Category: Grand Slams

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.

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.

Novak Djokovic and the Narrowing Slam Race

Italian translation at settesei.it

It doesn’t take a statistician, or even a spreadsheet, to recognize that the 2019 Australian Open wasn’t Novak Djokovic’s most difficult path to a major title. We can debate whether the straight-set win over Rafael Nadal in the final was due to Djokovic’s utter dominance or a subpar performance from (a possibly still recovering) Rafa. But there’s more to a grand slam title than the final, and the only top-18 opponent Novak faced in the first six rounds was Kei Nishikori, who retired after 52 minutes.

On the traditional grand slam leaderboard, quality of competition doesn’t matter. Roger Federer has 20, Nadal has 17, and now Djokovic has 15. As I’ve written before, the race is closer than that, since Nadal’s and Djokovic’s opponents have, on average, been stronger than Federer’s. My metric for “adjusted slams” estimates the likelihood that a typical major titlist would defeat the specific seven opponents that a player faced, based on their surface-weighted Elo at the time of the match. (I’ve also used this approach for Masters titles.) The explanation is a mouthful, but the underlying idea is simple: Some majors represent greater achievements than others, both because some eras offer stiffer competition and because some draws are particularly daunting.

A slam title against an average level of competition is worth exactly 1. Tougher paths are worth more than 1, and easier draws are worth less. Here is the current leaderboard, with each player’s raw tally, average difficulty rating of their titles, and adjusted total:

Player          Slams  Avg Diff  Adj Slams  
Roger Federer      20      0.88       17.7  
Rafael Nadal       17      1.01       17.1  
Novak Djokovic     15      1.11       16.6

(The numbers in this post do not all precisely agree with those I’ve published in the past, because I’ve improved the accuracy of my Elo-based rating system. All three of the players have seen their adjusted slam totals decrease, because the improved Elo algorithm eliminates some of the Elo “inflation” that overvalued recent achievements.)

These three guys have often had to go through each other, but Djokovic has had the toughest paths of all. The average difficulty of his first 12 majors was 1.2, higher than all but three of Rafa’s titles, one of Roger’s, and two of those won by Pete Sampras. Only recently has he been able to boost his total without quite so much of a challenge. His Australian Open title was worth 0.84 majors, only the fourth of his titles against a below-average set of opponents. It was, however, tougher than Wimbledon or the US Open last year, which were worth 0.77 and 0.65, respectively.

It’s unlikely, of course, that the current leaderboard–adjusted or otherwise–will be the final reckoning among these three men. But on the adjusted list, they will probably remain tightly packed. Because the rest of the pack has weakened, with Andy Murray and Stan Wawrinka no longer regular features of the second week, major titles aren’t what they used to be. Early in the decade, it wasn’t uncommon for a player to beat multiple members of the big four en route to a title and add at least 1.2 to his adjusted tally.

In 2018, slam difficulty was barely half of that recent peak level:

Year    Avg Diff  
2002        0.73  
2003        0.65  
2004        0.82  
2005        0.95  
2006        0.77  
2007        0.93  
2008        1.05  
2009        1.00  
2010        0.95  
2011        1.19  
2012        1.23  
2013        1.22  
2014        1.28  
2015        1.12  
2016        1.27  
2017        0.91  
2018        0.69

This could all change, especially if Djokovic wins a Roland Garros title by upsetting Nadal. (Nothing generates high competition-adjusted numbers like beating Nadal on clay.) But it’s more likely that these three men will have to keep incrementing their totals by 0.6s and 0.7s. While that could be enough to put Rafa or Novak on top by the end of the 2019, it won’t give anyone a commanding lead. It’s a good thing that there’s a lot more to the GOAT debate than slam totals, because slam totals–when properly adjusted for the difficulty of achieving them–make it awfully hard to pick a winner.

The Big Four and Grand Slam Title Blocks

Italian translation at settesei.it

This is a guest post by Edoardo Salvati

In the last fifteen years, Roger Federer, Rafael Nadal, Novak Djokovic, Andy Murray—the Big Four—have dominated the ATP tour like no one before them. It’s hard to find a better example of oligarchy outside of geopolitics.

Since Wimbledon 2003, Federer’s first Grand Slam title, they have amassed 54 of 62 majors (or 87%) and been involved in another four finals. Similarly, since Federer’s first Masters win at Hamburg in 2002, they have won 106 of 159 titles at that level (or 66%) and contested 12 more finals. Since 2003 they have won 12 of 16 ATP Finals (or 75%) and contested one of the other four finals. 2017 and 2018 was the first time that outsiders won back-to-back season-ending titles in fifteen years.

It is an unprecedented level of domination that has left little glory for other players. But who are these others and how much would have they won had they been able to overcome the Big Four? At the Match Charting Project, we like to collect data (and you’re always welcome to contribute). Recently, we started working on a subset of matches that comprises all the Slam semi-finals back to 1980. Plenty of those featured recurring names from this second tier, so I was intrigued to see which players would have benefitted most in a world where the Big Four were not as good.

Deep inside of a parallel universe

Starting from Wimbledon 2003, I considered a hard-to-imagine scenario: What if the Big Four never won a major semi-final or final? For instance, when Grigor Dimitrov reached the final four at the 2017 Australian Open, he would have beaten Nadal (instead of losing in five sets), and then defeated Federer to win the title. When Juan Martin del Potro played Nadal in the 2018 French Open semi-final (he lost in straight sets), we rewrite history to make Delpo the winner, going on to face Dominic Thiem in the final. At the same event, in our parallel universe, Thiem wins the final against Nadal (he really lost in straight sets) and becomes the French Open champion for a second theoretical time.

The resulting slam tallies aren’t a precise redistribution of some of the Slams won by the Big Four, because there can be two different parallel-universe winners for the same tournament. Nevertheless, the title and final counts provide a general idea of who would’ve thrived in a Big Four-less sport. The following table lists the additional titles and finals (to a player’s actual wins, not shown) belonging to a parallel universe of tennis. 

Player                 Extra Slams              Extra Finals      
Stan Wawrinka          6 (2 AO - 2 FO - 2 US)   0                 
David Ferrer           6 (2 AO - 2 FO - 2 US)   0                 
Andy Roddick           5 (1 AO - 3 WIM - 1 US)  2 (1AO - 1 WIM)   
Jo Wilfried Tsonga     4 (2 AO - 2 WIM)         0                 
Tomas Berdych          3 (1 AO - 1 FO - 1 US)   2 (WIM)           
Richard Gasquet        3 (2 WIM - 2 US)         0                 
Milos Raonic           3 (1 AO - 2 WIM)         0                 
Juan Martin del Potro  2 (1 WIM - 1 US)         3 (2 FO - 1 US)   
Marin Cilic            2 (1 AO - 1 WIM)         2 (1 AO - 1 US)   
Nicolay Davydenko      2 (1 FO - 1 US)          1 (US)            
Dominic Thiem          2 (FO)                   1 (FO)            
Marat Safin            2 (1 AO - 1 WIM)         0                 
Marcos Baghdatis       2 (1 AO - 1 WIM)         0                 
Robin Soderling        2 (FO)                   0                 
Kevin Anderson         2 (1 WIM - 1 US)         0                 
Grigor Dimitrov        2 (1 AO - 1 WIM)         0                 
Lleyton Hewitt         1 (US)                   2 (1 WIM - 1 US)  
Gael Monfils           1 (FO)                   1 (US)                       
Mark Philippoussis     1 (WIM)                  0                 
Andre Agassi           1 (US)                   0                 
Fernando Gonzalez      1 (AO)                   0                 
Jonas Bjorkman         1 (WIM)                  0                 
Mariano Puerta         1 (FO)                   0                 
Ivan Ljubicic          1 (FO)                   0                 
Rainer Schuettler      1 (WIM)                  0                 
Fernando Verdasco      1 (AO)                   0                 
Mikhail Youznhy        1 (US)                   0                 
Ernests Gulbis         1 (FO)                   0                 
Jerzy Janowicz         1 (WIM)                  0  
Kei Nishikori          0                        1 (US)                
Juan Carlos Ferrero    0                        1 (AO)            
Sebastian Grosjean     0                        1 (WIM)           
Tim Henman             0                        1 (US)            
Nicolas Kiefer         0                        1 (AO)            
David Nalbandian       0                        1 (FO)            
Tommy Haas             0                        1 (WIM)           
Hyeon Chung            0                        1 (AO)            
Jurgen Melzer          0                        1 (FO)            
Total                  62                       23

It’s no surprise to see Stan Wawrinka, a three-time winner and nine-time major semi-finalist, at the top. He would triple his overall count for each Slam he won, though Wimbledon would remain elusive. Had he beaten Federer in the quarter-final in 2014, he would have gotten as far as the semi-final against Milos Raonic.

There’s a group of players whose careers would look even more outstanding. David Ferrer, Jo Wilfried Tsonga, Tomas Berdych, Richard Gasquet and Raonic could all claim to be Slam winners. Ferrer lost all his semi-finals and a final to the Big Four, and winning a Slam would have been a fitting reward for his many years of elite-level performance.

And, of course, there’s Andy Roddick, who must have wished that the only illustrious citizen from Basel was Jacob Bernoulli. After winning the US Open in 2003, Roddick lost all the finals he played to Federer, including three Wimbledon Championships. 

One player who may deserve to be even higher on the list is del Potro, who had to face a member of the Big Four in every semi-final he played and never went beyond the quarter-finals at the Australian Open, twice knocked out by Federer. You would expect del Potro to have won more than two of these hypothetical majors.

The gatekeeper

A few years ago, in an article for FiveThirtyEight, Carl Bialik investigated the assumption that Nadal led all the Open-era greats as the biggest obstacle to Grand Slam titles. Inventing a stat called the “title block,” he quantified every loss to Nadal with a fraction of the title depending on the round: half a title block for a loss to Nadal in the finals, a quarter for the semi-finals, and so on. 

Let’s use that stat and extend the analysis to see how many titles, since Wimbledon 2003, the Big Four cost the other players, as shown in the following table. Walkovers and retirements were included. 

Blocked                  AO    RG   WIM   USO  Titles Cost  
Roger Federer          2.00  2.50  1.50  1.00         7.00  
Andy Murray            2.94  1.25  1.38  0.88         6.44  
Novak Djokovic         0.06  2.13  1.00  2.50         5.69  
Rafael Nadal           1.13  0.13  1.75  0.75         3.75  
Andy Roddick           0.50  0.00  1.78  0.88         3.16  
Tomas Berdych          1.03  0.19  1.31  0.25         2.78  
David Ferrer           0.88  1.13  0.13  0.51         2.63  
Stanislas Wawrinka     0.72  1.00  0.19  0.63         2.53  
Juan Martin Del Potro  0.25  0.70  0.45  1.03         2.43  
Marin Cilic            0.81  0.09  0.94  0.44         2.28  
Jo Wilfried Tsonga     0.94  0.19  0.81  0.34         2.28  
Lleyton Hewitt         0.25  0.19  0.56  0.78         1.78  
Milos Raonic           0.56  0.13  0.88  0.06         1.63  
Robin Soderling        0.00  1.13  0.23  0.25         1.62  
Richard Gasquet        0.03  0.38  0.63  0.41         1.46  
Gael Monfils           0.11  0.75  0.00  0.57         1.43  
Kevin Anderson         0.07  0.00  0.64  0.50         1.21  
Dominic Thiem          0.00  1.02  0.00  0.13         1.14  
Marcos Baghdatis       0.64  0.03  0.44  0.02         1.13  
Nikolay Davydenko      0.27  0.25  0.01  0.53         1.05  
Fernando Gonzalez      0.56  0.17  0.13  0.16         1.02  
Fernando Verdasco      0.30  0.25  0.13  0.28         0.96  
Kei Nishikori          0.38  0.20  0.13  0.25         0.96  
Mikhail Youzhny        0.05  0.06  0.41  0.42         0.95  
Grigor Dimitrov        0.47  0.03  0.31  0.06         0.88  
Marat Safin            0.53  0.00  0.28  0.00         0.81  
Andre Agassi           0.13  0.00  0.03  0.63         0.78  
Tommy Haas             0.11  0.22  0.41  0.00         0.73  
Tommy Robredo          0.19  0.13  0.11  0.25         0.67  
Feliciano Lopez        0.11  0.01  0.19  0.34         0.65  
Gilles Simon           0.30  0.06  0.19  0.03         0.58  
Juan Carlos Ferrero    0.25  0.00  0.32  0.00         0.57  
David Nalbandian       0.13  0.25  0.03  0.16         0.56  
Jurgen Melzer          0.10  0.25  0.06  0.09         0.51  
Mark Philippoussis     0.00  0.00  0.50  0.01         0.51  
Mariano Puerta         0.00  0.50  0.00  0.00         0.50  
Nicolas Almagro        0.06  0.41  0.00  0.03         0.50

As expected, the Big Four have blocked each other more than they have any other player, costing themselves a whopping 22.88 majors, with Federer and Murray paying the highest price, 7.00 and 6.44 respectively. Other familiar names are just below the top four. There are 17 players who were blocked from at least one major title.

Nadal retains his status as the Slam gatekeeper: you have to pass through him to win a major. Not only did the rest of the Big Four fails to block him as much as he did them–he has the lowest major titles cost among the Big Four at 3.75–but he also has blocked the rest of the quartet more than any other player.     

Blocker         Blocked         Titles cost  
Rafael Nadal    Roger Federer          3.75  
Rafael Nadal    Novak Djokovic         3.13  
Rafael Nadal    Andy Murray            1.44  
Total                                  8.32  
                                             
Novak Djokovic  Andy Murray            3.13  
Novak Djokovic  Roger Federer          3.00  
Novak Djokovic  Rafael Nadal           1.88  
Total                                  8.01  
                                             
Roger Federer   Andy Murray            1.88  
Roger Federer   Novak Djokovic         1.56  
Roger Federer   Rafael Nadal           1.50  
Total                                  4.94  
                                             
Andy Murray     Novak Djokovic         1.00  
Andy Murray     Rafael Nadal           0.38  
Andy Murray     Roger Federer          0.25  
Total                                  1.63

Nadal boasts a net credit of 2.25 major titles versus Federer, of 1.25 against Djokovic and of 1.06 compared to Murray. Just as the rest of the men’s tour would prefer that the Big Four had pursued a different sport, three-quarters of the Big Four have had plenty of reasons to wish that Rafa had shifted his focus to golf.

At this month’s Australian Open, Nadal continues to loom large. With the No. 2 seed, he is a potential semi-final opponent for Federer or Murray and, of course, a possible foe in the final for top seed Djokovic. There’s no guarantee that Nadal will stand in anyone’s way, but with these men accounting for the top three seeds at yet another major, the era of Big Four title blocks is far from over.

—

Edoardo Salvati is on a mission to raise the level of the Italian sports conversation. He founded settesei.it and has written about tennis and other sports for publications such as Contrasti, Undici, Il Tennis Italiano. He is a prolific and proud contributor to the Match Charting Project.

Eight Slams, Eight Women’s Champions. How About Nine?

Embed from Getty Images

Italian translation at settesei.it

Buried under the din of the Serena-Ramos story is a remarkable fact about parity in women’s tennis right now. Naomi Osaka was the eighth different grand slam champion in eight events, a streak dating back to Serena Williams’s victory at last year’s Australian Open. Since then, it’s been a different face with every trophy: Jelena Ostapenko, Garbine Muguruza, Sloane Stephens, Caroline Wozniacki, Simona Halep, Angelique Kerber, and Osaka. In the same time span, only three different men have won majors.

The women’s field is so deep that the streak could easily keep going. I built a possible Australian Open draw using the current top 128 players in the WTA rankings, then ran a forecast of the tournament based on each player’s current Elo rating. Here are the title chances for each of the last eight slam winners:

Player              Seed  Title Odds  
Simona Halep           1       16.7%  
Caroline Wozniacki     2        7.1%  
Angelique Kerber       3        5.7%  
Serena Williams       16        5.5%  
Naomi Osaka            7        4.9%  
Sloane Stephens        9        2.6%  
Garbine Muguruza      14        1.8%  
Jelena Ostapenko      10        0.5%  
TOTAL                          44.9%

Altogether, they add up to less than 50%! Put another way, there are better than even odds that we get a ninth different woman giving a victory speech in Melbourne. Here are the players with the best chances:

Player              Seed  Title Odds  
Elina Svitolina        6        8.8%  
Aryna Sabalenka       20        6.6%  
Petra Kvitova          5        5.9%  
Karolina Pliskova      8        3.7%  
Ashleigh Barty        17        3.5%  
Caroline Garcia        4        3.3%  
Madison Keys          18        2.6%  
Venus Williams        21        2.6%  
Mihaela Buzarnescu    23        2.3%  
Julia Goerges         11        2.2%

Ok, yes, Mihaela Buzarnescu seems a little out of place here. But of the other nine players, would any of them represent more of a surprise than Ostapenko, Stephens, or Osaka? By the numbers, three of the top five favorites for the Australian Open haven’t won a major in the last two years.

Given the sheer number of plausible contenders, it’s easy to imagine not just nine different slam winners in a row, but twelve, extending through the entire 2019 season. Consider the possibilities:

This is all rather fanciful, I know. But it’s barely even accurate to say there is a “favorite” when only one woman has a double-digit chance of winning the next major, and her odds are a mere one in six. No single player is likely to win any given grand slam, and only Halep has better than a fifty-fifty shot at winning one over the course of the year.

The chances that the streak extends to twelve are small, but not as low as, say, Osaka’s probability of winning the US Open before the tournament began. We’ve seen that the odds of a ninth different winner triumphing in Australia are about 55%. If that person wins, she’ll probably have earned a rosy forecast for Paris, so the probability of a new winner at the French is lower. And so on, after a tenth or eleventh different champion. If we lower the “new-winner” odds by seven percentage points for each slam, the chances of twelve-slam streak are 3.7%, the same as Pliskova’s probability of becoming number nine. Stranger things have happened. In women’s tennis, the unpredictable has become the norm.

Juan Martin del Potro’s Daunting Semi-final Assignments

Embed from Getty Images

Italian translation at settesei.it

This afternoon, Juan Martin del Potro will take on Rafael Nadal for a place in the 2018 US Open championship match. Forgive me if this sounds familiar: It’s the third time Delpo and Rafa have squared off in Flushing’s final four. Every time the Argentine has made it this far in New York, it’s been the King of Clay waiting on the other side of the net.

Del Potro could be forgiven for wondering if he was born in the wrong era. Today is his sixth major semi-final, and his fourth against Rafa. The other two weren’t cakewalks either. His first appearance in the last four of a grand slam was at the 2009 French Open against Roger Federer, and his best-ever performance at Wimbledon gave him a semi-final meeting with Novak Djokovic. The only slight positive in all this is that he faced Federer in Paris and Nadal so often in New York. Technically, it could have been worse.

Simply reaching six major semi-finals is an achievement in itself. Since 1977, there have been only 35 players to reach five or more. For each of those players, I calculated the average surface-specific Elo of their opponents, as well as their average chances of winning. Measured by opponent Elo, Delpo has had the fourth most difficult semi-final assignments of any of these players. The table below shows each player’s number of semi-finals, number of wins, average chance of winning those matches (“Avg p(W)”) and the Elo rating of their average opponent (“Avg Opp Elo”):

Player                 SFs  Wins  Avg p(W)  Avg Opp Elo  
David Ferrer             6     1       35%         2202  
Pat Cash                 5     3       22%         2194  
Stan Wawrinka            9     4       35%         2163  
Juan Martin del Potro    6     ?       35%         2161  
Vitas Gerulaitis         7     2       36%         2146  
Mats Wilander           14    11       48%         2122  
Jo Wilfried Tsonga       6     1       31%         2122  
Michael Chang            8     4       46%         2121  
Novak Djokovic          31    22       62%         2115  
Andy Murray             21    11       52%         2114

Like Delpo, many of these guys had one frequent foe. David Ferrer drew Djokovic in three semis. Pat Cash faced Ivan Lendl three times in his five chances. Vitas Gerulaitis kept earning meetings with Bjorn Borg. Stan Wawrinka hasn’t played more than two semis against any particular opponent, but that doesn’t mean his draws have been any easier: He’s faced Djokovic, Federer, and Andy Murray twice each.

Djokovic and Murray pop up at the bottom of the top ten largely because of Federer and Nadal. It’s a tough era, even if you hold a Big Four membership card. Roger and Rafa have had it easier, ranked 24th and 26th in opponent Elo*, in part due to the number of majors they contested before Djokovic and Murray had fully developed–and because they generally avoided playing each other.

* Federer’s average opponent has had an Elo of 2056, and Nadal’s has had a 2045 Elo. Michael Stich is the only player on this list whose opponents’ Elos averaged below 2000.

Today’s match gives Delpo an opportunity to put himself a bit closer to Wawrinka’s category and surpass the likes of Ferrer and Jo Wilfried Tsonga, who reached only one major final each. Based on his own Elo and those of his opponents, del Potro has had about a one-in-three chance of winning his semis. The 2018 US Open represents his sixth, meaning we’d expect two final appearances thus far. Then again, it’s one thing to run the numbers; it’s another thing to beat Rafael Nadal in a major semi-final … twice.

Simona Halep’s Grand Slam First Round Woes

Italian translation at settesei.it

In the first-ever match at the US Open’s new Louis Armstrong Stadium yesterday, No. 1 seed and reigning French Open champion Simona Halep lasted barely an hour, losing to the big-hitting Kaia Kanepi. Halep has held the top ranking for more than six months running, and only ten women have owned the top spot for more total weeks than she has. But Halep fans aren’t exactly the the target market for second-week tickets at the majors.

As Christopher Clarey pointed out on Twitter, yesterday’s loss was Halep’s 12th first-round exit in 34 tries. That isn’t quite as bad as it sounds: Seven of the losses came in her first 12 entries, before she entered the top 50, and since Wimbledon 2013, she’s a more respectable 17-5, with one of those losses to Maria Sharapova in New York last year. Still, it’s not the type of winning percentage you’d expect to see from someone of her caliber.

Just how bad is it? To give us some context, I compared her record in her first 34 majors to other grand slam winners, as well as everybody else whose career lasted long enough to enter at least 30 slam main draws. The deeper we dig, the worse it looks.

Simona vs slam winners

I found 32 major champions who played at least 30 slam first rounds*. Most of them played more than that, but to make sure we compare like to like, I’m focusing on each player’s first 34 majors. The list is topped by some of the usual suspects: Chris Evert, Monica Seles, and Serena Williams all went undefeated in their first 34 round-of-128 matches.

* I’ve excluded majors with fewer than 128 entrants, and my database might be missing first-round results from a few more events early in the Open era. Technically, I’m looking only at round-of-128 results.

The average grand slam champion went 29-5 in her first 34 major first rounds. Only four, including Halep, lost at least 12 of those matches: Angelique Kerber also went 22-12, while Flavia Pennetta and Samantha Stosur lost 13. Only two others lost more than seven first rounders: Marion Bartoli went 24-10 in her first 34 first-round efforts, and Iva Majoli ended up at 23-11.

Simona vs the pack

I found 199 players in Open era history who have contested at least 30 round-of-128 matches at majors. That’s a fairly elite crew–as we’ve seen, more than 15 percent of them are slam champions. It’s challenge enough to maintain a high enough ranking to enter nearly a decade’s worth of majors.

Thus, our remaining 167-player sample of non-champions is still better than average: Considering each of their first 34 majors, they won 57.4% of their opening round matches. That translates into a record of 20-14, only a couple of wins worse than how Halep has fared so far. 58 of the 167 women, about 35%, won at least 22 of their first 34. 45 of them, or 27%, outdid Simona and won at least 23.

Two explanations spring to mind for the discrepancy between Halep’s status at the top of the game and her mediocre career performance at the majors. First, players are taking longer to develop into stars. Simona’s 5-7 record in her first 12 first rounds isn’t indicative of her current level. Standouts of prior generations, like Serena and Seles, skipped that level of development entirely, springing onto the scene as instant contenders. Even Jelena Ostapenko, the almost-still-teenage winner of the 2017 French Open, was a modest 7-5 in her first dozen major first rounds. Sloane Stephens, who won 11 of her first 12 (including one against Halep), currently sits at a more modest 19-8.

The other reason is more prosaic: the parity at the top of the women’s game. Even as Simona racks up weeks as number one, she just isn’t as good as many previous top-ranked players. Her greatness stems from managing to stay at a reasonably high level more consistently than any of her peers. That means lots of of second-tier titles, impressive (overall) won-loss records, and on the flip side, some unfortunate losses on big stages. On a tour without a dominant presence, that’s good enough to make her, by a healthy margin, the best in the game. But “best” is more fragile than it used to be, even in the first round of the grand slams.

Everything You Always Wanted to Know About Marco Cecchinato’s Run to the Roland Garros Semifinal

This is a guest post by Peter Wetz.

When a 25 year old Italian tennis player named Marco Cecchinato defeated Marius Copil in the first round of this year’s edition of Roland Garros, some people may have noticed that it was one of the longer first round matches. With a duration of 3 hours and 41 minutes the match was the fifth longest of the 64 opening round matches. However, I am confident that no one suspected the winner of this encounter would go much farther in the draw. Little did we know.

After his unexpected four set win in the quarterfinal against a hard-fighting Novak Djokovic–bookmakers were giving him about an 11 percent chance of winning–many tweets emphasized the uniqueness of this achievement. Since it is difficult to provide more context in a tweet, I was interested in just how often something like this happened in the past. So I looked into the data and came up with more complete lists of the tweeted facts which are presented in the remainder of this post.

The first and obvious question is, when was the last time that a player ranked as high as Cecchinato reached a Grand Slam semifinal?

The following table shows players ranked outside of the top-70 that reached a Grand Slam semifinal. Rows denoting achievements at Roland Garros are bold.

Tourney Player		       Rank	Round
RG 18	Marco Cecchinato	 72	SF
W  08	Rainer Schuettler	 94	SF
W  08	Marat Safin		 75	SF
AO 04	Marat Safin		 86	F
W  01	Goran Ivanisevic	125	W
W  00	Vladimir Voltchkov	237	SF
RG 99	Andrei Medvedev		100	F
AO 99	Nicolas Lapentti	 91	SF
AO 98	Nicolas Escude		 81	SF
W  97	Michael Stich		 88	SF
RG 97	Filip Dewulf		122	SF
RG 92	Henri Leconte		200	SF
UO 91	Jimmy Connors		174	SF
AO 91	Patrick Mcenroe		114	SF

As the tweet points out the most recent comparable runs by Rainer Schuettler and Marat Safin happened after the players have reached top-10 rankings. Hence, the most recent really comparable run where the player has not reached his career high ranking at the time of the tournament, is by Vladimir Voltchkov, who reached the semifinal at Wimbledon 2000.*

Another unique thing about Cecchinato’s run is that until last week he did not win a single match at a Grand Slam event.

The following table shows players that won their first match at a Grand Slam event and went on to win more matches. To prevent showing an extremely short table, I relaxed the condition on how far the player should have gone when winning his first Grand Slam match to reaching the quarterfinal. The last column Attempts denotes the number of main draw appearances until his first main draw win.

Tourney   Player	   Rank    Reached Attempts
RG 18	  Marco Cecchinato   72	   SF	   6
AO 18     Tennys Sandgren    97	   QF	   3
RG 03	  Martin Verkerk     46	   F	   3
W  00     Alexander Popp    114	   QF	   2
W  97	  Nicolas Kiefer     98	   QF	   3
RG 97	  Galo Blanco	    111	   QF	   4
W  96	  Alex Radulescu     91	   QF	   1
RG 95	  Albert Costa	     36	   QF	   4
RG 94     Hendrik Dreekmann  89	   QF	   2
AO 93	  Brett Steven	     71	   QF	   1

As the table shows, rarely has a player gotten past the quarterfinal after recording his debut win at a Grand Slam, with the notable exception of Martin Verkerk, who reached the final 15 years ago at his third attempt. Still–especially in the 1990s–there were a few players who won four consecutive matches. Not included in the table, but not less impressive, is the run by Mikael Pernfors. Interestingly, he had not won a single Grand Slam match, but he had built himself a ranking of 26, when he reached the final round of Roland Garros 1986, where he also won his first main draw match.

When looking at male Grand Slam competitors from Italy, not many names besides Fabio Fognini, Andreas Seppi, Simone Bolelli, and Paolo Lorenzi spring to mind. With 150 main draw appearances, the quartet shares a mere ten appearances in the round of 16 and one quarterfinal appearance (Fabio Fognini at Roland Garros 2011). Marco Cecchinato is the first Italian player in the semifinal of a Grand Slam in 40 years.

The following table shows all appearances of Italian players past the round of 16.

Tourney   Player	    	Reached
RG 18	  Marco Cecchinato  	SF
RG 11	  Fabio Fognini		QF
W  98	  Davide Sanguinetti 	QF
RG 95	  Renzo Furlan	     	QF
AO 91	  Cristiano Caratti  	QF
RG 80	  Corrado Barazzutti 	QF
W  79     Adriano Panatta	QF
RG 78	  Corrado Barazzutti	SF
UO 77	  Corrado Barazzutti	SF
RG 77	  Adriano Panatta	QF
RG 76	  Adriano Panatta	W
RG 75	  Adriano Panatta	SF
RG 73	  Paolo Bertolucci	QF
RG 73	  Adriano Panatta	SF
RG 72	  Adriano Panatta	QF

Despite the fact that male Italian players seem strongest on the dirt, since 1978 no one reached the semifinal of a Grand Slam. Even Fabio Fognini’s quarterfinal appearance at Roland Garros 2011 was the first in 13 years. Marco Cecchinato is one win away of being the first Italian Grand Slam finalist since 1976.

Marco Cecchinato was not seeded. If we look at Grand Slam semifinals comprised of unseeded players an interesting pattern appears.

Tourney Player  	    	Reached
RG 18	Marco Cecchinato  	SF
AO 18	Hyeon Chung		SF
AO 18	Kyle Edmund		SF
W  08	Rainer Schuettler	SF
W  08	Marat Safin		SF
RG 08	Gael Monfils		SF
AO 08	Jo Wilfried Tsonga	F
UO 06	Mikhail Youzhny		SF
W  06	Jonas Bjorkman		SF
AO 06	Marcos Baghdatis	F
UO 05	Robby Ginepri		SF
RG 05	Mariano Puerta		F
W  04	Mario Ancic		SF
RG 04	Gaston Gaudio		W
AO 04	Marat Safin		F
W  03	Mark Philippoussis	F
RG 03	Martin Verkerk		F
AO 03	Wayne Ferreira		SF
W  01	Goran Ivanisevic	W
UO 00	Todd Martin		SF
W  00	Vladimir Voltchkov	SF
RG 00	Franco Squillari	SF

Since 2008 this is only the third time that an unseeded player reached the semifinal. All three occurrences happended this year. It appears that we can again get used to see new faces deep into the second week of a Grand Slam tournament.

Finally, let’s take a look at Grand Slam semifinals between players using a one-handed backhand. The decreasing popularity of the one-hander has already been discussed here and with this in mind it seems even more unique that Dominic Thiem–the player who Marco Cecchinato will face tomorrow in the semifinal–inititally played a two-hander, but then changed to a one-hander.

Tourney Player 1	    	Player 2
RG 18	Marco Cecchinato  	Dominic Thiem
AO 17	Roger Federer		Stanislas Wawrinka
UO 15	Roger Federer		Stanislas Wawrinka
W  09	Roger Federer		Tommy Haas
W  07	Roger Federer		Richard Gasquet
AO 07	Fernando Gonzalez	Tommy Haas
UO 04	Roger Federer		Tim Henman
UO 02	Pete Sampras		Sjeng Schalken
RG 02	Albert Costa		Alex Corretja
W  99	Pete Sampras		Tim Henman
UO 98	Patrick Rafter		Pete Sampras
W  98	Pete Sampras		Tim Henman

If we ignore Roger Federer and Stanislas Wawrinka, two players who brought the one-handed backhand back into discussion, the last Grand Slam semifinal between two one-handers was played between Fernando Gonzalez and Tommy Haas at the Australian Open 2007. Before that, Pete Sampras was involved in four of six such encounters. Without Roger and Pete the world of one-handed Grand Slam semifinals would look really thin.

Whatever the result of the semifinal between Marco Cecchinato and Dominic Thiem will be, we know already that Marco achieved what only few players have done before him, especially in recent years. Whether he will be able to repeat this feat at Wimbledon, where he will be seeded despite having never won a match on a grass court, is arguable. Still, placing a bet on his own first round loss probably won’t be a good idea–at the very least, a lot more fans will be watching his opening match than ever before.

* A previous version of this article wrongly stated that the Wimbledon 2001 championship run by Goran Ivanisevic is more similar to Marco Cecchinato’s run. However, in 2001 Ivanisevic had already achieved his career high ranking, which is not the case for Cecchinato. Thanks for @rtwkr at Twitter for pointing this out.

—

Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.

Roger Federer’s 20th, Easiest Grand Slam Title

Italian translation at settesei.it

After Rafael Nadal’s US Open title last fall, I wrote a piece for the Economist that attempted to measure each Grand Slam title by difficulty. If you’re interested in the methodology, you can review it there. The conclusion was intriguing: Nadal’s opponents en route to his 16 major titles were considerably more difficult than the routes Roger Federer took to his first 19. By “difficulty-adjusted” Slam titles, Rafa led by a whisker, 18.8 to 18.7.

Since then, Federer won the 2018 Australian Open, incrementing his major tally by one. Even though he faced rather weak competition, surely the additional title nudged his difficulty-adjusted total above Rafa’s, right?

It did, but not by much. Adjusted for difficulty, Roger’s seven wins in Melbourne were worth only 0.42 majors. By comparison, his previous low was the 2006 Australian, worth 0.61, and Rafa’s lowest was last year’s US Open, at 0.62. Federer’s previous average was 0.98, Nadal’s was 1.18, and Rafa’s route to the 2013 French Open was worth a whopping 1.65.

Fed’s draw was historically weak. Only a handful of majors in the professional era were easier for their champion, and they all came before 1985–most of them in Melbourne, which didn’t yet attract the best talent in the world. This year’s Australian Open path to the title was even weaker when put in the context of the current decade: The average major title from 2010-17 was worth 1.23, largely because the Big Four usually needed to overcome each other.

According to surface-specific Elo, the toughest challenge Federer faced last month was Tomas Berdych, closely followed by Marin Cilic. Even after deep runs in Australia, neither player even ranks in the current Elo top ten. The algorithm that adjusts slam titles considers how the average major champion would fare against a particular set of competition; against Berdych and Cilic, that hypothetical average champ is expected to win 88% and 89% of the time, respectively. Even Nadal had to get past Juan Martin del Potro in New York last year.

Still, Federer can claim the top spot on yet another list, as his 19.1 difficulty-adjusted Grand Slam titles exceed Rafa’s 18.8 as well as the 15.3 of Novak Djokovic. It doesn’t have quite the same ring that “20 majors” does, and it’s in considerably more immediate danger. If Nadal stays healthy and wins the French Open, he is virtually guaranteed to reclaim the difficulty-adjusted crown, and by a wider margin than Roger currently holds. Roland Garros has traditionally been tough: With the exception of 2010, all of Rafa’s trophies in Paris have been tougher than average. Unlike the traditional Grand Slam tally, the difficulty-adjusted ranking could yo-yo between the two rivals for as long as they remain competitive.

Quantifying Cakewalks, or The Time Rafa Finally Got Lucky

Italian translation at settesei.it

During this year’s US Open, much has been made of some rather patchy sections of the draw. Many great players are sitting out the tournament with injury, and plenty of others crashed out early. Pablo Carreno Busta reached the quarterfinals by defeating four straight qualifiers, and Rafael Nadal could conceivably win the title without beating a single top-20 player.

None of this is a reflection on the players themselves: They can play only the draw they’re dealt, and we’ll never know how they would’ve handled a more challenging array of opponents. The weakness of the draw, however, could affect how we remember this tournament.  If we are going to let the quality of the field color our memories, we should at least try to put this year’s players in context to see how they compare with majors in the past.

How to measure draw paths

There are lots of ways to quantify draw quality. (There’s an entire category on this blog devoted to it.) Since we’re interested in the specific sets of opponents faced by our remaining contenders, we need a metric that focuses on those. It doesn’t really matter that, say, Nick Kyrgios was in the draw, since none of the semifinalists had to play him.

Instead of draw difficulty, what we’re after is what I’ll call path ease. It’s a straightforward enough concept: How hard is it to beat the specific set of guys that Rafa (for instance) had to play?

To get a number, we’ll need a few things: The surface-weighted Elo ratings of each one of a player’s opponents, along with a sort of “reference Elo” for an average major semifinalist. (Or finalist, or title winner.) To determine the ease of Nadal’s path so far, we don’t want to use Nadal’s Elo. If we did that, the exact same path would look easier or harder depending on the quality of the player who faced it.

(The exact value of the “reference Elo” isn’t that important, but for those of you interested in the numbers: I found the average Elo rating of every slam semifinalist, finalist, and winner back to 1988 on each of the three major surfaces. On hard courts, those numbers are 2145, 2198, and 2233, respectively. When measuring the difficulty of a path to the semifinal round, I used the first of those numbers; for the difficulty of a path to the title, I used the last.)

To measure path ease, then, we answer the question: What are the odds that an average slam semifinalist (for instance) would beat this particular set of players? In Rafa’s case, he has yet to face a player with a weighted-hard-court Elo rating above 1900, and the typical 2145-rated semifinalist would beat those five players 71.5% of the time. That’s a bit easier than Kevin Anderson‘s path the semis, but a bit harder than Carreno Busta’s. Juan Martin del Potro, on the other hand, is in a different world altogether. Here are the path ease numbers for all four semifinalists, showing the likelihood that average contenders in each round would advance, giving the difficulty of the draws each player has faced:

Semifinalist   Semi Path  Final Path  Title Path  
Nadal              71.5%       49.7%       51.4%  
del Potro           9.1%        7.5%       10.0%  
Anderson           69.1%       68.9%       47.1%  
Carreno Busta      74.3%       71.2%       48.4%

(We don’t yet know each player’s path to the title, so I averaged the Elos of possible opponents. Anderson and Carreno Busta are very close, so for Rafa and Delpo, their potential final opponent doesn’t make much difference.)

There’s one quirk with this metric that you might have noticed: For Nadal and del Potro, their difficulty of reaching the final is greater than that of winning the title altogether! Obviously that doesn’t make logical sense–the numbers work out that way because of the “reference Elos” I’m using. The average slam winner is better than the average slam finalist, so the table is really saying that it’s easier for the average slam winner to beat Rafa’s seven opponents than it would be for the average slam finalist to get past his first six opponents. This metric works best when comparing title paths to title paths, or semifinal paths to semifinal paths, which is what we’ll do for the rest of this post.

Caveats and quirks aside, it’s striking just how easy three of the semifinal paths have been compared to del Potro’s much more arduous route. Even if we discount the difficulty of beating Roger Federer–Elo thinks he’s the best active player on hard courts but doesn’t know about his health issues–Delpo’s path is wildly different from those of his semifinal and possible final opponents.

Cakewalks in context

Semifinalist path eases of 69% or higher–that is, easier–are extremely rare. In fact, the paths of Anderson, Carreno Busta, and Nadal are all among the ten easiest in the last thirty years! Here are the previous top ten:

Year  Slam             Semifinalist               Path Ease  
1989  Australian Open  Thomas Muster                  84.1%  
1989  Australian Open  Miloslav Mecir                 74.2%  
1990  Australian Open  Ivan Lendl                     73.8%  
2006  Roland Garros    Ivan Ljubicic                  73.7%  
1988  Australian Open  Ivan Lendl                     72.2%  
1988  Australian Open  Pat Cash                       70.1%  
2004  Australian Open  Juan Carlos Ferrero            69.2%  
1996  US Open          Michael Chang                  68.8%  
1990  Roland Garros    Andres Gomez                   68.4%  
1996  Australian Open  Michael Chang                  66.2%

In the last decade, the easiest path to the semifinal was Stan Wawrinka‘s route to the 2016 French Open final four, which rated 59.8%. As we’ll see further on, Wawrinka’s draw got a lot more difficult after that.

Del Potro’s draw so far isn’t quite as extreme, but it is quite difficult in the historical context. Of the nearly 500 major semifinalists since 1988, all but 15 are easier than his 9.1% path difficulty. Here are the top ten, all of whom faced draws that would have given the average slam semifinalist less than an 8% chance of getting that far:

Year  Slam             Semifinalist              Path Ease  
2009  Roland Garros    Robin Soderling                1.6%  
1988  Roland Garros    Jonas Svensson                 1.9%  
2017  Wimbledon        Tomas Berdych                  3.7%  
1996  Wimbledon        Richard Krajicek               6.4%  
2011  Wimbledon        Jo Wilfried Tsonga             6.6%  
2012  US Open          Tomas Berdych                  6.8%  
2017  Roland Garros    Dominic Thiem                  6.9%  
2014  Australian Open  Stan Wawrinka                  7.0%  
1989  Roland Garros    Michael Chang                  7.1%  
2017  Wimbledon        Sam Querrey                    7.5%

Previewing the history books

In the long term, we’ll care a lot more about how the 2017 US Open champion won the title than how he made it through the first five rounds. As we saw above, three of the four semifinalists have a path ease of around 50% to win the title–again, meaning that a typical slam winner would have a roughly 50/50 chance of getting past this particular set of seven opponents.

No major winner in recent memory has had it so easy. Nadal’s path would rate first in the last thirty years, while Carreno Busta’s or Anderson’s would rate in the top five. (If it comes to that, their exact numbers will depend on who they face in the final.) Here is the list that those three men have the chance to disrupt:

Year  Slam             Winner                  Path Ease  
2002  Australian Open  Thomas Johansson            48.1%  
2001  Australian Open  Andre Agassi                47.6%  
1999  Roland Garros    Andre Agassi                45.6%  
2000  Wimbledon        Pete Sampras                45.3%  
2006  Australian Open  Roger Federer               44.5%  
1997  Australian Open  Pete Sampras                44.4%  
2003  Australian Open  Andre Agassi                43.9%  
1999  US Open          Andre Agassi                41.5%  
2002  Wimbledon        Lleyton Hewitt              39.9%  
1998  Wimbledon        Pete Sampras                39.1%

At the 2006 Australian Open, Federer lucked into a path that was nearly as easy as Rafa’s this year. His 2003 Wimbledon title just missed the top ten as well. By comparison, Novak Djokovic has never won a major with a path ease greater than 18.7%–harder than that faced by more than half of major winners.

Nadal has hardly had it easy as he has racked up his 15 grand slams, either. Here are the top ten most difficult title paths:

Year  Slam             Winner                Path Ease  
2014  Australian Open  Stan Wawrinka              2.2%  
2015  Roland Garros    Stan Wawrinka              3.1%  
2016  Us Open          Stan Wawrinka              3.2%  
2013  Roland Garros    Rafael Nadal               4.4%  
2014  Roland Garros    Rafael Nadal               4.7%  
1989  Roland Garros    Michael Chang              5.0%  
2012  Roland Garros    Rafael Nadal               5.2%  
2016  Australian Open  Novak Djokovic             5.4%  
2009  US Open          J.M. Del Potro             5.9%  
1990  Wimbledon        Stefan Edberg              6.2%

As I hinted in the title of this post, while Nadal got lucky in New York this year, it hasn’t always been that way. He appears three times on this list, facing greater challenges than any major winner other than Wawrinka the giant-killer.

On average, Rafa’s grand slam title paths haven’t been quite as harrowing as Djokovic’s, but compared to most other greats of the last few decades, he has worked hard for his titles. Here are the average path eases of players with at least three majors since 1988:

Player           Majors        Avg Path Ease  
Stan Wawrinka         3                 2.8%  
Novak Djokovic       12                11.3%  
Rafael Nadal         15                13.6%  
Stefan Edberg         4                14.6%  
Andy Murray           3                18.8%  
Boris Becker          4                18.8%  
Mats Wilander         3                19.8%  
Gustavo Kuerten       3                22.0%  
Roger Federer        19                23.5%  
Jim Courier           4                26.4%  
Pete Sampras         14                28.9%  
Andre Agassi          8                32.3%

If Rafa adds to his grand slam haul this weekend, his average path ease will take a bit of a hit. Still, he’ll only move one place down the list, behind Stefan Edberg. After more than a decade of battling all-time greats in the late rounds of majors, it’s fair to say that Nadal deserved this cakewalk.

Update: This post reads a bit differently than when I first wrote it: I’ve changed the references to “path difficulty” to “path ease” to make it clearer what the metric is showing.

Nadal and Anderson advanced to the final, so we can now determine the exact path ease number for whichever one of them wins the title. Rafa’s exact number remains 51.4%, and should he win, his career average across 16 slams will increase to about 15%. Anderson’s path ease to the title is “only” 41.3%, which would be good for ninth on the list shown above, and just barely second easiest of the last 30 US Opens.