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.

Anatomy of Alex de Minaur’s Serving Masterclass

The ATP Atlanta event is typically packed with big servers. John Isner won five titles in six years between 2013 and 2018, during which time the only man to stop him was Nick Kyrgios–in two tiebreaks, naturally. The last champion before Isner took over was Andy Roddick. It’s a fast hard court and the weather is often scorching, so the tournament tends to be a week-long ace festival.

The 2019 titlist posted another wave of eye-popping service numbers, winning four matches without facing a single break point, and winning more than 90% of his first serve points in each match. Those positively Isnerian numbers didn’t belong to the big man himself, nor were they posted by heir apparent Reilly Opelka. The serve king in Atlanta this year was the “six-feet tall” (sure, buddy) Australian grinder, Alex de Minaur.

Unlike many of his peers, de Minaur doesn’t make his money with a big serve. In the last 52 weeks, both Isner and Opelka have hit aces on one-quarter of their serve points. The Aussie’s 52-week rate is a mere 4.5%. He posted a tour-level career best of 14.8% against Taylor Fritz in the Atlanta final (excluding a Bernard Tomic retirement), but failed to reach double digits in second round against Bradley Klahn, or in the semi-final against Opelka. Last week, de Minaur proved that there are a lot of ways to win serve points without necessarily piling up the aces.

Strike one

The easiest non-ace route to victory is the unreturned serve. Players don’t have the same level of control over the rate of unreturned serves that they do with aces. But many great serves are reachable–if not effectively returnable–so they don’t go down in the ace column. The unreturned-but-not-ace category was de Minaur’s bread and butter in Atlanta.

According to the point-by-point log of the final in the Match Charting Project dataset, Fritz put only 57% of the Aussie’s serves back in play. Across over 1,300 MCP-charted hard court matches from the 2010s, the ATP tour average is 70% returned serves, and de Minaur’s opponents have traditionally done even better than that. De Minaur’s unreturned-serve rate of 43% is exceptionally good, ranking in the 90th percentile of service performances. He was even better against Opelka. Only 5 of his 93 service points went for aces, but 38 more didn’t come back. That’s an unreturned-serve rate of 46%, a 94th-percentile-level showing.

Strike two

De Minaur was even better when the serve wasn’t quite as good. Coaches and commentators like to talk about the “plus one” tactic: Hit a strong serve and get in position to make an aggressive play on whatever comes back. This is where the Aussie truly excelled in the title match.

In addition to the 43% of unreturned serves against Fritz, another 26% of his service points fell into the “plus one” category: second-strike shots that his opponent couldn’t handle. Tour average is 15%, and again, de Minaur hasn’t always been this good. His average over 15 charted hard-court matches in 2018 was only 12.6%. His 26% rate on Sunday ranks in the 98th percentile among charted hard-court matches. Of the 67 single-match performances on record that were better than 26%, 15 were recorded by Roger Federer. Most players never have such a good day in the plus-one category.

Strike three

Even the best servers have to deal with the occasional long rally. In our sample of charted hard-court matches, 40% of points see the returner survive the plus-one shot and put the ball back in play. From that point, the rally is more balanced, and returners win a bit more than half of points. (That’s partly because 4-shot rallies are more common than 5-shot rallies, and so on, and because a 4-shot rally, by definition, is won by the returner. Put another way, once you exclude 3-or-fewer-shot rallies, you bias the sample toward the returner; if you excluded 4-or-fewer-shot rallies, you would bias the sample toward the server, because 5-shot rallies make up a disproportionate amount of the remaining points.)

Serving like de Minaur did, he didn’t see nearly so many “long” rallies. 22% of his service points against Fritz, and 29% against Opelka, reached four shots. Facing the typical one-dimensional big server, this is the returner’s chance to even the score. But de Minaur is known more for his ground game than his service. In the final, he won 58% of these points, good enough for the 83rd percentile in our sample.

De Minaur’s performance on longer rallies didn’t really move the needle on Sunday, mostly because he so effectively prevented points from lasting that long. But the fact that he won more than half of the extended exchanges is a reminder that a great serving performance depends on more than just the serve. On a good day, even a six-footer can post numbers that leave Isner and Opelka in the dust. It isn’t always about the aces.

Podcast Episode 72: The Unbreakable Alex de Minaur, the Unfocused Alexander Zverev, and the Unaffiliated World Team Tennis

Episode 72 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, discusses the awkward position of World Team Tennis, which is loaded with stars but has a hard time succeeding outside the structure of the tennis tours. We ask whether tennis, which has become steadily more global, would connect better with its fans by shifting more focus to the local.

On court, they look at the spectacular serving performance of sub-six-foot Alex de Minaur, another disappointing loss for Alexander Zverev, and a shock comeback from Cedrik-Marcel Stebe.

Thanks for listening!

(Note: this week’s episode is about 62 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.

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.

Roger Federer Wasn’t Clutch, But He Was Almost Clutch Enough

Italian translation at settesei.it

The stats from the Wimbledon final told a clear story. Over five sets, Roger Federer did most things slightly better than did his opponent, Novak Djokovic. Djokovic claimed a narrow victory because he won more of the most important points, something that doesn’t show up as clearly on the statsheet.

We can add to the traditional stats and quantify that sort of clutch play. A method that goes beyond simply counting break points or thinking back to obviously key moments is to use the leverage metric to assign a value to each point, according to its importance. After every point of the match, we can calculate an updated probability that each player will emerge victorious. A point such as 5-all in a tiebreak has the potential to shift the probability a great deal; 40-15 in the first game of the match does not.

Leverage quantifies that potential. The average point in a best-of-five match has a leverage of about 4%, and the most important points are several times that. Another way of saying that a player is “clutch” is that he is winning a disproportionate number of high-leverage points, even if he underwhelms at low-leverage moments.

Leverage ratio

In my match recap at The Economist, I took that one step further. While Djokovic won fewer points than Federer did, his successes mattered more. The average leverage of Djokovic’s points won was 7.9%, compared to Federer’s 7.2%. We can represent that difference in the form of a leverage ratio (LR), by dividing 7.9% by 7.2%, for a result of 1.1. A ratio of that magnitude is not unusual. In the 700-plus men’s grand slam matches in the Match Charting Project, the average LR of the more clutch player is 1.11. Djokovic’s excellence in key moments was not particularly rare, but in a close match such as the final, it was enough to make the difference.

Recording a leverage ratio above 1.0 is no guarantee of victory. In about 30% of these 700 best-of-five matches, a player came out on top despite winning–on average–less-important points than his opponent did. Some of the instances of low-LR winners border on the comical, such as the 2008 French Open final, in which Rafael Nadal drubbed Federer despite a LR of only 0.77. In blowouts, there just isn’t that much leverage to go around, so the number of points won matters a lot more than their timing. But un-clutch performances often translate to victory even in closer matches. Andy Murray won the 2008 US Open semi-final over Nadal in four sets despite a LR of 0.80, and in a very tight Wimbledon semi-final last year, Kevin Anderson snuck past John Isner with a LR of 0.88.

You don’t need a spreadsheet to recognize that tennis matches are decided by a mix of overall and clutch performance. The numbers I’ve shown you so far don’t advance our understanding much, at least not in a rigorous way. That’s the next step.

DR, meet BLR

Regular users of Tennis Abstract player pages are familiar with Dominance Ratio (DR), a stat invented by Carl Bialik that re-casts total points won. DR is calculated by dividing a player’s rate of return points won by his rate of service points lost (his opponent’s rate of return points won), so the DR for a player who is equal on serve and return is exactly 1.0.

Winners are usually above 1.0 and losers below 1.0. In the Wimbledon final, Djokovic’s DR was 0.87, which is extremely low for a winner, though not unheard of. DR balances the effect of serve performance and return performance (unlike total points won, which can skew in one direction if there are many more serve points than return points, or vice versa) and gives us a single-number summary of overall performance.

But it doesn’t say anything about clutch, except that when a player wins with a low DR, we can infer that he outperformed in the big moments.

To get a similarly balanced view of high-leverage performance, we can adapt leverage ratio to equally weight clutch play on serve and return points. I’ll call that balanced leverage ratio (BLR), which is simply the average of LR on serve points and LR on return points. BLR usually doesn’t differ much from LR, just as we often get the same information from DR that we get from total points won. Djokovic’s Wimbledon final BLR was 1.11, compared to a LR of 1.10. But in cases where a disproportionate number of points occur on one player’s racket, BLR provides a necessary correction.

Leverage-adjusted DR

We can capture leverage-adjusted performance by simply multiplying these two numbers. For example, let’s take Stan Wawrinka’s defeat of Djokovic in the 2016 US Open final. Wawrinka’s DR was 0.90, better than Djokovic at Wimbledon this year but rarely good enough to win. But win he did, thanks to a BLR of 1.33, one of the highest recorded in a major final. The product of Wawrinka’s DR and his BLR–let’s call the result DR+–is 1.20. That number can be interpreted on the same scale as “regular” DR, where 1.2 is often a close victory if not a truly nail-biting one. DR+ combines a measure of how many points a player won with a measure of how well-timed those points were.

Out of 167 men’s slam finals in the Match Charting Project dataset, 14 of the winners emerged triumphant despite a “regular” DR below 1.0. In every case, the winner’s BLR was higher than 1.1. And in 13 of the 14 instances, the strength of the winner’s BLR was enough to “cancel out” the weakness of his DR, in the sense that his DR+ was above 1.0. Here are those matches, sorted by DR+:

Year  Major            Winner              DR   BLR   DR+  
2019  Wimbledon        Novak Djokovic    0.87  1.11  0.97  
1982  Wimbledon        Jimmy Connors     0.88  1.20  1.06  
2001  Wimbledon        Goran Ivanisevic  0.95  1.16  1.10  
2008  Wimbledon        Rafael Nadal      0.98  1.13  1.10  
2009  Australian Open  Rafael Nadal      0.99  1.13  1.12  
1981  Wimbledon        John McEnroe      0.99  1.16  1.15  
1992  Wimbledon        Andre Agassi      0.97  1.19  1.16  
1989  US Open          Boris Becker      0.96  1.22  1.18  
1988  US Open          Mats Wilander     0.98  1.21  1.18  
2015  US Open          Novak Djokovic    0.98  1.21  1.18  
2016  US Open          Stan Wawrinka     0.90  1.33  1.20  
1999  Roland Garros    Andre Agassi      0.98  1.25  1.23  
1990  Roland Garros    Andres Gomez      0.94  1.34  1.26  
1991  Australian Open  Boris Becker      0.99  1.30  1.29

167 slam finals, and Djokovic-Federer XLVIII was the first one in which the player with the lower DR+ ended up the winner. (Some of the unlisted champions had subpar leverage ratios and thus DR+ figures lower than their DRs, but none ended up below the 1.0 mark.) While Federer was weaker in the clutch–notably in tiebreaks and when he held match points–his overall performance in high-leverage situations wasn’t as awful as those few memorable moments would suggest. More often than not, a player who combined Federer’s DR of 1.14 with his BLR of 0.90 would conclude the Wimbledon fortnight dancing with the Ladies’ champion.

Surprisingly, 1-out-of-167 might understate the rarity of a winner with a DR+ below 1.0. Only one other best-of-five match in the Match Charting Project database (out of more than 700 in total) fits the bill. That’s the controversial 2019 Australian Open fourth-rounder between Kei Nishikori and Pablo Carreno Busta. Nishikori won with a 1.06 DR, but his BLR was a relatively weak 0.91, resulting in a DR+ of 0.97. Like the Wimbledon final, that Melbourne clash could have gone either way. Carreno Busta may have been unlucky with more than just the chair umpire’s judgments.

What does it all mean?

We knew that the Wimbledon final was close–now we have more numbers to show us how close it was. We knew that Djokovic played better when it mattered, and now we have more context that indicates how much better he was, which is not a unusually wide margin. Federer has won five of his slams despite title-match BLRs below 1.0, and two others with DRs below 1.14. He’s never won a slam with a DR+ of 1.03 or lower, but then again, there had never before been a major final that DR+ judged to be that close. Roger is no one’s idea of a clutch master, but he isn’t that bad. He just should’ve saved a couple of doses of second-set dominance for more important junctures later on.

If you’re anything like me, you’ll read this far and be left with many more questions. I’ve started looking at several, and hope to write more in this vein soon. Is Federer usually less clutch than average? (Yes.) Is Djokovic that much better? (Yes.) How about Nadal? (Also better.) Is Nadal really better, or do his leverage numbers just look good because important points are more likely to happen in the ad court? (No, he really is better.) Does Djokovic have Federer’s number? (Not really, unless you mean his mobile number. Then yes.) Did everything change after Djokovic hit that return? (No.)

There are many interesting related topics beyond the big three, as well. I started writing about leverage for subsets of matches a few years ago, prompted by another match–the 2016 Wimbledon Federer-Raonic semi-final–in which Roger got outplayed when it mattered. Just as we can look at average leverage for points won and lost, we can also estimate the importance of points in which a player struck an ace, hit a backhand unforced error, or chose to approach the net.

Matches are decided by a combination of overall performance and high-leverage play. Commonly-available stats do a pretty good job at the former, and fail to shine much light on the latter. The clutch part of the equation is often left to the speculation of pundits. As we build out a more complete dataset and have access to more and more point-by-point data (and thus leverage numbers for each point and match), we can close the gap, enabling us to better quantify the degree to which situational performance affects every player’s bottom line.

Another Match Charting Project Milestone: 6,000 Matches!

Italian translation at settesei.it

It has been a very productive year for the Match Charting Project. The MCP is a collaborative effort to record every shot of professional tennis matches. Since 2013, over one hundred volunteers have charted matches, ranging from 1970’s grand slam finals to marathon Big Four clashes to obscure challenger and ITF matches. The resulting dataset is unique, and represents a rare, public resource in a sport where the best stuff is usually locked up by tournaments, federations, and the companies that collect data for them.

The 6,000th match–a Bucharest quarter-final between Kristyna Pliskova and Patricia Maria Tig, one of over two hundred charted by Zindaras–comes less than six months after the 5,000th. In that time, we’ve logged a huge number of French Open and Wimbledon matches, in addition to every tour-level final. As part of an ongoing sub-project, we’ve also boosted our coverage of vintage major semi-finals, adding many men’s semis from the late 80’s and early 90’s, plus all the vintage women’s semi-finals from the French Open and Wimbledon for which we’ve found video.

(Maybe you could help us find some of the video we’re looking for?)

The resulting data–much of which is easily accessible to researchers on GitHub–has made it possible to research subjects on a scale never before possible. For example, early in the Wimbledon fortnight, I delved into how net play has changed, using shot-by-shot stats from the 1970s to the present at the All England club. And after Simona Halep’s pristine performance in the final, John Burn-Murdoch used MCP data to contextualize her stunningly low unforced error rate.

More casual fans are also steadily discovering the wealth of available MCP data. For all of these thousands of matches, you can look up thousands of match-specific stats, with easy comparisons to player averages. If you’ve never explored these pages, I highly recommend that you do so. One recently-added match that shows off the depth of the MCP stats is the 1987 Australian Open semi-final between Ivan Lendl and Pat Cash. You can also explore aggregate stats for particular players, on pages like this one, for Sloane Stephens.

If you find any of this interesting, now’s a great time to pitch in. Charting matches isn’t rocket science: it requires only attention to detail and a basic knowledge of tennis. Also helpful are a love of the sport and an interest in minutiae–two qualities shared by many of the most prolific contributors. I’ve written more about the benefits of charting here, and when you’re ready to get started, here’s the official Quick Start Guide.

While tennis remains a bit of an analytical backwater, we continue to make progress. We’re completely independent of the tours and federations spending untold sums on consultants that seem to always produce shiny new websites with little new data. This site isn’t shiny (to put it mildly!) but we’re unencumbered by the politics, conflicting priorities, and sheer inertia that hold back so much of the sport. This Match Charting Project milestone is just the latest reminder that the most interesting work often happens far from the biggest platforms.

Podcast Episode 71: An Analytical Approach to the Tennis Hall of Fame

Episode 71 of the Tennis Abstract Podcast, features guest co-host Jeff McFarland, the man behind Hidden Game of Tennis. You may remember Jeff from his previous appearance on episode 52. Following this year’s Hall of Fame induction ceremony in Newport, we take an deep dive into the tennis institution, looking at who deserves to be there, who doesn’t, and how we ought to decide.

Much of our conversation stems from Jeff’s attempts to quantify career accomplishment, including Transformed Wins, men’s Championship Shares, and women’s Championship Shares. We discuss whether the Hall should be big or small, whether the grand slams should be as important as they seem to be, and how to handle greatness on the doubles court.

Thanks for listening!

(Note: this week’s episode is about 68 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.

Economist: Novak Djokovic wins the most thrilling men’s tennis match ever

My latest article at The Economist’s Game Theory blog delves into one way in which the Wimbledon men’s championship match was the most exciting major final of the last four decades:

Sunday’s final registered an [Excitement Index] of 7.5%. Not only was that the highest of the tournament, but it tops every men’s grand-slam final of the last four decades (see chart). (A handful of women’s finals, which are best of three sets, score higher, because the high-leverage deciding set accounts for a larger fraction of the match.) The Wimbledon decider in 1980 between John McEnroe and Bjorn Borg—thrilling enough to spawn films and re-enactments—is next, at 7%. Another clash often dubbed the most thrilling of all time, the Wimbledon final in 2008 between Mr Federer and Mr Nadal, ranks third, at 6.9%.

Read the whole thing.

Podcast Episode 70: Djokovic, Federer, Simona, Serena, and a Wimbledon Finals Weekend to Remember

Episode 70 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, attacks the five-hour Djokovic-Federer men’s final from all sorts of angles, including Novak’s excellence on key points, Fed’s surprisingly decent backhand, and the first, awkward tiebreak at 12 games all.

We also celebrate what might have been Simona Halep’s best-ever performance, and question how much of the lopsided final result could be attributed to Halep peaking, and how much to an off-day for Serena Williams. Neither woman is our pick to win the US Open, so we discuss the status of the many of the big names who remain threats in an unstable WTA field.

Thanks for listening!

(Note: this week’s episode is about 66 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.

Will a Back-To-Normal Federer Backhand Be Good Enough?

Italian translation at settesei.it

After Roger Federer’s 2017 triumph over Rafael Nadal at the Australian Open, I credited his narrow victory to his backhand. He came back from the injury that sidelined him for the second half of 2016 having strengthened that wing, ready with the tactics necessary to use it against his long-time rival. Since that time, he has beaten Nadal in five out of six meetings, suggesting that the new-and-improved weapon has remained a part of his game.

The Swiss is riding high after defeating Rafa once again in the Wimbledon semi-finals on Friday. But unlike in Melbourne two-and-a-half years ago, the backhand wasn’t responsible for the victory. In the Australian Open final, Federer’s stylish one-hander earned him 11 more points than in a typical contest, enough to flip the result in his favor. On Friday, Nadal had little reason to fear a Federer backhand that was only a single point better than average. The Swiss owes his semi-final result to some stellar play, but not from his backhand.

BHP redux

I’m deriving these numbers from a stat called Backhand Potency (BHP), which uses Match Charting Project shot-by-shot data to isolate the effect of each one of a player’s shots. The formula is straightforward:

[A]dd one point for a winner or an opponent’s forced error, subtract one for an unforced error, add a half-point for a backhand that set up a winner or opponent’s error on the following shot, and subtract a half-point for a backhand that set up a winning shot from the opponent. Divide by the total number of backhands, multiply by 100, and the result is net effect of each player’s backhand.

The average player hits about 100 backhands per match, so the final step of multiplying by 100 gives us an approximate per-match figure. BHP hands out up to 1.5 “points” per tennis point, since credit is given for both a winning shot and the shot that set it up. Thus, to translate BHP (or any other potency metric, like Forehand Potency, FHP) to points, multiply by two-thirds. In the 2017 Australian Open final, Federer’s backhand was worth +17 BHP, equal to about 11 points.

On Friday, Roger’s backhand was worth only +1 BHP. The best thing we can say about that is that it didn’t hold him back–the sort of comment we might have made as he racked up wins for the first 15 years of his career.

The semi-final performance wasn’t an outlier. In a year-to-year comparison based on the available (admittedly incomplete) MCP data, the 2019 backhand looks an awful lot like the pre-injury backhand:

Year(s)     BHP  
1998-2011  +0.1  
2012       +0.4  
2013       -1.8  
2014       -1.1  
2015       +1.3  
2016       -0.3  
2017       +3.5  
2018       +1.3  
2019       +0.8

There are still good days, like Fed’s whopping +16 BHP against Kei Nishikori in this week’s quarter-finals. But when we tally up all the noise of good and bad days, effective and ineffective opponents, and fast and slow conditions, the net result is that the backhand just doesn’t rack up points the way it did two years ago.

The backhand versus Novak

Federer’s opponent in today’s final, Novak Djokovic, is known for his own rock-solid groundstrokes. Like Nadal did for many years, Djokovic is able to expose the weaker side of Federer’s baseline game. The Serbian has won the last five head-to-head meetings, and nine of the last eleven. In most of those, he reduces Roger’s backhand to a net negative:

Year  Tournament        Result  BHP/100  
2018  Paris             L         -11.0  
2018  Cincinnati        L         -11.0  
2016  Australian Open   L         -12.6  
2015  Tour Finals (F)   L          -4.8  
2015  Tour Finals (RR)  W          +0.7  
2015  US Open           L          +0.8  
2015  Cincinnati        W          -2.2  
2015  Wimbledon         L         -13.4  
2015  Rome              L         -12.2  
2015  Indian Wells      L          -5.0  
2015  Dubai             W          -5.9  
…                                        
2014  Wimbledon         L          -3.1  
2012  Wimbledon         W          +9.6

Out of 438 charted matches, Federer’s BHP was below -10 only 27 times. On nine of those occasions–and two of the five since Fed’s 2017 comeback–the opponent was Djokovic. Incidentally, Novak would do well to study how Borna Coric dismantles the Federer backhand, as Fed suffered his two worst post-injury performances (-20 at 2018 Shanghai, and -19 at 2019 Rome) against the young Croatian.

It is probably too much to ask for Federer to figure out how to beat Djokovic at his own game. The best he can do is minimize the damages by serving big and executing on the forehand. The Swiss has a career average +9 Forehand Potency (FHP), but falls to only +4 FHP against Novak. In last year’s Cincinnati final, Djokovic reduced his opponent to an embarrassing -13 FHP, the worst of his career. It wasn’t a fluke: four of Fed’s five worst single-match FHP numbers have come against the Serb.

If Federer is to win a ninth Wimbledon title, he’ll need to rack up points on at least one wing–either his typical forehand, or the backhand in the way he did against Djokovic in the 2012 semi-final. Whichever one does the damage, he’ll also need the other one to remain steady. His forehand was plenty effective in the semi-final against Nadal, worth +12 FHP in that match. Against a player like Novak who defends even better on a fast surface, Federer will need to somehow tally similar results. It’s a lot to ask, and one thing is certain: No one would be able to complain that his 21st major title came cheaply.