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.

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!

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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!

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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.

Podcast Episode 15: Return of the Podcast

The long-awaited Episode 15 of the Tennis Abstract Podcast is Carl Bialik’s and my lightning-round update on the summer of tennis and a midway-point checkup of the US Open. I boldly select Diego Schwartzman and Anastasija Sevastova as my picks to win it all, while Carl says much more sensible things.

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!

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How Elo Rates US Open Finalists Flavia Pennetta and Roberta Vinci

Among the many good things that have happened to Flavia Pennetta and Roberta Vinci after reaching the final of this year’s US Open, both enjoyed huge leaps in Monday’s official WTA rankings. Pennetta rose from 26th to 8th, and Vinci jumped from 43rd to 19th.

Such large changes in rankings are always a little suspicious and expose the weakness of systems that award points based on round achieved. A lucky draw or one incredible outlier of a match doesn’t mean that a player is suddenly massively better than she was a couple of weeks ago.

To put it another way: As they are, the official rankings do a decent job of representing how a player has performed. What they don’t do so well is represent how well someone is playing, or the closely related issue of how well she will play.

For that, we can turn to Elo ratings, which Carl Bialik and Benjamin Morris used at the beginning of the US Open to compare Serena Williams to other all-time greats [1]. Elo awards points based on opponent quality, not the importance of the tournament or round. As such, the system provides a better estimate of the current skill level of each player than the official rankings do.

Sure enough, Elo agrees with my hypothesis, that Pennetta didn’t suddenly become the 8th best player in the world. Instead, she rose to 17th, just behind Garbine Muguruza (another Slam finalist overestimated by the rankings) and ahead of Elina Svitolina. Vinci didn’t really return to the top 20, either: Elo places her 34th, between Camila Giorgi and Barbora Strycova.

While her official ranking of 8th is Pennetta’s career high, Elo disagrees again. The system claims that Pennetta peaked during the US Open six years ago, after a strong summer that involved semifinal-or-better showings in four straight tournaments, plus a fourth-round win over Vera Zvonareva in New York. She’s more than 100 points below that career-high level, equivalent to the present gap between her and 7th-Elo-rated Angelique Kerber.

The current Elo rankings hold plenty of surprises like this, having little in common with the official rankings:

Rank  Player                 Elo  
1     Serena Williams       2460  
2     Maria Sharapova       2298  
3     Victoria Azarenka     2221  
4     Simona Halep          2204  
5     Petra Kvitova         2174  
6     Belinda Bencic        2144  
7     Angelique Kerber      2130  
8     Venus Williams        2126  
9     Caroline Wozniacki    2095  
10    Lucie Safarova        2084

Rank  Player                 Elo   
11    Ana Ivanovic          2078  
12    Carla Suarez Navarro  2062  
13    Agnieszka Radwanska   2054  
14    Timea Bacsinszky      2041  
15    Sloane Stephens       2031  
16    Garbine Muguruza      2031  
17    Flavia Pennetta       2030  
18    Elina Svitolina       2023  
19    Madison Keys          2019  
20    Jelena Jankovic       2016

While Victoria Azarenka is still nearly 200 points shy of her peak, Elo gives her credit for the extremely tough draws that have met her return from injury. Another player rated much higher here than in the WTA rankings is Belinda Bencic, whose defeat of Serena launched her into the top ten.

The oldest final

Pennetta and Vinci are both unusually old for Slam finalists, not to mention players who reached that milestone for the first time. Elo doesn’t consider them among the very best players active today, but next to other 32- and 33-year-olds in WTA history, they compare very well indeed.

Among players 33 or older, Pennetta’s current rating is sixth best in the last thirty-plus years [2]. As the all-time list shows, that puts her in extraordinarily good company:

Rank  Player                Age   Elo  
1     Martina Navratilova  33.4  2527  
2     Serena Williams      33.9  2480  
3     Chris Evert          33.4  2412  
4     Venus Williams       33.3  2175  
5     Nathalie Tauziat     33.9  2088  
6     Flavia Pennetta      33.5  2030  
7     Wendy Turnbull       33.1  2018  
8     Conchita Martinez    33.3  2014

In the 32-and-over category, Vinci stands out as well. Her lower rating, combined with the somewhat larger pool of players who remained competitive to that ago, means that she holds 24th place in this age group. For a player who has never cracked the top ten, 24th of all time is an impressive accomplishment.

Keep an eye out for more Elo-based analysis here. Soon, I’ll be able to post and update Elo ratings on Tennis Abstract and, once a few more kinks are worked out, use them to improve the WTA tournament forecasts on the site as well.

Continue reading How Elo Rates US Open Finalists Flavia Pennetta and Roberta Vinci

Break Point Conversions and the Close Matches Federer Isn’t Winning

The career head-to-head between Roger Federer and Novak Djokovic sits at 21-21, but the current era of this rivalry is hardly even. Since the beginning of 2011, Djokovic has won 15 of 23, including last night’s US Open final.

These matches tend to be close ones. In only 7 of the 23 matches has either player won more than 55% of points, and in more than half (12 of 23), neither player has won more than 53% of points, fitting my proposed definition of lottery matches.

In the 12 lottery matches between Fed and Novak since 2011, the player who won the most points always won the match. Yet Djokovic wins far more (9 of 12) of these close matches. Last night was a perfect example: Federer won more return points than his opponent, and it was the third time since the 2012 Tour Finals that the Novak beat Fed while winning 50.3% of points.

When a player wins 50.3% of points, he wins the match only 59% of the time. Even at 51.8%, Novak’s total points won in three other Federer matches, the player with more points wins only 91% of the time.

If many of the matches are close, and one player is winning so many of the matches, there must be more to the story.

Back to break points

Clearly, Novak is winning more big points than Roger is. Since Federer has won more than half of the tiebreaks between them, the next logical place to look is break points.

Federer’s perceived inability to convert break points has been a concern for years. Early last year, I wrote about his success rate on break points, and found that while he does, in fact, convert fewer break points than expected, it’s only a few percentage points. Further, it’s not a new problem: He was winning fewer break points than he should have been back when he was the unchallenged top player in the game.

Against Novak, though, it’s another story, and since they’ve faced each other so often, we can no longer write off a poor break-point performance as an outlier.

In these last 23 matches–including last night’s 4-for-23 on break points–Federer has converted 15% fewer break points than expected, twice as bad as his worst single-season mark. Djokovic, on the other hand, has converted break points at almost the same rate as other return points.

I’m often hesitant to use the c-words, but the evidence is piling up that in these particular clutch situations, Roger is choking. At the very least, we can eliminate a couple of alternative explanations, those based on break point opportunities and on performance in the ad court.

Let’s start with break point opportunities. 4-for-23 on break points is painful to look at, but there is a positive: You have to play very well to generate 23 break point chances against a top player. In fact, there’s a very clear, almost linear relationship between return points won and break point chances generated, and Federer beat expectations by 77% yesterday. Over 21 return games, a player who won 39% of return points, as Roger did, would be expected to create only 13 break point opportunities. A 4-for-13 mark would still be disappointing, but it wouldn’t induce nearly as many grimaces.

In these 23 matches, Federer has generated exactly as many break point chances as expected. Djokovic has done the same. The story here is clearly about performance at 30-40 or 40-AD, not on anything earlier in the game. On non-break points yesterday, Fed returned more effectively.

The other explanation would be that Roger’s poor break point record has to do with the ad court. Against Rafael Nadal, that might be true: Much of the Spaniard’s effectiveness saving break points has to do with the way he skillfully uses left-handed serving in that court.

But in the Novak-Fed head-to-head, we can rule this out as well.  According to Match Charting Project data, which includes more than 40 Djokovic matches and 90 Federer matches, neither player performs much better in either half of the court. Djokovic wins more service points in the deuce court–65% to 64% in general, 66% to 64% on hard courts, and Federer wins return points at the same rate in both courts.

Pundits like to say that tennis is a game of matchups, and in this rivalry, both players defy their typical patterns. Over the course of his career, Novak has saved break points more effectively than average, but not nearly as well as he does against Federer. Federer, for his part, has turned in some of his best return performances against Djokovic … except for these dismal efforts converting break points, when he is far worse than his already-weak averages.

Perhaps the only solution for Roger is to find even more ways to improve his world-class service games. In the previous match against Novak, he converted only one of eight break point chances–the sort of stat that would easily explain a loss. That day in Cincinnati, though, Federer’s one break of serve was better than Djokovic’s zero.

Fed won 56.4% of total points in that match, his third highest rate against Djokovic since 2011. If Novak is going to play better clutch tennis and win the close matches, that leaves Federer with an unenviable alternative. To win, he must decisively outplay the best player in the world.