Forecasting the Laver Cup

This weekend brings us the first edition of the Laver Cup, a star-studded three-day affair that pits Europe against the rest of the world. The European team features Roger Federer and Rafael Nadal, and even though several other elites from the continent are missing due to injury, the European team is still much stronger on paper.

Here are the current rosters, along with each competitor’s weighted hard court Elo rating and rank among active players:

EUROPE                  Elo Rating  Elo Rank  
Roger Federer                 2350         2  
Rafael Nadal                  2225         4  
Alexander Zverev              2127         7  
Tomas Berdych                 2038        14  
Marin Cilic                   2029        15  
Dominic Thiem                 1995        17  
WORLD                   Elo Rating  Elo Rank  
Nick Kyrgios                  2122         8  
John Isner                    1968        22  
Jack Sock                     1951        23  
Sam Querrey                   1939        25  
Denis Shapovalov              1875        36  
Frances Tiafoe                1574       153  
Juan Martin del Potro*        2154         5

*del Potro has withdrawn. I’ve included his singles Elo rating and rank to emphasize how damaging his absence is to the World squad.

“Weighted” surface Elo is the average of overall (all-surface) Elo and surface-specific Elo. The 50/50 split is a much better predictor of match outcomes than either number on its own.

Nick Kyrgios can hang with anybody on a hard court. But despite some surface-specific skills represented by the American contingent, every other member of the World team rates lower than every member of team Europe. This isn’t a good start for the rest of the world.

What about doubles? Here are the D-Lo (Elo for doubles) ratings and rankings for all twelve participants, plus Delpo:

EUROPE                  D-Lo rating  D-Lo rank  
Rafael Nadal                   1895          4  
Tomas Berdych                  1760         28  
Marin Cilic                    1676         76  
Roger Federer**                1650         90  
Alexander Zverev               1642         99  
Dominic Thiem                  1521        185  
WORLD                   D-Lo rating  D-Lo rank  
Jack Sock                      1866          8  
John Isner                     1755         29  
Nick Kyrgios                   1723         45  
Sam Querrey                    1715         49  
Denis Shapovalov**             1600        130  
Frances Tiafoe                 1546        166  
Juan Martin del Potro*         1711         55

** Federer hasn’t played tour-level doubles since 2015, and Shapovalov hasn’t done so at all. These numbers are my best guesses, nothing more.

Here, the World team has something of an edge. While both sides feature an elite doubles player–Rafa and Jack Sock–the non-European side is a bit deeper, especially if they keep Denis Shapovalov and last-minute Delpo replacement Frances Tiafoe on the sidelines. Only one-quarter of Laver Cup matches are doubles (plus a tie-breaking 13th match, if necessary), so it still looks like team Europe are the heavy favorite.

The format

The Laver Cup will take place in Prague over three days (starting Friday, September 22nd), and consist of four matches each day: three singles and one doubles. Every match is best-of-three sets with ad scoring and a 10-point super-tiebreak in place of the third set.

On the first day, the winner of each match gets one point; on the second day, two points, and on the third day, three points. That’s a total of 24 points up for grabs, and if the twelve matches end in a 12-12 deadlock, the Cup will be decided with a single doubles set.

All twelve participants must play at least one singles match, and no one can play more than two. At least four members of each squad must play doubles, and no doubles pairing can be repeated, except in the case of a tie-breaking doubles set.

Got it? Good.

Optimal strategy

The rules require that three players on each side will contest only one singles match while the other three will enter two each. A smart captain would, health permitting, use his three best players twice. Since matches on days two and three count for more than matches on day one, it also makes sense that captains would use their best players on the final two days.

(There are some game-theoretic considerations I won’t delve into here. Team World could use better players on day one in hopes of racking up each points against the lesser members of team Europe, or could drop hints that they will do so, hoping that the European squad would move its better players to day one. As far as I can tell, neither team can change their lineup in response to the other side’s selections, so the opportunities for this sort of strategizing are limited.)

In doubles, the ideal roster deployment strategy would be to use the team’s best player in all three matches. He would be paired with the next-best player on day three, the third-best on day two, and the fourth-best on day one. Again, this is health permitting, and since all of these guys are playing singles, fatigue is a factor as well. My algorithm thus far would use Nadal five times–twice in singles and three times in doubles–and I strongly suspect that isn’t going to happen.

The forecast

Let’s start by predicting the outcome of the Cup if both captains use their roster optimally, even if that’s a longshot. I set up the simulation so that each day’s singles competitors would come out in random order–if, say, Querrey, Shapovalov, and Tiafoe play for team World on day one, we don’t know which of them will play first, or which European opponent each will face. So each run of the simulation is a little different.

As usual, I used Elo (and D-Lo) to predict the outcome of specific matchups. Because of the third-set super-tiebreak, and because it’s an exhibition, I added a bit of extra randomness to every forecast, so if the algorithm says a player has a 60% chance of winning, we knock it down to around 57.5%. When I dug into IPTL results last winter, I discovered that exhibition results play surprisingly true to expectations, and I suspect players will take Laver Cup a bit more seriously than they do IPTL.

Our forecast–again, assuming optimal player usage–says that Europe has an 84.3% chance of winning, and the median point score is 16-8. There’s an approximately 6.5% chance that we’ll see a 12-12 tie, and when we do, Europe has a slender 52.4% edge.

If Delpo were participating, he would increase the World team’s chances by quite a bit, reducing Europe’s likelihood of victory to 75.5% and narrowing the most probable point score to 15-9.

What if we relax the “optimal usage” restriction? I have no idea how to predict what captains John McEnroe and Bjorn Borg will do, but we can randomize which players suit up for which matches to get a sense of how much influence they have. If we randomize everything–literally, just pick a competitor out of a hat for each match–Europe comes out on top 79.7% of the time, usually winning 15-9. There’s a 7.6% chance of a tie-breaking 13th match, and because the World team’s doubles options are a bit deeper, they win a slim majority of those final sets. (When we randomize everything, there’s a slight risk that we violate the rules, perhaps using the same doubles pairing twice or leaving a player on the bench for all nine singles matches. Those chances are very low, however, so I didn’t tackle the extra work required to avoid them entirely.)

We can also tweak roster usage by team, in case it turns out that one captain is much savvier than the other. (Or if a star like Nadal is unable to play as much as his team would like.) The best-case scenario for our World team underdogs is that McEnroe chooses the best players for each match and Borg does not. Assuming that only European players are chosen from a hat, the probability that the favorites win falls all the way to 63.1%, and the typical gap between point totals narrows all the way to 13-11. The chance of a tie rises to 10%.

On the other hand, it’s possible that Borg is better at utilizing his squad. After all, it doesn’t take an 11-time grand slam winner to realize that Federer and Nadal ought to be on court when the stakes are the highest. This final forecast, with random roster usage from team World and ideal choices from Borg, gives Europe a whopping 92.3% chance of victory, and median point totals of 17 to 7. The World team would have only a 4% shot at reaching a deadlock, and even then, the Europeans win two-thirds of the tiebreakers.

There we have it. The numbers bear out our expectation that Europe is the heavy favorite, and they give us a sense of the likely margin of victory. Tiafoe and Shapovalov might someday be part of a winning Laver Cup side, but it looks like they’ll have to wait a few years before that happens.

Update: One more thing… What about doubles specialists? Both captains have two discretionary picks to use on players regardless of ranking. Most great doubles players are much worse at singles, but as we’ve seen, a player can be relegated to a lone one-point singles match on day one, and as a doubles player, he can have an effect on three different matches, totaling six points.

Sure enough, swapping out Dominic Thiem (a very weak doubles player for whom indoor hard courts are less than ideal) for Nicolas Mahut would have increased Europe’s chances of winning from 84.3% to 88.5%. On the slight chance that the Cup stayed tight through the final doubles match and into a tiebreaker, the doubles team of Mahut-Nadal (however unorthodox that sounds) would be among the best that any captain could put on the court.

There’s even more room for improvement on the World side, especially with del Potro out. At the moment, the third-highest rated hard court player by D-Lo is Marcelo Melo, who would be a major step down in singles but a huge improvement on most of the potential partners for Sock in doubles. If we give him a singles Elo of 1450 and put him on the roster in place of Tiafoe and pit the resulting squad against the original Europe team (with Thiem, not Mahut), it almost makes up for the loss of Delpo–World’s chances of winning increase from 15.7% to 19.3%.

Unfortunately, Borg and McEnroe may have missed their chance to eke out extra value from their six-man rosters–this is a trick that will only work once. If both teams made this trade, Mahut-for-Thiem and Melo-for-Tiafoe, each side’s win probability goes back to near where it started: 85.8% for Europe. That’s a boost over where we started (84.3%), just because Mahut is better suited for the competition than Melo is, as an elite doubles specialist who is also credible on the singles court. No one available to the World team (except for Sock, who is already on the roster) fits the same profile on a hard court. Vasek Pospisil comes to mind, though he has taken a step back from his peaks in both singles and doubles. And on clay, Pablo Cuevas would do nicely, but on a faster surface, he would represent only a marginal improvement over the doubles players already playing for team World.

Maybe next year.


A Preface to All GOAT Arguments

Earlier this week, The Economist published my piece about Rafael Nadal’s and Roger Federer’s grand slam counts. I made the case that, because Nadal’s paths to major titles had been more difficult (the 2017 US Open notwithstanding), his 16 slams are worth more–barely!–than Federer’s.

Inevitably, some readers reduced my conclusion to something like, “stats prove that Nadal is the greatest ever.” Whoa there, kiddos. It may be true that Nadal is better than Federer, and we could probably make a solid argument based on the stats. But a rating of 18.8 to 18.7, based on 35 tournaments, can’t quite carry that burden.

There are two major steps in settling any “greatest ever” debate (tennis or otherwise). The first is definitional. What do we mean by “greatest?” How much more important are slams than non-slams? What about longevity? Rankings? Accomplishments across different surfaces? How much weight do we give a player’s peak? How much does the level of competition matter? What about head-to-head records? I could go on and on. Only when we decide what “greatest” means can we even attempt to make an argument for one player over another.

The second step–answering the questions posed by the first–is more work-intensive, but much less open to debate. If we decide that the greatest male tennis player of all time is the one who achieved the highest Elo rating at his peak, we can do the math. (It’s Novak Djokovic.) If you pick out ten questions that are plausible proxies for “who’s the greatest?” you won’t always get the same answer. Longevity-focused variations tend to give you Federer. (Or Jimmy Connors.) Questions based solely on peak-level accomplishments will net Djokovic (or maybe Bjorn Borg). Much of the territory in between is owned by Nadal, unless you consider the amateur era, in which case Rod Laver takes a bite out of Rafa’s share.

Of course, many fans skip straight to the third step–basking in the reflected glory of their hero–and work backwards. With a firm belief that their favorite player is the GOAT, they decide that the most relevant questions are the ones that crown their man. This approach fuels plenty of online debates, but it’s not quite at my desired level of rigor.

When the big three have all retired, someone could probably write an entire book laying out all the ways we might determine “greatest” and working out who, by the various definitions, comes out on top. Most of what we’re doing now is simply contributing sections of chapters to that eventual project. Now or then, one blog post will never be enough to settle a debate of this magnitude.

In the meantime, we can aim to shed more light on the comparisons we’re already making. Grand slam titles aren’t everything, but they are important, and “19 is more than 16” is a key weapon in the arsenal of Federer partisans. Establishing that this particular 19 isn’t really any better than that particular 16 doesn’t end the debate any more than “19 is more than 16” ever did. But I hope that it made us a little more knowledgeable about the sport and the feats of its greatest competitors.

At the one-article, 1,000-word scale, we can achieve a lot of interesting things. But for an issue this wide-ranging, we can’t hope to settle it in one fell swoop. The answers are hard to find, and choosing the right question is even more difficult.


Fun With Service Point Ratios

In Rafael Nadal‘s comprehensive victory over Kevin Anderson in the 2017 US Open final, Nadal didn’t face a single break point. Anderson didn’t even earn very many deuces. Nadal, on the other hand, constantly challenged in his opponent’s service games.

This produced an unusual ratio: Anderson had to play way more service points than Nadal did, even though they served the same number of games. Rafa toed the line only 72 times to the South African’s 108, for a ratio of 2/3 or, rounded, 0.67. In this week’s podcast, I speculated that this service point ratio is a handy way of spotting winners–if one man is getting through his service games much quicker than the other, it’s probably because he is holding easily and his opponent is not.

It wasn’t the best hypothesis I’ve ever put forward. It’s true, but not by an overwhelming margin. In the average ATP match, the ratio of the winner’s service points played to the loser’s service points played is 0.96 — equivalent to Rafa serving 88 times to Anderson’s 92. The winnner plays fewer service points in 57% of contests. We’ve hardly discovered the next IBM Key to the Match here.

Instead of discovering a useful proxy for success in the most basic of match stats, we’ve come upon yet another item to add to the list of Nadal’s extreme accomplishments. Of nearly 13,000 completed grand slam singles matches since 1991, only 147 of the winners–barely one percent–had service point ratios below 0.67. Out of 106 major finals with stats available, Rafa’s ratio on Sunday was the lowest on record. He just edged out Roger Federer‘s 0.68 ratio from the 2007 Australian Open final against Fernando Gonzalez.

It turns out that the service point ratio is as fluky for Rafa as it is for men as a whole. Of his 16 victories in grand slam finals, he has posted a ratio below 1.0 in eight of them, equal to 1.0 once, and above 1.0 seven times. His average is an uninteresting 0.98.

There you have it: Over the course of a single week, we’ve seen an oddity, devised a stat to capture it, and determined that it doesn’t tell us much. Analytics, anyone?

For a more serious look at Rafa’s career accomplishments after bringing home his 16th major title, check out my analysis posted yesterday at The Economist’s Game theory blog.

Denis Shapovalov and Fast ATP Starts

18-year-old Canadian lefty Denis Shapovalov has had one heck of a summer. In Montreal, he defeated Juan Martin del Potro and Rafael Nadal in back-to-back matches, and at the US Open, he qualified for the main draw, upset Jo Wilfried Tsonga, and reached the fourth round in only his second appearance at a major.

Thanks to those wins and the big stages on which he achieved them, he has cracked the ATP top 60, despite playing fewer than 20 tour-level matches. The Elo rating system, which awards points based on opponent quality, is even more optimistic. By that measure, with his win over Tsonga, Shapovalov improved to 1950–good for 34th on tour–before losing about 25 Elo points in his loss to Pablo Carreno Busta.

While an Elo score of 1950 is an arbitrary number–there’s nothing magical about any particular Elo threshold; it’s just a mechanism to compare players to each other–it gives us a way to compare Shapovalov’s hot start with other players who made quick impacts at tour level. Since the early 1980s, only 13 players have reached a 1950 Elo score in fewer matches than the Canadian needed. As usual with early-career accomplishments, there are a few unexpected names in the mix, but overall, it’s very promising company for an 18-year-old:

Player               Matches   Age  
Lleyton Hewitt             7  16.9  
Jarkko Nieminen            7  20.2  
Juan Carlos Ferrero       10  19.4  
David Ferrer              12  20.4  
Kenneth Carlsen           12  19.4  
Tommy Haas                13  19.1  
Peter Lundgren            13  20.7  
John Van Lottum           14  21.8  
Sergi Bruguera            14  18.4  
Julian Alonso             15  20.0

Player               Matches   Age   
Xavier Malisse            16  18.6  
Jan Siemerink             16  20.9  
Ivo Minar                 16  21.2  
Florian Mayer             17  20.7  
Cristiano Caratti         17  20.7  
Nick Kyrgios              17  19.3  
Denis Shapovalov          17  18.4  
Martin Strelba            17  22.1  
Jay Berger                17  20.2  
Andy Roddick              18  18.6

I identified just over 350 players who, at some point in their careers, peaked with an Elo score of at least 1950. On average, these players needed 75 matches to reach that level (the median is 59), and two active tour-regulars, Gilles Muller and Albert Ramos, needed almost 300 matches to achieve the threshold.

Shapovalov’s record so far is equally impressive when we consider it in terms of age. Again, he’s among the top 20 players in modern tennis history: Only 11 players got to 1950 before their 18th birthday. The Canadian is only a few months beyond his. And many of the other ATPers who reached that score at an early age needed much more tour experience. I’ve included the top 30 on this list to show how Shapovalov compares to so many of the game’s greats:

Player                  Matches   Age  
Aaron Krickstein             25  16.4  
Michael Chang                32  16.5  
Lleyton Hewitt                7  16.9  
Boris Becker                 27  17.5  
Mats Wilander                27  17.5  
Guillermo Perez Roldan       26  17.6  
Andre Agassi                 46  17.6  
Pat Cash                     66  17.6  
Goran Ivanisevic             35  17.7  
Andrei Medvedev              22  17.8  

Player                  Matches   Age
Rafael Nadal                 44  17.9  
Sammy Giammalva              21  18.0  
Horst Skoff                  19  18.1  
Jimmy Arias                  61  18.2  
Kent Carlsson                56  18.3  
Sergi Bruguera               14  18.4  
Denis Shapovalov             17  18.4  
Andy Murray                  22  18.4  
Juan Martin del Potro        31  18.4  
Fabrice Santoro              59  18.5  

Player                  Matches   Age
John McEnroe                 28  18.5  
Roger Federer                40  18.5  
Stefan Edberg                40  18.5  
Andy Roddick                 18  18.6  
Pete Sampras                 56  18.6  
Thomas Enqvist               28  18.6  
Xavier Malisse               16  18.6  
Novak Djokovic               33  18.8  
Jim Courier                  51  18.8  
Yannick Noah                 41  18.8

There are no guarantees when it comes to tennis prospects, but this is very good company. On average, the 23 other players to reach the 1950 Elo threshold at age 18 improved their Elo ratings to 2100 before age 20, and rose to 2250 at some point in their careers. The first number would be good for 12th on today’s list, and the second would merit 5th place, just behind the Big Four. Nadal and del Potro were the first of Shapovalov’s high-profile victims, and judging from this sharp career trajectory, they won’t be the last.

Podcast Episode 17: US Open in Review

Episode 17 of the Tennis Abstract Podcast, with Carl Bialik, is our US Open recap. We start with a discussion of Sloane Stephens–her performance here as well as what we expect from her, and we delve into possible explanations of her impressive performance in particular against aggressive players.

We then talk Nadal and his no-nonsense strategy to defeat Kevin Anderson, and consider best-case scenarios for the rest of Kev’s career. We finish up with some doubles and a bit on this weekend’s Davis Cup ties. As always, thanks for listening!

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

Podcast Episode 16: The Second Half of our Second Week Chat

Episode 16 of the Tennis Abstract Podcast, with Carl Bialik, didn’t quite work out as planned — my microphone malfunctioned for much of the first half of the recording — but the second half of our conversation could be salvaged. Thus, this episode is missing the big news of the second week, the all-American women’s semifinals, but we still touched on a variety of burning US Open topics, like the youngsters making news in New York and the inevitable hypotheticals of the players who weren’t able to participate in Flushing this year.

This is a shorter-than usual episode, clocking in at 34 minutes; we hope to return on Friday with another mid-Slam update. Thanks for listening!

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

Quantifying Cakewalks, or The Time Rafa Finally Got Lucky

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.