were equally aggressive.

Far more points were opened with a serve-and-volley: almost 81% in the 1990s compared to 7% in this decade. Even with the server claiming the net so early and so often, there were still many more non-serve-and-volley net approaches two decades ago. Then, there were about 85 “other” net approaches per match; this decade, there have been about 27. Thus, it is reasonable to assume that the typical net approach started from a less favorable position. These days, players only approach when the point has developed in a particularly inviting way.

Here is another diagram, this one showing what happened following 1990s net approaches:

1990s Wimbledon Net ApproachesApps → Pass1 In: 65.5%Pass1 In → V1 In: 44.4%Apps → Unret App: 34.5%Unret App → App’er Wins: 34.5%V1 In → Unret V1: 23.9%Unret V1 → App’er Wins: 23.9%Pass1 In → Unret Pass1: 21.1%Unret Pass1 → App’er Loses: 21.1%V1 In → Pass2 In: 20.5%Pass2 In → V2 In: 10.7%Pass2 In → Unret Pass2: 9.8%Unret Pass2 → App’er Loses: 9.8%V2 In → Unret V2: 7.8%Unret V2 → App’er Wins: 7.8%V2 In → Rally Continues: 2.9%Rally Continues → App’er Loses: 1.8%Rally Continues → App’er Wins: 1.1%Apps: 100%Apps: 100%Unret App: 34.5%Unret App: 34.5%Pass1 In: 65.5%Pass1 In: 65.5%V1 In: 44.4%V1 In: 44.4%Unret Pass1: 21.1%Unret Pass1: 21.1%Unret V1: 23.9%Unret V1: 23.9%Pass2 In: 20.5%Pass2 In: 20.5%V2 In: 10.7%V2 In: 10.7%Unret Pass2: 9.8%Unret Pass2: 9.8%Unret V2: 7.8%Unret V2: 7.8%Rally Continues: 2.9%Rally Continues: 2.9%App’er Wins: 67.3%App’er Wins: 67.3%App’er Loses: 32.7%App’er Loses: 32.7%

It’s striking to see that, back when net play was much more common, with a master such as Sampras dominating our sample, net approaches were less successful than they are today, resulting in a 67% win rate instead of 69%. However, it’s tough to know how today’s players–even a confident aggressor like Roger Federer or a volleying wizard like Rafael Nadal–would fare if they came forward four times as much. Assuming they pick their spots wisely, their success rate would be lower than 69%. The only question is how much lower.

Contrary to my inital hypothesis, passing shots seemed to be higher-risk and higher-reward in the 1990s than in the 2010s. Two decades ago, only 65.5% of initial passing shot attempts were put in play (compared to 72.6% today), though nearly as many of those attempts resulted in winners (21.1% to 21.4%). It was the volleyers who were either more conservative or less powerful in the 1990s. Then, barely half of first volleys ended the point in the netman’s favor; now, the number is closer to 60%. Again, this could be because today’s players pick their spots more carefully, allowing them to hit easier first volleys.

The early days

We’ve seen how net approaches developed in the 1990s and the 2010s. It would be reasonable to assume that the 1980s (with several late ’70s matches thrown in) were like the 1990s, but more so. Instead, the results are more of a mixed bag, with some characteristics that look like the ’90s, and others that are closer to today’s numbers.

Here is the diagram:

1980s Wimbledon Net ApproachesApps → Pass1 In: 70.4%Pass1 In → V1 In: 48.9%Apps → Unret App: 29.6%Unret App → App’er Wins: 29.6%V1 In → Pass2 In: 26.1%V1 In → Unret V1: 22.8%Unret V1 → App’er Wins: 22.8%Pass1 In → Unret Pass1: 21.5%Unret Pass1 → App’er Loses: 21.5%Pass2 In → V2 In: 15.6%V2 In → Unret V2: 10.8%Unret V2 → App’er Wins: 10.8%Pass2 In → Unret Pass2: 10.5%Unret Pass2 → App’er Loses: 10.5%V2 In → Rally Continues: 4.8%Rally Continues → App’er Loses: 2.8%Rally Continues → App’er Wins: 2%Apps: 100%Apps: 100%Unret App: 29.6%Unret App: 29.6%Pass1 In: 70.4%Pass1 In: 70.4%V1 In: 48.9%V1 In: 48.9%Unret Pass1: 21.5%Unret Pass1: 21.5%Unret V1: 22.8%Unret V1: 22.8%Pass2 In: 26.1%Pass2 In: 26.1%V2 In: 15.6%V2 In: 15.6%Unret Pass2: 10.5%Unret Pass2: 10.5%Unret V2: 10.8%Unret V2: 10.8%Rally Continues: 4.8%Rally Continues: 4.8%App’er Wins: 65.2%App’er Wins: 65.2%App’er Loses: 34.8%App’er Loses: 34.8%

In the 1980s, nearly as many passing shot attempts were put in play as they are today, in contrast to the lower rate during the 1990s. First volleys are a similar story. When passing shot attempts came back, approaching players put a volley (or other net shot) back in the court about 70% of the time–similar numbers in the 1980s and 2010s, but a couple percentage points higher than in the 1990s.

What is different is what happened next. In the 1980s, if the approaching player put his first volley back in play, it came back again 53% of the time. That rate is one of the few clear trends over time: It fell to 46% in the 1990s, 45% in the 2000s, and 37% in the 2010s. As a result, the ’80s saw far more second volleys and points that extended even further, compared to more recent eras. The lack of first-volley putaways meant that net approaches only converted into points won about 65% of the time.

A cautious narrative

There is no simple explanation that accounts for all of these numbers, because we are not seeing the direct result of a single factor, like the shift from wooden rackets or to more topspin-friendly string. Technological changes certainly have an impact, but as soon as the balance between approacher and opponent shifts, players adjust their strategy accordingly.

For instance, the rate of points won on net approaches appears to have steadily increased, from 65% in the 1980s to 67% in the 1990s to 69% today. The first rise could be attributed to racket technology, which gave aggressors more power and control. But the second rise came over a time period in which string technology offered more help to defenders. The higher rate of approach points won isn’t because players are better at it, it’s because they picked their spots more carefully.

What we might focus on instead, then, is how much these diagrams look alike, even though they represent vastly different eras. While there isn’t exactly a net-approach-strategy equilibrium that has held through the decades, player decision-making has kept these rates from varying too wildly. If passing shot winners start going up, we’ll probably see even fewer approaches–with the remaining approaches in still more favorable moments–or a continued increase in the percentage of approaches to the backhand side. That’s another clear trend over the last few decades, but it’s a topic for another day.

Rather than succumbing to nostalgia and bemoaning the decline of net play, it’s better to celebrate the adaptability of tennis players at the highest level. While the game a whole has become more defensive, backcourt denizens from Bjorn Borg (94 approaches per charted grass-court match) to Novak Djokovic (21 approaches per match) have reminded us that adjustments work in both directions. With parameters such as technology, surface, and opponent skills constantly changing, we can’t expect winning strategy to remain the same.

Thanks to SankeyMATIC for making it easy to create the diagrams.

Economist: Cori Gauff announces herself at Wimbledon

At the Economist’s Game Theory blog, I wrote about Cori Gauff’s historic upset of Venus Williams:

IT IS hard to avoid the impression that the tennis world has witnessed a changing of the guard. On July 1st , the opening day of the 2019 Championships at Wimbledon, Cori Gauff, a 15-year-old American prospect, upset the five-times champion Venus Williams in straight sets. Ms Williams, aged 39, was not the highest-ranked player to fall on the first day of the tournament; that honour belonged to the reigning US Open champion, Naomi Osaka, the second seed. But no first-round winner has garnered more attention than Ms Gauff, whose youth causes her to establish new records every time she steps on court.

Read the whole thing.