Category: Forecasting

Monkeying Around With Rafael Nadal’s 19 Grand Slams

The gap is closing. With his marathon victory last night in the US Open final over Daniil Medvedev, Rafael Nadal is up to 19 career major titles, second only to Roger Federer, who holds 20. Lurking in third place is Novak Djokovic, with 16, who was favored at Flushing Meadows this year, but retired due to injury in the fourth round.

Just two weeks ago, Djokovic seemed to be the biggest threat to Federer’s place atop the leaderboard. Now, with Nadal only one back and Djokovic dealing with another round of physical problems, Rafa has the momentum. Federer, now 38 years old, appears increasingly unlikely to pad his own total.

In an attempt to foresee the future of the grand slam leaderboard, I built a straightforward algorithm last month to predict future major titles. In the spirit of baseball’s “Marcel” projection system, it aims to be so simple that a monkey could do it. It uses the bare minimum of inputs: final-four performance at the last two years’ worth of slams, and age. It trades some optimization in favor of simplicity and ease of understanding. The result is pretty darn good. You can review the algorithm itself and look at how it would have performed in the past in my earlier article here.

Solve for RN = 19 + x

Before the US Open, the algorithm seemed tailor-made to aggravate as many fanbases as possible. It predicted that, over the next five years, Djokovic would win four more majors, Nadal two more, and Federer none, leaving the big three in a tie.

One more slam in the books, and the numbers have changed. Here is the revised forecast, reflecting both Nadal’s 19th slam and his rosier outlook after adding another title to his list of recent results:

Player          Slams  Forecast  Total  
Rafael Nadal       19       3.5   22.5  
Roger Federer      20       0.3   20.3  
Novak Djokovic     16       3.5   19.5

Rafa is in line to improve his total by at least three slams. By the time he’s done, perhaps he will have left Djokovic and Federer in the dust, and we’ll be speculating about whether he’ll catch Serena Williams … or Margaret Court.

More forecasts

My basic algorithm allows us to generate future slam forecasts for any player with at least one major semi-final in the last two years. Keep in mind that I’m not forecasting career slam totals–I’m looking ahead to only the next five years. For the big three, I’m assuming we don’t need to worry about 2025 and beyond.

We have current projections for 18 players:

Player                 Forecast  
Novak Djokovic              3.5  
Rafael Nadal                3.5  
Daniil Medvedev             0.8  
Dominic Thiem               0.7  
Stefanos Tsitsipas          0.6  
Matteo Berrettini           0.5  
Hyeon Chung                 0.4  
Lucas Pouille               0.3  
Kyle Edmund                 0.3  
Roger Federer               0.3  
Grigor Dimitrov             0.1  
Marco Cecchinato            0.1  
Marin Cilic                 0.0  
Juan Martin del Potro       0.0  
Roberto Bautista Agut       0.0  
Kevin Anderson              0.0  
Kei Nishikori               0.0  
John Isner                  0.0

Most of these guys have only a single recent semi-final to their name, and the only thing to separate them is their age. It seems logical to be more optimistic about the future slam performance of Stefanos Tsitsipas (age 21) than that of Roberto Bautista Agut (age 31), even though the algorithm sees their results so far–one semi-final appearance in the last 12 months–as identical.

Five years means 20 slams, and you might notice that the above table doesn’t get close to accounting for all of them. The projections add up to 10.8 majors, leaving plenty of room for players who haven’t even qualified for the list–Alexander Zverev and Felix Auger-Aliassime come to mind. At the 2024 US Open, we’re sure to look back at our late-2019 prognostications and laugh.

Federer will keep his spot at the top of the game’s most important leaderboard for at least four more months. Djokovic will probably be the top pick in Melbourne, so Roger could well enjoy nine more months as the only 20-slam man. But you won’t need an algorithm–even a simple one–to identify the favorite at Roland Garros next year. Organized men’s tennis lasted over a century without a 20-time major champion. In less than a year, we could have two.

GOAT Races: Forecasting Future Slams With a Monkey

After Novak Djokovic won his 16th career major at Wimbledon this year, more attention than ever focused on the all-time grand slam race. Roger Federer has 20, Rafael Nadal has 18, and Djokovic is–by far–the best player in the world on the surface of the next two slams. This is anybody’s ballgame.

Forecasting tennis is hard, and that’s just if you’re trying to pick the results of tomorrow’s matches. Players improve and regress seemingly at random, making it difficult to predict what the ranking table will look like only a few months from now. Fans love to speculate about which of the big three will, in the end, win the most slams, but there are an awful lot of unknowns to contend with.

One can imagine some way to construct a crystal ball to get these numbers in a rigorous way. Consider each player’s age, his likely career length, his chances of injury, his recent performance at each of the four slams, his current ranking, the quality of the field on each surface, and probably more, and maybe you could come up with some plausible numbers. Or… what if we skip most of that, and build the simplest model possible?

Enter the monkey

Baseball statheads are familiar with the Marcel projection system, named after a fictional monkey because it “uses as little intelligence as possible.” Just three years of results and an age adjustment. It isn’t perfect, and there are plenty of “obvious” improvements that it leaves on the table. But as in tennis, baseball stats are noisy. For most purposes, a “basic” forecasting system is as good as a complicated one, and over the years, Marcel has outperformed a lot of models that are considerably more complex.

Let’s apply primate logic to slam predictions. First, I’m going to slightly re-cast the question to something a bit more straightforward. Instead of forecasting “career” slam results, we’re going to focus on major titles over the next five years. (That should cover the big three, anyway.) And in keeping with Marcel, we’ll use just a few inputs: slam semi-finals, finals, and titles for the last three years, plus age. Actually, we’re going to lop off a bit of the monkey’s brain right away, because slam results from three years ago aren’t that predictive. So our list of inputs is even shorter: two years of slam semi-finals, finals, and titles, plus age.

The resulting model is pretty good! For players who have reached a major semi-final in any of the last eight slams, it predicts 40% of the variation in next-five-years slam titles. Without building the hyper-complex, optimal model, we don’t know exactly how good that is, but for a forecast that extends so far into the future, capturing almost half of the player-to-player variation in slam results sounds good to me. Think of all the things we don’t know about the slams in 2022, let alone 2024: who is still playing, who gets hurt, who has improved enough to contend, which prospects have come out of nowhere, and so on. Point being, the best model is going to miss a lot, so we shouldn’t set our standards too high.

Follow the monkey

The two-years-plus-age algorithm is so simple that you can literally do it on the back of an envelope. For any player, count his semi-final appearances (won or lost), final appearances (won or lost), and titles at the last four slams, then do the same for the previous four. Then note his age at the start of the next major. Start with zero points, then follow along:

  • add 15 points for each semi-final appearance in the last four slams
  • add 30 points for each final appearance in the last four slams
  • add 90 points for each title in the last four slams
  • add 6 points for each semi-final appearance in the previous four slams
  • add 12 points for each final appearance in the previous four slams
  • add 36 points for each title in the previous four slams
  • if the player is older than 27, subtract 8 points for each year he is older than 27
  • if the player is younger than 27, add 8 points for each year he is younger than 27
  • divide the sum by 100

That’s it! Let’s try Djokovic. In the last four majors, he’s won three titles and made one more semi-final. In the four before that, he won one title. He’ll enter the US Open at 32 years of age. Here goes:

  • +60 (15 points for each of his four semi-finals in the last four slams)
  • +90 (30 points for each of his three finals in the last four slams)
  • +270 (90 points for each of his three titles in the last four slams)
  • +6 (6 points for his 2017 Wimbledon semi-final)
  • +12 (12 points for his 2017 Wimbledon final)
  • +36 (36 points for his 2017 Wimbledon title)
  • -40 (Novak is 32, so we subtract 8 points for each of the 5 years he is older than 27)

Add it all up, and you get 434. Divide by 100, and we’re predicting 4.34 more slams for Novak.

Next-level GOAT trolling

I promise, I went about this project solely as a disinterested analyst. I just wanted to know how accurate a bare-bones long-term slam forecast could be. My goal was not to make you tear your hair out. But hey, you were probably going to lose your hair anyway.

Here is the number of slams that the model predicts for the big three between the 2019 US Open and 2024 Wimbledon:

  • Djokovic: 4.34
  • Nadal: 2.22
  • Federer: 0.26

You probably don’t need me to do the math for the next step, but you know I can’t not do it. Projected career totals:

  • Djokovic: 20.34
  • Federer: 20.26
  • Nadal: 20.22

Or, since we live in a world where you can’t win fractional majors:

  • Djokovic: 20
  • Federer: 20
  • Nadal: 20

Ha.

Back to the model

Djokovic’s forecast of 4.34 is quite high, in keeping with a player who has won three of the last four majors. For each year since 1971, I calculated a slam prediction for every player who had made a major semi-final in the previous two years–a total of more than 800 forecasts. Only 14 of those forecasts were higher than 4.34, and several of those belonged to the big three. Here are the top ten:

Year  Player         Age   Predicted  Actual     
2008  Roger Federer   26        6.38       5     
2007  Roger Federer   25        5.86       7     
2016  Novak Djokovic  28        5.20       6  *  
2005  Roger Federer   23        4.91      11     
2011  Rafael Nadal    24        4.89       5     
2006  Roger Federer   24        4.86      10     
2017  Novak Djokovic  29        4.79       4  *  
2012  Novak Djokovic  24        4.68       8     
1989  Mats Wilander   24        4.65       0     
1988  Ivan Lendl      27        4.56       2

* actual slam counts that could still increase

All of these predictions are based on data available at the beginning of the named year. So the top row, 2008 Federer, is the forecast for Federer’s 2008-12 title count, based on his 2006-07 performance and his age entering the 2008 Australian. Had the model existed back then, it would have guessed he’d win a half-dozen slams in that time period. He came close, winning five.

There will be plenty of noise at the extreme ends of any model like this. At the beginning of 2005, the algorithm pegged Federer to win “only” five of the next twenty majors. Instead, he won 11. I can’t imagine any data-based system would have been so optimistic as to guess double digits. On the flip side, the 1989 edition of the monkey would’ve been nearly as hopeful for Mats Wilander, who was coming off a three-slam campaign. Sadly for the Swede, a gang of youngsters overtook him and he never made another major final.

Let’s also take a look at the next 10 rosiest forecasts, plus the current guesstimate for Djokovic:

Year  Player          Age  Predicted  Actual     
2010  Roger Federer    28       4.48       2     
1981  Bjorn Borg       24       4.47       1     
1996  Pete Sampras     24       4.47       6     
1975  Jimmy Connors    22       4.45       2     
Curr  Novak Djokovic   32       4.34       0  *  
1980  Bjorn Borg       23       4.28       3     
2013  Novak Djokovic   25       4.24       7     
2009  Roger Federer    27       4.20       4     
1995  Pete Sampras     23       4.16       7     
2009  Rafael Nadal     22       4.12       8     
1979  Bjorn Borg       22       4.09       5

Plenty more noise here, with outcomes between 0 and 8 slams. Still, the average result of the 10 other predictions on this list is 4.5 slams, right in line with our forecast for Novak.

Missing slams…

The model expects that the big three will win around seven of the next twenty slams. You might reasonably wonder: What about the other thirteen?

The monkey only considers players with a slam semi-final in the last eight majors, so the forecasts shouldn’t add up to 20. There’s a chance that the champions in 2023 and 2024 aren’t yet on our radar, and many young names of interest to pundits these days, like Alexander Zverev, Felix Auger Aliassime, and Daniil Medvedev, haven’t yet reached the final four of a major. Here are the players for whom we can make predictions:

Player                 Predicted Slams  
Novak Djokovic                    4.34  
Rafael Nadal                      2.22  
Dominic Thiem                     0.71  
Stefanos Tsitsipas                0.63  
Hyeon Chung                       0.38  
Lucas Pouille                     0.31  
Kyle Edmund                       0.30  
Roger Federer                     0.26  
Juan Martin del Potro             0.19  
Marco Cecchinato                  0.06  
----------------                  ----  
TOTAL                             9.40

(The five other players with semi-final appearances since the 2017 US Open are forecast to win zero slams.)

Yeah, I know, Lucas Pouille and Hyeon Chung aren’t really better bets to win a slam than Federer is. But they are (relatively) young, and the model recognizes that many players who reach slam semi-finals early in their careers are able to build on that success.

More to the point, we’re leaving a lot of majors on the table. If the overall forecast is correct, that list of players will win fewer than half of the next 20 slams, leaving at least ten championships to players who have yet to win a major quarter-final.

…and age

Remember, I retro-forecasted every five-year period back to 1971-75. Over the 44 five-year spans starting each season between 1971 and 2014, the model typically predicted that the players it knew about–the ones who had reached slam semi-finals in the last two years–would win 13 of the next 20 slams. In fact, those on-the-radar players combined to win an average of 12 majors in the ensuing five-year spans.

Only in the last few years has the total number of predicted slams fallen below 10. The culprit is age: Recall that every forecast has an age adjustment, and we subtract 8 points (0.08 slams) for each year a player is older than 27. That’s a 0.4-slam penalty for both Djokovic and Nadal, and it’s 0.8 slams erased from Federer’s future tally. Thus, the model predicts that the big three are fading, and there aren’t many youngsters (like Pouille and Chung) on the list to compensate.

How you interpret these big three forecasts in light of the “missing” slams depends on a couple of factors:

  • Has the aging curve for superstars has changed? Is 30 the new 25; 32 the new 27?
  • Will the next few generations of players soon be good enough to topple the big three?

There’s plenty of evidence that the aging curve has changed, that we should expect more from 30-somethings these days than we did in the 1980s and 1990s. That would close much of the gap. Let’s say we set the new peak age at 31, four years later than the men’s Open Era average of 27. That would add 0.32 slams to every player’s forecast, possibly adding one more slam to each of the big three’s forecasted total. Overall, it would add a bit more than an additional three slams to the total of the the previous table, putting that number close to the historical average of 13.

Shifting the age adjustment doesn’t disentangle the big three, though, because it affects them all equally. It just means a three-way tie at 21 is a bit more likely than a three-way tie at 20.

The second question is the more important–and less predictable–one. It’s hard enough to know how well a single player will be competing in three, four, or five years. (Or, sometimes, tomorrow.) But even if we could puzzle out that problem, we’d be left with the still more difficult task of predicting the level of competition. Entering the 2003 season, the monkey would have opined that the then-current crop of stars–men who made slam semis in 2001 and 2002–would account for a combined 13 majors between 2003 and 2007. That included 2.5 for Lleyton Hewitt, plus one apiece for Thomas Johansson, Albert Costa, Pete Sampras, Marat Safin, David Nalbandian, and Juan Carlos Ferrero. Those seven men won only two. The entire group of 20 players who merited forecasts entering the 2003 Australian Open won only three.

We’ll probably never establish exactly how strong that group was in comparison with other eras. What we know for sure is that none of those men were as good as Federer in 2003-05, and by the end of the five-year span, they’d been shunted aside by Nadal as well. (Only Nalbandian ranked in the 2007 year-end top ten.) The generation of Zverev/Tsitsipas/Auger-Aliassime/etc won’t be as good as peak Big Four, but the course of the next 20 slams will depend a lot more on those players that it will on the (relatively) more predictable career trajectories of Djokovic, Federer, and Nadal.

So we’re left with a stack of known unknowns and error bars wider than a shanked Federer backhand. But based on what we do know, the top of the all-time slam leaderboard is going to get even more crowded. At least, that’s what the monkey says.

New Feature: Forecasting the Next Major

I’ve added a pair of new pages to Tennis Abstract, both of which will be updated weekly:

I know many of you are avid followers of the ATP and WTA forecasts accessible each week from the Tennis Abstract front page. We’re still several weeks from the US Open, but it’s interesting to see how the men’s and women’s fields are shaping up for that tournament, as well.

Each week, I’ll generate an updated report by constructing a hypothetical 128-player field, consisting of the top 128 players in the official rankings. Of course, that isn’t exactly what the field will look like, but it would be a fool’s errand to predict qualifiers at this point. And for the purposes of simulating the top of the draw, where most of the interest in, the specific players making up the last 20 or 30 names in the bracket don’t have too much of an effect.

Then we run 100,000 simulations of the 128-player field, using the most current surface-weighted Elo ratings. It’s the same way that I run my live forecasts. The only difference is that some of the player ratings will change between now and then. The US Open forecast a month from now will probably be better than anything we come up with today, but especially for the top names in each field, we have a pretty good sense of their relative strength at this point.

The early men’s US Open forecast shows a field that is just about as lopsided as you’d expect. Novak Djokovic is the favorite, at about 35%, which is often the degree to which my forecasts favor the best man in a hard-court major field. Roger Federer is a close second, at 29%, with Rafael Nadal coming third, at 18%. Dominic Thiem and Kei Nishikori are the only other men above 2%, and only five more–including Juan Martin del Potro, who is injured and will not play–with better than a 1-in-100 chance.

The women’s forecast looks very different. Ashleigh Barty is a strong favorite, with a 25% chance of claiming the title, despite her early exit at Wimbledon. Simona Halep is next at 14%, and after Karolina Pliskova, Petra Kvitova, and Elina Svitolina, defending champ Naomi Osaka comes in 6th with a 1-in-20 shot. 12 women have a 2% or better chance of winning, and seven more are at 1% or above, including the probably-unseeded Victoria Azarenka.

The early forecasts also give us another way of keeping tabs on probable seedings, as players make their final attempts to break into the top 32 before the bracket is set. On the women’s side, Maria Sakkari looks to be the least deserving of protected draw placement, with only a 58% chance of advancing to the second round and a mere 32% shot of living up to her seed and reaching the final 32.

Still, those numbers are better than the ones facing Laslo Djere, a player who may hang on to a seed on the strength of some solid clay-court performances. He has only a one-in-three chance of winning his first match, and less than a 10% shot of reaching the third round. For both Sakkari and Djere, the seeds are among the few advantages they have. If they fall out of the top 32 before the US Open draw ceremony, their chances will fall even further.

I hope you enjoy these new reports. I’ll update them every Monday, and when the US Open is behind us, we can use them to get a head start on the road to Melbourne.

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.

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.

A History of Wide-Open French Open Women’s Draws

For the last few years, we’ve been hearing a lot about “depth” in women’s tennis. No player has emerged as a dominant force since Serena Williams began her maternity leave after the 2017 Australian Open. On yesterday’s podcast, I argued that this year’s French Open felt particularly wide-open, especially after seeing a Rome final contested between Karolina Pliskova and Johanna Konta, two women who aren’t known for their clay-court prowess.

When the tape stopped rolling, I generated a forecast for the tournament, using surface-specific Elo ratings for a field made up of the top 128 women in the official rankings. (The makeup of the actual draw will differ, but the exact qualifiers and wild cards typically don’t affect the results very much.) Reigning champ Simona Halep comes out on top, with a 22.2% chance of defending her title. Petra Kvitova is next, just above 10%, followed by Kiki Bertens, who narrowed missed double digits.

The forecast gives two more entrants a 5% chance at the title, five more a 3% or better probability, and another nine a 1% chance. That’s a total of 19 women (see below) with at least a 1-in-100 shot, including such underdogs as Anett Kontaveit and Petra Martic. Maria Sakkari, winner in Rabat and semi-finalist in Rome, is 20th favorite, just below the 1% threshold. There isn’t much to separate the players in the bottom half of this list, and when the draw dishes out shares of good and bad fortune, the order will surely shift.

This all seems … pretty wide-open. It’s certainly a shift from the French Open of 30 years ago, when a dominant Steffi Graf entered with a 68% probability of securing the title, one of only five players with better than a 1% chance. (The tennis gods scoffed at our future retro-forecasts: Arantxa Sanchez Vicario carried her 1.5% pre-tournament odds to the championship.)

The 19-strong gang of one-percenters is, indeed, a very recent development. In the previous 30 years, the average number of players going into the tournament with 1%-or-better title odds was 11.5, and it only reached 19 three times, two of which were 2017 and 2018. (The other was 2010, with a whopping 23 one-percenters, and not a single player above a 13% chance of winning.) As recently as 2004, only eight women had reason to be so optimistic before the first balls were struck.

The second-tier group of favorites–entrants with a 1% shot at the title, but not much more–is the most distinctive feature of recent French Opens, and it lends credence to the argument that women’s tennis is particularly deep these days. You may not take the chances of 17th-seeded Kontaveit too seriously, but she is more a factor than similarly-seeded players 15 years ago.

When we narrow our focus to competitors meeting higher thresholds, like 3% or 5% title-winning probabilities, the present era looks less novel. From 1989 to 2018, the typical field included 6.5 women with 3%-or-better chances, and 4.8 women at 5% or higher. This year’s group includes ten in the first category and five–roughly the historical average–in the second. Only the army of one-percenters sets the 2019 bracket apart from, say, the 1997 field, when nine women headed to Paris with a 3% shot, seven of them at 5% or better.

What has changed is the dominance of the player at the top of the list. The average favorite of the last three decades opened with a one-in-three chance of winning, while Halep hasn’t exceeded 23% in her three years as frontrunner. Here are the ten “weakest” Roland Garros favorites from 1989 to 2019:

Year  Favorite            Fave Odds     
2010  Venus Williams          12.9%     
2018  Simona Halep            19.1%  *  
2011  Caroline Wozniacki      22.0%     
2019  Simona Halep            22.2%     
2017  Simona Halep            23.0%     
2006  Justine Henin           23.3%  *  
2005  Justine Henin           23.4%  *  
2012  Victoria Azarenka       24.1%     
2008  Maria Sharapova         24.5%     
2009  Dinara Safina           24.7%

* Favorites who went on to win

The French Open has traditionally made the women’s field look deep, even when it wasn’t particularly so. The favorite has only claimed the trophy in 8 of the last 30 tournaments, a 27% mark that would almost qualify for the above list. Sanchez Vicario twice won with sub-2% pre-tourney odds, Anastasia Myskina’s 2004 title was a 0.8% shot, and Jelena Ostapenko entered the 2017 event as 27th favorite, behind Mona Barthel and Katerina Siniakova, with a 0.4% probability of winning.

Surprises, then, have always been part of the program in Paris. Without an overwhelming force at the top of the draw with a “1” next to her name, the field has finally caught up. No individual has a particularly good chance of going on a victory tour, but a staggering array of contenders have reason to hope for a magical fortnight.

–

The complete list of “favorites” sorted by chance of winning: Halep, Kvitova, Bertens, Pliskova, Ashleigh Barty, Angelique Kerber, Elina Svitolina, Caroline Wozniacki, Garbine Muguruza, Naomi Osaka, Sloane Stephens, Marketa Vondrousova, Madison Keys, Konta, Serena, Kontaveit, Caroline Garcia, Victoria Azarenka, and Martic.

Forecasting Future Felix With ATP Aging Patterns

Italian translation at settesei.it

It’s been an exceptional six weeks for Felix Auger-Aliassime. He broke into the top 100 with a runner-up performance on clay in Rio de Janeiro, won two matches each at Sao Paulo and Indian Wells (including an upset of Stefanos Tsitsipas), and raced to a semi-final at the Miami Masters, the youngest player ever to make the final four of that event. Four months away from his 19th birthday, his ranking is up to 33rd in the world, and he has few points to defend until June.

Felix is the youngest man in the top 100, and he’s reaching milestones early enough to draw comparisons with some of the best young players in the sport’s history. Will he follow in the footsteps of past wunderkinds such as Rafael Nadal and Lleyton Hewitt? To answer that question, let’s take a look at typical ATP aging patterns, what they say about when players hit their peaks, and what they can show us about the fate of the best 18 year olds.

The standard curve

Last week, I looked at WTA aging curves and found that women tend to peak around age 23 or 24, an age that has not changed even as the sport has gotten older. I also discovered that there is a surprisingly modest gap–about 70 Elo points–between 18-year-old performance and a woman’s peak level. The men’s results are different.

To calculate the average ATP aging curve, I found over 700 players who were born between 1960 and 1989 and played at least 20 tour-level, tour qualifying, or challenger-level matches in each of five seasons. Overall, peak age was 25, though the difference from age 24 to 27 is only a few Elo points, so small as to be negligible.

As the tour has gotten older, the men’s peak age has also increased. Of the nearly 300 players born between 1980 and 1989, peak age is 26-27, with ages 28 and 29 also within 10 Elo points of the age 26-27 peak. Plenty of players are peaking at older ages, and many of those who aren’t are remaining close to their best levels into their late twenties. The peak age could be even higher still–a few of the players in the 1980-89 cohort turn 30 this year, and could conceivably still improve on their career bests.

The following graph shows the trajectory of the average player (with peak year-end Elo set to 1,850) born in the 1960s and the pattern of the average player born in the 1980s:

It’s a long ascent from the performance level at age 18 to the typical peak, especially for more recent players. There’s even a hefty bit of selection bias that should inflate the level of 18 year olds, since only about 10% of the players in the overall sample qualified for a year-end Elo rating when they were 18. The ones who did were, in general, the best of the bunch.

Felix forward

Through the Miami semi-final, Auger-Aliassime’s Elo rating is 1,848. The average player in the entire dataset who played at least 20 matches in their age-18 season went on to add another 281 Elo points to their rating between the end of their age-18 season and their peak. In the narrower, more recent cohort of 1980-89 births, the players with year-end ratings as 18 year olds improved their Elos by a whopping 369 points before reaching their peaks.

Adding either of those numbers to Felix’s current rating gives us quite the rosy forecast:

Cohort   Current  Increase  Proj. Peak  
1960-89     1848       281        2129  
1980-89     1848       369        2217

There’s a bit of slight of hand in how I’m doing this, since my study uses players’ year-end ratings, and I’m using Felix’s rating in April. However, there’s no natural law that says one artificial 12-month span is better than another, and Felix’s current age of 18.6 is roughly in the middle of the ages of the year-end 18-year-olds with whom I’m comparing him.

An Elo rating of 2,129 would be good enough for fourth place on the current list, behind only the big three. The rating of 2,217 is better than any of the big three can boast at the moment, and would be the fourth-best peak year-end rating among active players, again trailing only the big three. (And Andy Murray, if you consider him active.) Only 15 Open era players have managed year-end Elo peaks above 2,217.

No comparisons

It’s tough to say whether this method, of finding the typical difference between 18-year-old and peak Elo ratings, is adequate to handle the extremes. Some players peak earlier than average, and it stands to reason that the best young talents are more likely to do so. Boris Becker posted a whopping 2,212 Elo rating at the end of his age-18 season, which didn’t leave much room for improvement. He gained another 90 points before the end of his age-19 season, which was his career best.

Becker’s career path is not particularly helpful to our effort to forecast Felix’s, in part because the German was so unique, and also because his experience reflects such a different era. But even among less unique players, there are few useful comparables. No one born since 1987 managed a better age-18 Elo rating than Felix’s 1,848, and only a handful of active or recently-retired players even reached 1,750 by that age.

Lacking the data for a more precise approach, let’s repeat what I did for Bianca Andreescu last week, and see how the nearest 18-year-old comparisons fared. Of the players whose age-18 year-end Elos were closest to Felix’s 1,848, here are the 10 above him and the 10 below him on the list:

Player               BirthYr  18yo Elo  Incr  Peak Elo  
Stefan Edberg           1966      1916   350      2266  
John Mcenroe            1959      1912   496      2408  
Guillermo Coria         1982      1909   145      2055  
Pat Cash                1965      1907   151      2058  
G. Perez Roldan         1969      1884    41      1925  
Andy Murray             1987      1878   465      2343  
Roger Federer           1981      1871   487      2359  
Thomas Enqvist          1974      1865   216      2081  
Rafael Nadal            1986      1862   452      2314  
Jim Courier             1970      1849   283      2132  
…                                                       
Jimmy Brown             1965      1834     0      1834  
Andy Roddick            1982      1815   291      2106  
Aaron Krickstein        1967      1812   246      2058  
Yannick Noah            1960      1812   299      2112  
Fabrice Santoro         1972      1805    85      1890  
Andreas Vinciguerra     1981      1803    16      1819  
Novak Djokovic          1987      1792   645      2436  
Sergi Bruguera          1971      1790   265      2055  
Thomas Muster           1967      1788   329      2117  
Dominik Hrbaty          1978      1779   133      1913

The average increase among this group is 270 Elo points, close to the overall average for players who qualified for a year-end Elo rating at age 18. The youngest members of this list are encouraging: the big four, Andy Roddick, and Andreas Vinciguerra. Most promising youngsters would happily take a two-in-three shot at having a career at the level of the big four.

Perhaps the best comparison for Felix is a player who didn’t quite make that list, Alexander Zverev. The 21-year-old German posted a year-end Elo of 1,768 as an 18 year old, and already boosted that number by more than 300 points at the end of his 2018 campaign. Zverev is only an approximate comparison, he’s just a single data point, and we don’t know where he’ll end up, but his experience is a decade more recent than those of Novak Djokovic, Murray, and Nadal.

Forecasting the career performance of young tennis players is an inexact science, at best. Potential outcomes for Auger-Aliassime range from teenage flameout to double-digit major winner. Based on the limited information he’s given us so far, the latter seems within reach. What we know for sure is that he’s playing better tennis than any 18 year old we’ve seen in a decade. If that’s not reason for optimism, I don’t know what is.

Nick Kyrgios is More Predictable Than We Think

Italian translation at settesei.it

There is a persistent belief among tennis fans and commentators that some players are particularly inconsistent. For today’s purposes, I’m talking about match-to-match results, the players who have a knack for upsetting higher-ranked opponents but are also particularly susceptible to losses against weaker players. We have a range of words for this, like unpredictable, dangerous, tricky, and the preferred term for Nick Kyrgios: mercurial.

So far in 2019, Kyrgios has provided a perfect example of the inconsistent type. After early losses to Jeremy Chardy and Radu Albot, he bounced back to win last week’s ATP 500 in Acapulco, knocking out Rafael Nadal, Stan Wawrinka, John Isner, and Alexander Zverev. There’s no question that the Australian possesses more talent than his ranking would suggest. This is a guy who has yet to crack the top ten, but holds a .500 record in completed matches against the Big 3, a feat managed by no other active player (minimum 5 matches, excepting Nadal and Novak Djokovic themselves).

He sounds inconsistent. His results look unpredictable. But compared to the uncertainty that comes with every tennis match between highly-ranked professionals, how does he stack up? As my headline suggests, it’s not as clear-cut as it seems.

Measuring predictability

Consider the opposite type, a player who reliably beats lower-ranked opponents and usually loses against his betters. Roberto Bautista Agut has this type of reputation. As we’ll see, the numbers bear it out, notwithstanding his Doha upset of Djokovic a couple of months ago. If someone really is so predictable, that should show up in a comparison of his pre-match forecasts to his results. For a Bautista Agut type, the forecasts would be particularly accurate, while for a Kyrgios type, the forecasts would be much less reliable.

We already have a metric for this. Brier Score measures the accuracy of forecasts, considering not just how often predictions proved correct, but how close they came. For instance, after Kyrgios beat Zverev in Saturday’s Acapulco final, those prognosticators who gave the Aussie a 90% chance of winning were “more” correct than those who gave him a 60% shot. On the other hand, too much confidence runs the risk of a worse Brier Score–if you’re always giving tennis favorites a 90% chance of winning, you’ll often be wrong. Brier Score is the average of the squared difference between the pre-match forecast (e.g. 90%) and the result (1 or 0, depending if the pick was correct).

Brier Scores for ATP forecasting hover around the 0.2 mark. A lower Brier Score is better, representing less difference between prediction and results, so if you can come in much lower than 0.2, you should be making money betting on matches. If you’re much higher than 0.2, you might as well be flipping a coin. If we use random, 50/50 pre-match predictions, the resulting Brier Score is 0.25.

Brier-gios

If a player is truly unpredictable, the Brier Score for his matches should approach the 0.25 mark, and it should definitely exceed the tour-typical 0.2. To measure the reliability of pre-match forecasts for Kyrgios and other players, I used my surface-weighted Elo ratings for every completed tour-level main draw match since 2000 and generated percentage forecasts for each one. By this method, Zverev had a 67.4% probability of winning the Acapulco final.

So far in 2019, Kyrgios does look truly unpredictable. The Brier Score of his ten match results is 0.318, meaning that we’d have done better by simply flipping a coin to forecast the result of each of his matches. Even if we retroactively increase his chances of winning each match to account for the fact that he’s playing better than his Elo rating predicted, the Brier Score is 0.277, still worse than coin flips.

On the other hand, it’s just ten matches. Several other players have 2019 Brier Scores well over the 0.25 threshold, including Frances Tiafoe, Joao Sousa, Juan Ignacio Londero, and Felix Auger Aliassime. In a handful of tournaments, you’ll always get a few oddball results, either because of marked improvements (as is likely with Auger Aliassime) or extreme good or bad luck. Unless we’re willing to say that Sousa and Londero are remarkably unpredictable players, we shouldn’t draw the same conclusion based on Kyrgios’s last ten matches.

What you predict is what you get

The Brier Score for Elo-based forecasts of Kyrgios’s career matches at tour level is 0.219. That’s higher–and thus less predictable–than average, but not by that much. Of the 280 players with at least 100 tour-level matches this century, Kyrgios ranks 84th, more reliable than 30% of his peers. In 2017, his results were quite unpredictable, with a Brier Score of 0.244, but in 2015 and 2016 they generated a more pedestrian 0.210, and last year they looked downright predictable, at 0.177.

The Australian may be quite unpredictable in tactics, point-to-point performance, or on-court behavior, but his results just aren’t that unusual. The following table shows the 15 most unpredictable active players, as measured by Brier Score, along with Kyrgios, followed by the 15 most predictable active players:

Player                 Matches  Brier  
Lucas Pouille              189  0.247  
Andrey Rublev              106  0.245  
Benoit Paire               377  0.239  
Ivo Karlovic               650  0.239  
Stefanos Tsitsipas         100  0.232  
Karen Khachanov            154  0.231  
Peter Gojowczyk            102  0.231  
Federico Delbonis          225  0.227  
Marius Copil               108  0.227  
Damir Dzumhur              173  0.227  
Ernests Gulbis             420  0.226  
Pablo Cuevas               338  0.226  
Mischa Zverev              297  0.226  
Joao Sousa                 323  0.226  
Borna Coric                210  0.226  
...                                       
Nick Kyrgios               191  0.219  
...                                       
Matthew Ebden              171  0.188  
David Goffin               344  0.188  
Marin Cilic                684  0.186  
Richard Gasquet            770  0.183  
Tomas Berdych              911  0.182  
Milos Raonic               448  0.178  
David Ferrer              1048  0.177  
Jo Wilfried Tsonga         600  0.175  
Roberto Bautista Agut      384  0.172  
Kei Nishikori              517  0.167  
Juan Martin Del Potro      560  0.160  
Andy Murray                802  0.146  
Roger Federer             1350  0.121  
Novak Djokovic             951  0.117  
Rafael Nadal              1060  0.114

Lucas Pouille’s results have been almost impossible to forecast. The Brier Score generated by his 2018 results was nearly 0.3, suggesting it would have been smarter to calculate a forecast and then bet against it! Ivo Karlovic also shows up among the less reliable players, though it’s not clear whether that’s due to his unusual game style. Isner, the only decent parallel we have, is as reliable as the tour in general, with a career Brier Score of 0.201. Reilly Opelka, the other towering ace machine in the ATP top 100, has defied the odds so far in 2019, but he hasn’t yet amassed enough data to draw any conclusions.

At the other end of the spectrum, the most reliable players are many of the best. That adds up: A dominant player not only wins most of the matches he should, but his performance also allows us to make more aggressive forecasts. Nadal often enters matches with a 90% or better probability of winning, and confident predictions like that–as long the player converts them into wins–are what generate the lowest Brier Scores.

Consistent consistency results

We all tend to read too much into unusual results. Kyrgios has given us plenty of those, and we’ve repaid the favor by making him out to be even more of a wild card than he is. A couple of weeks ago, I took on a similar question and found that ATPers don’t really “play their way in” to tournaments, earning better or worse results in different rounds. This isn’t quite the same issue, but it all comes back to similar truths: Existing forecasts are pretty good, there’s always going to be a lot of randomness in the results, and the stories we invent to account for the randomness don’t really explain much at all.

Kyrgios is an immensely interesting player–I joked in yesterday’s podcast that readers should prepare themselves for a ten-part series–and digging into his point-by-point stats could reveal characteristics that are unique among tour players. That is still true. But at the match level, the likelihood that his contests will end in upsets isn’t unique at all–even if he is the proud new owner of a sombrero that says otherwise.

The Best Draw That Money Can Buy

Italian translation at settesei.it

Last week featured two events on the WTA calendar. First, both chronologically and by every conceivable ranking except for “most Hungarian,” was the Dubai Open, a Premier 5 event offering over $500,000 and 900 ranking points for the winner. The other was the Hungarian Open in Budapest, a WTA International tournament with $43,000 and 280 ranking points going to the champion. No top player would seriously consider going to Budapest, even before considering potential appearance fees and WTA incentives.

Fifteen of the top twenty ranked women went to Dubai, and the top seed in Budapest, defending champ Alison Van Uytvanck, was ranked 50th. Every Budapest entrant ranked in the top 72 got a top-eight seed, including a couple of players who would have needed to play qualifying just to earn a place in the Dubai main draw.

The rewards offered by the Dubai event and supported by the structure of the WTA tour make this an easy scheduling decision for many players. But at some point, if the rest of the field is zigging toward the Gulf, might it be better to zag toward Central Europe? Van Uytvanck would have been an underdog to reach even the third round of the richer event, yet she defended her title in Budapest. Marketa Vondrousova, who would have been stuck in Dubai qualifying, reached the Hungarian Open final. Opting for the smaller stage almost definitely proved the wise choice for those two women. Did other, better-ranked players leave money or ranking points on the table?

Motivations

Scheduling decisions depend on a lot of factors. Some women might prefer to play the event with the highest-quality field, both to test themselves against the best and to give themselves an opportunity for the circuit’s richest prizes. Others might head for the marquee events because of their doubles prowess: Timea Babos was part of the top-seeded doubles team in Dubai, but was the lowest-ranked direct entry in singles. Still others might choose to play closer to home or at tournaments they’ve enjoyed in the past.

For all that, ranking points should come first, with prize money also among the top considerations. Ranking points determine one’s ability to enter future events and to remain on tour. Prize money is necessary to cover the vast expenses necessary to bankroll a traveling support staff.

Dubai-versus-Budapest offers a fairly “pure” experiment, because both are played on similar surfaces and neither event is in the middle of a mini-circuit of events in a single region. Yes, Dubai immediately follows Doha, but that trip requires a flight, and most players headed back to Europe or North America after the tournament. Opting for one event over the other doesn’t substantially complicate anyone’s travel plans, like it would for an ATPer to mix and match destinations from the South American golden swing and the simultaneous European indoor circuit.

Revealed preferences

Let’s see which of the two main factors played a bigger role in scheduling decisions last week. To determine each player’s options, I tried to reconstruct as much as possible what information each woman had at her disposal six weeks earlier, on January 7th, when entry applications and stated preferences for Dubai and Budapest were due. I used the January 7th rankings to project how a player would be seeded at either event, and Elo ratings as of that date to forecast how far she would advance in each draw.

The major difficulty of this kind of simulation is the composition of the draws themselves. From our vantage point after the events, we know who opted for each draw as well as which players were unable to compete. In early January, none but the best-connected players would have known which of her peers would head in which direction, and no one at all could have known that Caroline Wozniacki would be a late withdrawal from Dubai, or that a viral illness would knock Kirsten Flipkens out of the Hungarian Open. Still, the resulting 2019 draws were very similar to what players could have predicted based on the player fields in 2018. So to simulate each player’s options, we’ll use the fields as they turned out to be.

Let’s start with Carla Suarez Navarro, the highest-ranked woman (at the January 7th entry deadline) who wasn’t seeded in Dubai. She ended up reaching the quarter-finals at the Premier event, in part because Kristina Mladenovic did her the favor of ousting Naomi Osaka from that section of the draw. For her efforts, Suarez Navarro grabbed 190 ranking points and almost $60,000. She would have needed to win the Budapest title to garner more points. And with a champion’s purse of “only” $43,000 in Hungary, she would have needed to rob a bank to improve on her Dubai prize money check.

However, that isn’t what Suarez Navarro should have anticipated taking home from Dubai. Sure, she should be optimstic about her own potential, but smart scheduling demands some degree of realism. I ran simulations of both the Dubai tournament (before the draw was made, so she doesn’t always end up in Osaka’s quarter) and the Budapest event with the Spaniard as the top seed and the rest of the field (minus last-in Arantxa Rus) unchanged. These forecasts suggest that Suarez Navarro only had a 12% chance of reaching the Dubai quarters, and that her expected ranking points in the Gulf were much lower:

Event     Points  Prize Money  
Dubai         76     $28.121   
Budapest     111     $15.384

(prize money in thousands of USD)

In all of these simulations, I’ve calculated points and prize money as weighted averages. Suarez Navarro had a 37% chance of a first-round loss, so that’s a 37% chance of one ranking point and first-round-loser prize money. And so on, for all of the possible outcomes at each event. For the Spaniard, her expected ranking points were nearly 50% higher as the top seed in Budapest. But because the Dubai prize pot is so much larger, her expected check was almost twice as big at the tournament she chose.

Consistent incentives

The total purse in Dubai was more than eleven times bigger than the prize money on offer in Hungary, while the points differed by only a factor of three. Thus, it’s no surprise that Suarez Navarro’s incentives are representative of those faced by many more women. I ran the same simulations for 26 more players: All of the competitors who gained direct entry into Dubai but were unseeded, plus Bernarda Pera, who would have been seeded in Budapest but instead played qualifying in the Gulf.

The following table shows each player’s expected points and prize money for Dubai (D-Pts and D-Prize), along with the corresponding figures for Budapest (B-Pts and B-Prize):

Player                    D-Pts   D-Prize   B-Pts   B-Prize   
Dominika Cibulkova           96   $36.794     130   $18.291   
Lesia Tsurenko               84   $31.528     119   $16.695   
Carla Suarez Navarro         76   $28.121     111   $15.384   
Aliaksandra Sasnovich        75   $27.920     111   $15.364   
Dayana Yastremska            72   $26.716     107   $14.803   
Anastasia Pavlyuchenkova     72   $26.590     106   $14.721   
Barbora Strycova             67   $24.809     102   $14.096   
Donna Vekic                  66   $24.143     100   $13.717   
Katerina Siniakova           63   $23.157      95   $13.062   
Ekaterina Makarova           58   $21.543      90   $12.265   
                                                              
Player                    D-Pts   D-Prize   B-Pts   B-Prize   
Petra Martic                 57   $21.019      88   $11.960   
Su Wei Hsieh                 54   $19.863      84   $11.396   
Belinda Bencic               53   $19.813      84   $11.372   
Ajla Tomljanovic             53   $19.530      82   $11.181   
Shuai Zhang                  49   $18.350      77   $10.416   
Sofia Kenin                  46   $17.109      72    $9.659   
Ons Jabeur                   45   $17.077      71    $9.624   
Viktoria Kuzmova             45   $17.009      70    $9.432   
Alize Cornet                 44   $16.823      69    $9.280   
Saisai Zheng                 40   $15.436      62    $8.307   
                                                              
Player                    D-Pts   D-Prize   B-Pts   B-Prize   
Vera Lapko                   37   $14.618      57    $7.695   
Mihaela Buzarnescu           36   $14.465      56    $7.548   
Alison Riske                 35   $14.309      55    $7.445   
Kristina Mladenovic          34   $13.910      51    $6.969   
Timea Babos                  32   $13.354      48    $6.572   
Yulia Putintseva             32   $13.407      48    $6.484   
Bernarda Pera*               25   $11.830      36    $5.061

Every single player could have expected more points in Budapest and more money in Dubai. The ratios are all similar to Suarez Navarro’s. The one possible expection is Pera (hence the asterisk). My simulation assumed she came through qualifying to make the main draw, and calculated only her expected points and prize money from main draw matches. Yet simply qualifying for the main draw is worth 30 ranking points, plus whatever points a player earns by winning main draw matches. Pera was no lock to qualify, but she was favored, and usually a couple of lucky loser spots make the main draw even more achieveable. It’s possible that if we ran all those scenarios, Pera is the one player for whom Dubai offered better hopes of prize money and points.

Loss aversion and game theory

It’s no accident that Van Uytvanck was one of the few players to choose the high-points, low-prize money route. She was defending 280 points from last year’s Hungarian Open, meaning that opting for a bigger check in Dubai would have a negative impact on her ranking. The thought of losing a couple hundred ranking points has a greater influence on behavior than the chance of gaining the same amount for a player who has few to defend.

For the majority of women who will face the same decision in 2020 without many points to defend, what should they do? Assuming, as I do, that they and their coaches will all carefully study this article, what happens if more top-70 players decide to chase ranking points and flock to the smaller event?

If the Budapest field gets stronger, each entrant’s expected points and prize money will decrease; if Dubai’s field weakens, each player there can anticipate a better chance of more points and even more money. As the entry system is currently structured, in which each player must state their preferences without knowledge of their peers’ choices, we can’t count on reaching an equilibrium. Even if every single player aimed solely to maximize ranking points, there wouldn’t be enough information available to reliably make the right choice. It’s conceivable, though unlikely, that a Budapest could attract a stronger field and end up offering lower expected prize money checks and ranking points.

But don’t fret, dear readers and schedule optimizers. There are external factors and there always will be. And in this case, virtually all of those factors pull players to the bigger money event. (Even Hungarian heroine Babos skipped her home tournament.) At least a half-dozen of the players listed above are doubles elites, making it likely they’ll choose the Premier event. Others–probably many others–will go where the money is, because they like money.

Even those who don’t play doubles and don’t like money will chase the biggest available pot of ranking points, not entirely unlike the way people play the lottery. The WTA offers a very limited set of opportunities to earn 900 points in a single week. You can get close to 900 points with three International championships, but there’s a finite number of weeks on the annual schedule–not to mention a limited number of matches in each player’s body! Lots of people stock up on lottery tickets despite unfavorable odds, and players will continue to enter higher-profile events even if their expected points are higher on smaller stages. The chance of a prestigious title, however slim, doesn’t show up in a purely actuarial calculation.

The success of Belinda Bencic–expected Dubai points, 53; expected Budapest points, 84; actual Dubai points, 900–will keep players chasing the big prizes. That’s good news for level-headed would-be optimizers. Those players willing to forego the skyscrapers, the shopping malls, and the prize money next year aren’t about to lose this opportunity. Budapest will almost certainly remain a better option for players who want to improve their ranking.

Dominic Thiem, Tennys Sandgren, and Playing Your Way In

Dominic Thiem is one of the best clay-court players on earth, with eight titles and a Roland Garros final to his credit. But his impressive track record wasn’t worth much last night, when he lost his opening-round match in Rio de Janeiro. The straight-set defeat to 90th-ranked Laslo Djere calls to mind other first-match failures, such as Thiem’s loss to Martin Klizan last summer in Hamburg, or his truly gobsmacking upset at the hands of 222nd-ranked Ramkumar Ramanathan on grass in Antalya two years ago.

It’s also not the first time this season that a top seed has proven unable to live up to their billing. Two weeks ago, the No. 1 seeds in three different ATP events all lost their first matches. I dug a bit deeper and discovered that top seeds underperform by a modest amount at these smaller tournaments. Rio is technically a higher-profile event, but the result is the same: An elite player at a non-mandatory event, heading home early.

You’ll hear all sorts of theories for this sort of thing. In ATP 250s, when top seeds get a bye, it’s possible that the elites are in danger because their opponents have played their way into form. At any optional events, it’s possible that the top seeds are not particularly motivated, making the trip for a quick appearance fee and nothing more. Finally, there’s the old saw that some competitors need to get used to their surroundings. In other words, they need to “play their way in” to the tournament. It’s this last theory that I’d like investigate.

Present and prepared

If a player needs time to get comfortable, we would expect him to underperform in the first round, and possibly continue playing below average to a lesser extent in the second round. The flip side of that is that the player would need to overperform in later rounds–if he didn’t, the earlier underperformance wouldn’t be below average, it would just be bad. These under- and over-performances are effects we can quantify.

Let’s start with Thiem. I went through his career results at the ATP level and broke his matches into several categories (some overlapping), like first match, second match, first match at a non-mandatory event, second-or-later match, finals, and so on. For each of those categories, I tallied up his results and compared them to expecatations (Expected Wins, or “ExpWins” in the table), based on what Elo forecasted at the time. Here are Thiem’s results:

Category     Matches  ExpWins  Wins  
1st              141     94.3    94  
1st (small)       84     52.9    54  
1st/2nd          238    151.3   151  
2nd               97     59.9    60  
2nd+             203    117.7   118  
3rd               58     34.9    35  
3rd+             106     60.7    61  
4th               32     18.5    19  
Finals            17     10.2    10

The Austrian has been almost comically predictable. In 84 non-mandatory tournaments through last week, Elo expected that he would win his first match 53 times. He won 54. In all tournaments, he has won his first match 94 times, exactly in line with the Elo estimation. In the nine categories shown here, his performances was never more than a 1.1 matches better or worse than expected. If he’s playing his way into tournaments, he’s doing it in a way that doesn’t show up in the results.

What about Tennys?

Thiem has suffered some rough early-round upsets, but over the course of his career, he’s usually ended up on the winning side. Maybe we’d do better to focus on a true feast-or-famine player, someone who more often loses his first-round encounters, but is dangerous when he advances further.

A great recent example of such a player is Tennys Sandgren. The American raced to the quarter-finals of last year’s Australian Open, reached a final in Houston, and won a title in Auckland to start the 2019 season. Other than that, he rarely turns up on the tennis fan’s radar. He acknowledged his inconsistency on a recent Thirty Love podcast, explaining from a player’s perspective why he thinks his results are so erratic. Like Thiem, he lost easily in an opening match last night, winning only four games against Reilly Opelka in Delray Beach.

Sandgren’s round-by-round results are less predictable than Thiem’s, but for an apparently extreme example of the go-big-or-go-home-early phenomenon, there’s not much support for it in the numbers. Because Sandgren has played fewer tour events than Thiem, I included his Challenger results before separating his matches into the same categories:

Category     Matches  ExpWins  Wins  
1st              124     64.7    62  
1st (small)      113     60.2    60  
1st/2nd          186     96.4    98  
2nd               62     31.7    36  
2nd+             120     60.3    63  
3rd               35     17.3    15  
4th               15      7.3     9  
Finals             8      4.2     3

The American has underperformed a bit in his first matches and beaten expectations in his second rounders, but the effect disappears after two matches are in the books. In any case, none of the over- or under-performances are even close to statistically significant. His extra first-match losses have about a one-in-three probability of happening by chance, and his bonus second-match wins would occur about one time in six. There could be something interesting going on here, but the effects are small, and it’s very likely that we’re seeing nothing more than randomness.

Positive results, anyone?

So far, we’ve investigated two players who seemed likely to over- or under-perform in certain groups of matches. Yet we found nothing. The “playing your way in” theory will surely survive this blog post, but let’s make sure there aren’t players who embody it, even if Thiem and Sandgren don’t.

I went through the same steps for the other 98 men in this week’s top 100, grouping their matches into categories, tallying up Elo-based expected wins and actual wins, and calculating the probability that their results–above or below expectations–are due to chance. The result is 1,043 player-categories, from Novak Djokovic’s finals to Pedro Sousa’s first matches. (The number of player-categories isn’t a round number because not every player has matches in every category, like 6th matches or finals.)

Of those 1,000 player-categories, only 29 meet the usual standard of statistical significance, in that there is less than a 5% chance they can be explained by randomness. A familiar example is Gael Monfils’s record in finals. Even with last week’s title in Rotterdam, his eight wins are outweighed by 21 losses. But such cases are extremely rare. Since fewer than 3% of the player-categories meet the 5% threshold, it’s wrong to say that these categories represent real trends (like, perhaps, a psychological basis for Monfils’s inability to win tournaments). When we test over one thousand groups of matches, dozens of them should look like outliers.

In other words, there’s no statistical support for the claim that certain players are more or less effective in certain rounds. It’s always possible that a very small number of guys have certain characteristics along these lines, but among the 29 player-categories with particularly unlikely results, only Monfils’s finals record fits any kind of narrative I’ve heard before. Richard Gasquet has won 120 times–11 more than expected–in first matches at non-mandatory events. That overperformance is just as unlikely as Monfils’s letdown in finals, so maybe we should be talking about how assiduously he prepares for the start of each tournament, no matter the stakes?

It’s always possible that the top men do, in fact, play their way into tournaments. But based on this evidence, it’s only the case if everyone rounds their way into form at approximately the same rate. Maybe first rounders are lower in quality than semi-finals. But if we’re interested in predicting outcomes–even Thiem’s first-round results against journeymen–we’d do better to ignore the theories. Opening matches just aren’t that unique, even for the players who think they are.