Del Potro’s Draws and the Possible Persistence of Bad Luck

Tennis’s draw gods have not been kind to Juan Martin del Potro this year.

In Acapulco and Indian Wells, he drew Novak Djokovic as his second-match opponent. In Miami, Delpo got a third-rounder with Roger Federer. In each of the March Masters events, with 1,000 ranking points at stake, del Potro was handed the most difficult opponents for his first round against a fellow seed. Thanks in part to the resulting early exits, one of the most dangerous players on tour is still languishing outside of the top 30 in the ATP rankings.

When I wrote about the Indian Wells quarter of death–the section of the draw containing del Potro, Djokovic, Federer, Rafael Nadal, and Nick Kyrgios–I attempted to quantify the effect of the draw on each player’s expected ranking points. Before each player’s name was placed in the bracket, my model predicted that Delpo would earn about 150 ranking points–the weighted average of his likelihood of reaching the third round, the fourth round, and so on–and after the draw was conducted, his higher probability of a clash with Djokovic knocked that number down to just over 100. That negative effect was one of the worst of any player in the tournament.

The story in Miami is similar, if less extreme. Pre-draw, Delpo’s expected points were 183. Post draw: 155. In the four tournaments he has entered this year, he has been uniformly unlucky:

Tournament    Pre-Draw  Post-Draw  Effect  
Delray Beach      89.3       74.0  -17.1%  
Acapulco         121.5       97.1  -20.1%  
Indian Wells     154.6      102.5  -33.7%  
Miami            182.9      155.4  -15.0%  
TOTAL            548.2      429.0  -21.7%

*The numbers above for Indian Wells are slightly different than what I published in the Indian Wells article, since the simulations I ran for this post consider the entire 96-player field, not just the 64-player second round.

The good news, as we’ll see, is that it’s virtually impossible for this degree of misfortune to continue. The bad news is that those 119 points are gone forever, and at Delpo’s current position in the ranking table, that disadvantage will affect his tournament seeds, which in turn will result in worse draws (earlier meetings with higher-ranked players, independent of luck) for at least another few weeks.

Before we go any further, let me review the methodology I’m using here. (If you’re not interested, skip this paragraph.) For “post-draw” expected points, I’m taking jrank-based forecasts–like the ones on the front page of Tennis Abstract–and using each player’s probability of each round to calculate a weighted average of expected points. “Pre-draw” forecasts are much more computationally demanding. In Miami, for instance, Delpo could’ve faced any of the 64 unseeded players in the second round and been slated to meet any of the top eight seeds in the third round. For each tournament, I ran a Monte Carlo simulation with the tournament seeds, generating a new draw and simulating the tournament–100,000 times, then summing all those outcomes. So in the pre-draw forecast, Delpo had a one-eighth chance of getting Fed in the third round, a one-eighth chance of getting Kei Nishikori there, and so on.

It seems clear that a 22%, 119-point rankings hit over the course of four tournaments is some seriously bad luck. Last year, there were about 750 instances of a player being seeded at an ATP tournament, and in fewer than 60 of those, the draw resulted in an effect of -22% or worse on the player’s expected ranking points. And that’s just one tournament! The odds that Delpo would get such a rough deal in all four of his 2017 tournaments are 1 in more than 20,000.

Over the course of a full season, draw luck mostly evens out. It’s rare to see an effect of more than 10% in either direction. Last year, Thiemo de Bakker saw a painful difference of 18% between his pre-draw and post-draw expected points in 12 ATP events, but everyone else with at least that many tournaments fell between -11% and +11%, with three-quarters of players between -5% and +5%. Even when draw luck doesn’t balance itself out, the effect isn’t as bad as what Delpo has seen in 2017.

Del Potro’s own experience in 2016 is a case in point. His most memorable event of the season was the Olympics, where he drew Djokovic in the first round, so it’s easy to recall his year as being equally riddled with bad luck. But in his 12 other ATP events, the draw aided him in six–including a +34% boost at the US Open–and hurt him at the other six. Altogether, his 2016 ATP draws gave him a 5.9% advantage over his “pre-draw” expected points–a bonus of 17 ranking points. (I didn’t include the Olympics, since no ranking points were awarded there.)

Taken together, Delpo’s 2016-17 draws have deprived him of about 100 ranking points, which would move him three spots up the ranking table. So even with a short stretch of extreme misfortune, draw luck hasn’t affected him that much. Last year’s most extreme case among elite players, Richard Gasquet, suffered a similar effect: His draws knocked down his expected take by 9%, or 237 points, a difference that would bump him up from #22 to #19 in this week’s ranking list.

There are many reasons to believe that del Potro is a much better player than his current ranking suggests, such as his Elo rating, which stands at No. 7. But his ATP ranking reflects his limited schedule and modest start last year much more than it does the vagaries of each week’s brackets. The chances are near zero that he will continue to draw the toughest player in each tournament’s field in the earliest possible round, so we’ll soon have a better idea of what exactly he is capable of, and where exactly he should stand in the rankings.

Are Taller Players the Future of Tennis?

This is a guest post by Wiley Schubert Reed.

This week, the Memphis Open features the three tallest players ever to play professional tennis: 6-foot-10″ John Isner, 6-foot-11″ Ivo Karlovic, and 6-foot-11″ Reilly Opelka. And while these three certainly stand out among all players in the sport, they are by no means the only giants in the game. Also in the Memphis draw: 6-foot-5″ Dustin Brown, 6-foot-6″ Sam Querrey, and 6-foot-8″ Kevin Anderson. (Brown withdrew due to injury, and with Opelka’s second-round loss yesterday, Isner and Karlovic are the only giants remaining in the field.)

We got tall guys. #MemphisOpen

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There is no denying that the players on the ATP and WTA tours are taller than the ones who were competing 25 years ago. The takeover by the tall has been obvious for some time in the men’s game, and it’s extended to near the very top of the women’s game as well. But despite alarms raised about the unbeatable giants among men, the merely tall men have held on to control of the game.

The main reason: The elegant symmetry at the game’s heart. The tallest players have an edge on serve, but that’s just half of tennis. And on the return, extreme height–at least for the men–turns out to be a big disadvantage. But a rising crop of tall men have shown promise beyond their service games. If one of the tallest young stars is going to challenge the likes of Novak Djokovic and Andy Murray, he’ll have to do it by trying to return serve like them, too.

Sorting out exactly how much height helps a player is a complicated thing. Just looking at the top 100 pros, for instance, makes the state of things look like a blowout win in favor of the tall. The median top-100 man is nearly an inch taller today than in 1990, and the average top-100 woman is 1.5 inches taller [1]. The number of extremely tall players in the top 100 has gone up, too:

                                    1990  Aug 2016  
Top 100 Men      Median Height  6-ft-0.0  6-ft-0.8  
               At least 6-ft-5        3%       16%  
Top 100 Women    Median Height  5-ft-6.9  5-ft-8.5  
                 At least 6-ft        8%        9%

Height is clearly a competitive advantage, as taller young players rise faster through the rankings than their shorter peers. Among the top 100 juniors each year from 2000 to 2009 [2], the tallest players (6-foot-5 and over for men and 6-foot and over for women) [3] typically sit in the middle of the rankings. But they do better as pros: They were ranked on average approximately 127 spots higher than shorter players their age after four years for men and approximately 113 spots higher after four years for women.

Boys' pro ranking by height Girls' pro ranking by height

 

Thus, juniors who are very tall have the best chance to build a solid pro career. But does that advantage hold within the top 100 of the pro rankings? Are the tallest pros the highest ranked? 

For the women, they clearly are. From 1985 to 2016, the median top 10 woman was 1.2 inches taller than the median player ranked between No. 11 and No. 100, and the tallest women are winning an outsize portion of titles, with women 6-foot and taller winning 15.0 percent of Grand Slams, while making up only 6.6 percent of the top 100 over the same period. Most of these wins were by Lindsay Davenport, Venus Williams and Maria Sharapova. Garbiñe Muguruza became the latest 6-foot women’s champ at the French Open last year [4]. 

It’s a different story for the men, however. From 1985 to 2016, the median height of both the top 10 men and men ranked No. 11 to No. 100 was the same: 6-foot-0.8. And in those same 32 years, only three Grand Slam titles (2.4 percent) were won by players 6-foot-5 or taller (one each by Richard Krajicek, Juan Martin del Potro and Marin Cilic), while over the same period, players 6-foot-5 and above made up 7.7 percent of the top 100. In short, the tallest women are overperforming, while the tallest men are underperforming.

Why have all the big men accomplished so little collectively? One big reason is that whatever edge the tallest men gain in serving is cancelled out by their disadvantage when returning serve. I compared total points played by top-100 pros since 2011, and found that while players 6-foot-5 and over have a clear service advantage and return disadvantage, their height doesn’t seem to have a major impact on overall points won:

Height            % Svc Pts Won  % Ret Pts Won  % Tot Pts Won  
6-ft-5 and above          66.8%          35.7%          51.2%  
6-ft-1 to 6-ft-4          64.5%          37.8%          51.1%  
6-ft-0 and below          62.3%          39.1%          51.1%

Taller players serve better for two reasons. First, their height lets them serve at a sharper angle by changing the geometry of the court. With a sharper angle available to them, they have a greater margin for error to clear the top of the net while still getting the ball to bounce on or inside the service line. And a sharper angle also makes the ball bounce higher, up and out of returners’ strike zone [5].

Serve trajectory

Disregarding spin, for a 6-foot player to serve the ball at 120 miles per hour at the same angle as a 6-foot-5 player, he would need to stand more than 3 feet inside the baseline.

Second, a taller player’s longer serving arm allows him to whip the ball faster. For you physics fans, the torque (in this case magnitude of force imparted on the ball) is directly proportional to the radius of the lever arm (in this case the server’s extended arm and racket). As radius (arm length) increases, so does torque. There is no way for shorter players to make up this advantage. Six-foot-8 Kevin Anderson, current No. 74 in the world and one of the tallest players ever to make the top 10, told me, “I always say it’ll be easier for me to move like Djokovic than it will be for Djokovic to serve like me.”

One would think that height could be an advantage on return as well, with increased wingspan offering greater reach. 18-year-old, 6-foot-11 Reilly Opelka, who is already as tall as the tour’s reigning giant Ivo Karlovic and who ESPN commentator Brad Gilbert said will be “for sure the biggest ever,” told me his height gives him longer leverage. “My reach is a lot longer than a normal tennis player, so I’m able to cover a couple extra inches, which is pretty huge in tennis.”

But Gilbert and Tennis Channel commentator Justin Gimelstob said they believe tall players struggle on return because their higher center of gravity hurts their movement. If a very tall man can learn to move like the merely tall players that have long dominated the sport––Djokovic, Murray (6-foot-3), Roger Federer (6-foot-1) and Rafael Nadal (6-foot-1)–– Gilbert thinks he could be hard to stop. “If you’re 6-foot-6 and are able to move like that, I can easily see that size dominating,” he said.

Interestingly, Gilbert pointed out that some of the best returners in the women’s game––such as Victoria Azarenka (6-foot-0) and Maria Sharapova (6-foot-2)––are among its tallest players [6]. Carl Bialik asked three American women — 5-foot-11 Julia Boserup, 5-foot-10 Jennifer Brady and 5-foot-4 Sachia Vickery — why they think taller women aren’t at a disadvantage on return. They cited two main reasons: 1) Women are returning women’s serves, which are slower and have less spin, on average, than men’s serves, so they have more time to make up for any difficulty in movement; and 2) Women play on the same size court that men do, but a height that’s relatively tall for a woman is about average for men, and it’s a height that works well for returning, no matter your gender.

“On the women’s side, we don’t really have anyone who’s almost 6-foot-11 or 7-foot tall,” Brady said. While she’s above average height on the women’s tour, “I’m not as tall as Reilly Opelka,” she said.

Another reason players as tall as Opelka tend to struggle on return could be that they focus more in practice on improving their service game, which exacerbates the serve-oriented skew of their games. “Being tall helps with the serve and you maybe tend to focus on your serve games even more,” Karlovic, the tallest top 100 player at 6-foot-11 [7], said in an interview conducted on my behalf by members of the ATP World Tour PR & Marketing staff at the Bucharest tournament in April. “Shorter players aren’t as strong at serve so they work their return more.”

Charting the careers of all active male players 6-foot-5 and above who at some point ranked year-end top 100 bears this out. Their percentage of service points won increased by about 6 percentage points over their first eight years on tour [8], while percentage of return points won only increased by about 1.5 percentage points. In contrast, Novak Djokovic has steadily improved his return points won from 36.7 percent in 2005 to 43.9 percent in 2016.

When very tall men break through, it’s usually because of strong performance on return: del Potro and Cilic, who are both 6-foot-6, boosted their return performances to win the US Open in 2009 and 2014, respectively. At the 2009 US Open, del Potro won 44 percent of return points, up from his 40 percent rate on the whole year, including the Open. At the 2014 US Open, Cilic won 41 percent of return points, up from 38 percent that year. And they didn’t improve their return games by facing easy slates of opponents: Each man improved on his return-point winning rates against those same opponents over his career by about the same amount as he elevated his return game compared to the season as a whole.

“It’s a different type of pressure when you’re playing a big server who is putting pressure on you on both the serve and the return,” Gimelstob said. “That’s what Cilic was doing when he won the US Open. That’s the challenge of playing del Potro because he hits the ball so well, but obviously serves so well, also.” To put things into perspective, if del Potro and Cilic had returned at these levels across 2016, each would have ranked among the top seven returners in the game, joining Djokovic, Nadal, Murray, 5-foot-11 David Goffin, and 5-foot-9 David Ferrer. Neither man, though, has been able to return to a Slam final; del Potro has struggled with injury and Cilic with inconsistency.

For the tallest players, return performance is the difference between making the top 50 and the top 10. On average, active players 6-foot-5 and above who finished a year ranked in the top 10 won 67.7 percent of service points that year, while those who finished a year ranked 11 through 50 won 68.1 percent of service points, on average. That’s a difference of only 0.4 percentage points. The difference in return performance between merely making the top 50 and reaching the top 10, however, is far more striking: Tall players who made the top 10 win return points at a rate nearly 4 percentage points higher than do players ranked 11 through 50.

Tall players' points won

A solid-serving player 6-foot-5 or taller who can consistently win more than 38 percent of points on return has an excellent chance of making the top 10. Tomas Berdych and del Potro have done it, and Milos Raonic is approaching that mark, one reason he reached his first major final this year at Wimbledon. Today there are several tall young men who look like they could eventually win 38 percent of return points or better. Alexander Zverev (ranked 18) and Karen Khachanov (ranked 48) are both 6-foot-6, each won about 38 percent of return points in 2016, and neither is older than 20. Khachanov has impressed Gilbert and Karlovic. “That guy moves tremendous for 6-foot-6,” Gilbert said.

Other giants have impressed recently. Jiri Vesely, who is 23 and 6-foot-6, beat Novak Djokovic last year in Monte Carlo and won nearly 36 percent of return points in 2016. Opelka reached his first tour-level semifinal, in Atlanta. Most of the top 10 seeds at Wimbledon lost to players 6-foot-5 or taller. Del Potro won Olympic silver, beating Djokovic and Nadal along the way.

But moving from the top 10 to the top 1 or 2 is another question. Can a taller tennis player develop the skills to move as well as the top shorter players, and win multiple major titles? Well, it’s happened in basketball. “We haven’t had a big guy play tennis that’s like 6-foot-6, 6-foot-7, 6-foot-8, that’s moved like an NBA guy,” Gilbert said. “When you get that, that’s when you get a multiple Slam winner.” Anderson agrees that height is not the obstacle to movement people play it up to be: “You know, LeBron is 6-foot-8. If he can move as well as somebody who’s 5-foot-10, his size now is a huge advantage; there’s not a negative to it.”

Opelka, who qualified for his first grand slam main draw at the 2017 Australian Open where he pushed 11th-ranked David Goffin to five sets, says he is specifically focusing on the return part of his game in practice. “I’ve been spending a ton of time working on my return. When you look at the drills I’m doing in the gym, they work on explosive movement.” But he also points out that basketball players “move better than [tennis players] and are more explosive than [tennis players]” because of their incredible muscle mass, which won’t work for tennis. “I don’t know how they’d be able to keep up for four or five hours with that mass and muscle.” Put LeBron on Arthur Ashe Stadium at the U.S. Open in 100 degree heat for an afternoon, “it’s tough to say how they’ll compare.”

Zverev, who is 19 and 6-foot-6, agrees that tall tennis players face unique challenges: “Movement is much more difficult, and I think building your body is more difficult as well.” But the people I talked to believe that both Opelka and Zverev could be at the top of the game in a few years’ time. “Zverev––that guy could be No. 1 in the world,” Gilbert said. “He serves great, he returns great and he moves great.” And as for Opelka, Gilbert says: “Right now he’s got a monster serve. If he can develop movement, or a return game, who knows where he could go?”

Whether the tallest guys can develop the skills to consistently return at the level of a Djokovic or a Murray remains to be seen. But starting out with a huge serve is a major step toward eventually challenging them. As Opelka says, “every inch is important.”

 

Wiley Schubert Reed is a junior tennis player and fan who has written about tennis for fivethirtyeight.com. He is a senior at the United Nations International School in New York and will be entering Harvard University in the fall.

 

Continue reading Are Taller Players the Future of Tennis?

Benchmarks for Shot-by-Shot Analysis

In my post last week, I outlined what the error stats of the future may look like. A wide range of advanced stats across different sports, from baseball to ice hockey–and increasingly in tennis–follow the same general algorithm:

  1. Classify events (shots, opportunities, whatever) into categories;
  2. Establish expected levels of performance–often league-average–for each category;
  3. Compare players (or specific games or tournaments) to those expected levels.

The first step is, by far, the most complex. Classification depends in large part on available data. In baseball, for example, the earliest fielding metrics of this type had little more to work with than the number of balls in play. Now, batted balls can be categorized by exact location, launch angle, speed off the bat, and more. Having more data doesn’t necessarily make the task any simpler, as there are so many potential classification methods one could use.

The same will be true in tennis, eventually, when Hawkeye data (or something similar) is publicly available. For now, those of us relying on public datasets still have plenty to work with, particularly the 1.6 million shots logged as part of the Match Charting Project.*

*The Match Charting Project is a crowd-sourced effort to track professional matches. Please help us improve tennis analytics by contributing to this one-of-a-kind dataset. Click here to find out how to get started.

The shot-coding method I adopted for the Match Charting Project makes step one of the algorithm relatively straightforward. MCP data classifies shots in two primary ways: type (forehand, backhand, backhand slice, forehand volley, etc.) and direction (down the middle, or to the right or left corner). While this approach omits many details (depth, speed, spin, etc.), it’s about as much data as we can expect a human coder to track in real-time.

For example, we could use the MCP data to find the ATP tour-average rate of unforced errors when a player tries to hit a cross-court forehand, then compare everyone on tour to that benchmark. Tour average is 10%, Novak Djokovic‘s unforced error rate is 7%, and John Isner‘s is 17%. Of course, that isn’t the whole picture when comparing the effectiveness of cross-court forehands: While the average ATPer hits 7% of his cross-court forehands for winners, Djokovic’s rate is only 6% compared to Isner’s 16%.

However, it’s necessary to take a wider perspective. Instead of shots, I believe it will be more valuable to investigate shot opportunities. That is, instead of asking what happens when a player is in position to hit a specific shot, we should be figuring out what happens when the player is presented with a chance to hit a shot in a certain part of the court.

This is particularly important if we want to get beyond the misleading distinction between forced and unforced errors. (As well as the line between errors and an opponent’s winners, which lie on the same continuum–winners are simply shots that were too good to allow a player to make a forced error.) In the Isner/Djokovic example above, our denominator was “forehands in a certain part of the court that the player had a reasonable chance of putting back in play”–that is, successful forehands plus forehand unforced errors. We aren’t comparing apples to apples here: Given the exact same opportunities, Djokovic is going to reach more balls, perhaps making unforced errors where we would call Isner’s mistakes forced errors.

Outcomes of opportunities

Let me clarify exactly what I mean by shot opportunities. They are defined by what a player’s opponent does, regardless of how the player himself manages to respond–or if he manages to get a racket on the ball at all. For instance, assuming a matchup between right-handers, here is a cross-court forehand:

illustration of a shot opportunity

Player A, at the top of the diagram, is hitting the shot, presenting player B with a shot opportunity. Here is one way of classifying the outcomes that could ensue, together with the abbreviations I’ll use for each in the charts below:

  • player B fails to reach the ball, resulting in a winner for player A (vs W)
  • player B reaches the ball, but commits a forced error (FE)
  • player B commits an unforced error (UFE)
  • player B puts the ball back in play, but goes on to lose the point (ip-L)
  • player B puts the ball back in play, presents player A with a “makeable” shot, and goes on to win the point (ip-W)
  • player B causes player A to commit a forced error (ind FE)
  • player B hits a winner (W)

As always, for any given denominator, we could devise different categories, perhaps combining forced and unforced errors into one, or further classifying the “in play” categories to identify whether the player is setting himself up to quickly end the point. We might also look at different categories altogether, like shot selection.

In any case, the categories above give us a good general idea of how players respond to different opportunities, and how those opportunities differ from each other. The following chart shows–to adopt the language of the example above–player B’s outcomes based on player A’s shots, categorized only by shot type:

Outcomes of opportunities by shot type

The outcomes are stacked from worst to best. At the bottom is the percentage of opponent winners (vs W)–opportunities where the player we’re interested in didn’t even make contact with the ball. At the top is the percentage of winners (W) that our player hit in response to the opportunity. As we’d expect, forehands present the most difficult opportunities: 5.7% of them go for winners and another 4.6% result in forced errors. Players are able to convert those opportunities into points won only 42.3% of the time, compared to 46.3% when facing a backhand, 52.5% when facing a backhand slice (or chip), and 56.3% when facing a forehand slice.

The above chart is based on about 374,000 shots: All the baseline opportunities that arose (that is, excluding serves, which need to be treated separately) in over 1,000 logged matches between two righties. Of course, there are plenty of important variables to further distinguish those shots, beyond simply categorizing by shot type. Here are the outcomes of shot opportunities at various stages of the rally when the player’s opponent hits a forehand:

Outcomes of forehand responses based on number of shots

The leftmost column can be seen as the results of “opportunities to hit a third shot”–that is, outcomes when the serve return is a forehand. Once again, the numbers are in line with what we would expect: The best time to hit a winner off a forehand is on the third shot–the “serve-plus-one” tactic. We can see that in another way in the next column, representing opportunities to hit a fourth shot. If your opponent hits a forehand in play for his serve-plus-one shot, there’s a 10% chance you won’t even be able to get a racket on it. The average player’s chances of winning the point from that position are only 38.4%.

Beyond the 3rd and 4th shot, I’ve divided opportunities into those faced by the server (5th shot, 7th shot, and so on) and those faced by the returner (6th, 8th, etc.). As you can see, by the 5th shot, there isn’t much of a difference, at least not when facing a forehand.

Let’s look at one more chart: Outcomes of opportunities when the opponent hits a forehand in various directions. (Again, we’re only looking at righty-righty matchups.)

Outcomes of forehand responses based on shot direction

There’s very little difference between the two corners, and it’s clear that it’s more difficult to make good of a shot opportunity in either corner than it is from the middle. It’s interesting to note here that, when faced with a forehand that lands in play–regardless of where it is aimed–the average player has less than a 50% chance of winning the point. This is a confusing instance of selection bias that crops up occasionally in tennis analytics: Because a significant percentage of shots are errors, the player who just placed a shot in the court has a temporary advantage.

Next steps

If you’re wondering what the point of all of this is, I understand. (And I appreciate you getting this far despite your reservations.) Until we drill down to much more specific situations–and maybe even then–these tour averages are no more than curiosities. It doesn’t exactly turn the analytics world upside down to show that forehands are more effective than backhand slices, or that hitting to the corners is more effective than hitting down the middle.

These averages are ultimately only tools to better quantify the accomplishments of specific players. As I continue to explore this type of algorithm, combined with the growing Match Charting Project dataset, we’ll learn a lot more about the characteristics of the world’s best players, and what makes some so much more effective than others.

How Argentina’s Road Warriors Defied the Davis Cup Home-Court Odds

The conventional wisdom has long held that there is a home court advantage in Davis Cup. It makes sense: In almost every sport, there is a documented advantage to playing at home, and Davis Cup gives us what seem to be the most extreme home courts in tennis.

However, Argentina won this year’s competition despite playing all four of their ties on the road. After the first round this season, only one of seven hosts managed to give the home crowd a victory. Bob Bryan has some ideas as to why:

https://twitter.com/Bryanbros/status/803244964784308227

Which is it? Do players excel in front of an enthusiastic home crowd, on a surface chosen for their advantage? Or do they suffer from the distractions that Bryan cites?

To answer that question, I looked at 322 Davis Cup ties, encompassing all World Group and World Group Play-off weekends back to 2003. Of those, the home side won 196, of 60.9% of the time. So far, the conventional wisdom looks pretty good.

But we need to do more. To check whether the hosting teams were actually better, meaning that they should have won more ties regardless of venue, I used singles and doubles Elo ratings to simulate every match of every one of those ties. (In cases where the tie was decided before the fourth or fifth rubber, I simulated matches between the best available players who could have contested those matches.) Based on those simulations, the hosts “should” have won 171 of the 322 ties, or 53.1%.

The evidence in favor of home-court advantage–and against Bryan’s “distractions” theory–is strong. Home sides have won World Group ties about 15% more often than we would expect. Some of that is likely due to the hosts’ ability to choose surface. I doubt surface accounts for the whole effect, since some court types (like the medium-slow hard court in Croatia last weekend) don’t heavily favor either side, and many ties are rather lopsided regardless of surface. Teasing out the surface advantage from the more intangible home-court edge is a worthy subject to study, but I won’t be going any further in that direction today.

If distractions are a danger to hosts, we might expect see the home court advantage erode in later rounds. Many early-round matchups are minor news events compared to semifinals and finals. (On the other hand, there were over 100 representatives of the Argentinian press in Croatia last weekend, so the effect isn’t entirely straightforward.) The following table shows how home sides have fared in each round:

Round         Ties  Home Win %  Wins/Exp  
First Round    112       58.9%      1.11  
Quarterfinal    56       60.7%      1.16  
Semifinal       28       82.1%      1.30  
Final           14       57.1%      1.14  
Play-off       112       58.9%      1.14

Aside from a blip at the semifinal level, home-court advantage is quite consistent from one round to the next. The “Wins/Exp” shows how much better the hosts fared than my simulations would have predicted; for instance, in first-round encounters, hosts won 11% more ties than expected.

There is also no meaningful difference between home court advantage on day one and day three. The hosts’s singles players win 15% more matches than my simulations would expect on day one, and 15% more on day three. The day three divide is intriguing: Home players win the fourth rubber 12% more often than expected, but they claim the deciding fifth rubber a whopping 23% more frequently than they would in neutral environments. However, only 91 of the 322 ties involved five live rubbers, so the extreme home advantage in the deciding match may just be nothing more than a random spike.

The doubles rubber is less likely to be influenced by venue. Compared to the 15% advantage enjoyed by World Group singles players, the hosting side’s doubles pairings win only 6% more often than expected. This again raises the issue of surface: Not only are doubles results less influenced by court speed than singles results, but home sides are less likely to choose a surface based on the desire of their doubles team, if that preference clashes with the needs of their singles players.

Argentina on the road

In the sense that they never played at home or chose a surface, Argentina beat the odds in all four rounds this year. Of course, home court advantage can only take you so far; it helps to have a good squad. My simulations indicate that the Argentines had a nearly 4-in-5 chance of defeating their Polish first-round opponents on neutral ground, while Juan Martin del Potro and company had a more modest 59% chance of beating the Italians in Italy.

For the last two rounds, though, the Argentines were fighting an uphill battle. The semifinal venue in Glasglow didn’t matter much; the prospect of facing the Murray brothers meant Argentina had less than a 10% chance of advancing no matter what the location. And as I wrote last week, Croatia was rightfully favored in the final. Playing yet another tie on the road simply made the task more difficult.

Once we adjust my simulations of each tie for home court advantage, it turns out that Argentina’s chances of winning the Cup this year were less than 1%, barely 1 in 200. The following table shows the last 14 winners, along with the number of ties they played at home and their chances of winning the Cup in my simulations, given which countries they ended up facing and the players who turned up for each tie:

Year  Winner  Home Ties  Win Prob  
2016  ARG             0      0.5%  
2015  GBR             3     18.9%  
2014  SUI             2     54.7%  
2013  CZE             1     10.5%  
2012  CZE             3     19.7%  
2011  ESP             2     12.2%  
2010  SRB             3     17.6%  
2009  ESP             4     44.0%  
2008  ESP             1     14.3%  
2007  USA             2     24.4%  
2006  RUS             2      1.7%  
2005  CRO             2      7.4%  
2004  ESP             3     23.8%  
2003  AUS             3     15.9%

In the time span I’ve studied, only the 2006 Russian squad managed anything close to the same season-long series of upsets. (I don’t yet have adequate doubles data to analyze earlier Davis Cup competitions.)  At the other end of the spectrum, the simulations emphasize how smoothly Switzerland swept through the bracket in 2014. A wide-open draw, together with Roger Federer, certainly helps.

It was tough going for Argentina, and the luck of the home-court draw made it tougher. Without a solid #2 singles player or an elite doubles specialist, it isn’t likely to get much easier. For all that, they’ll open the 2017 Davis Cup campaign against Italy with at least one unfamiliar weapon in their arsenal: They finally get to play a tie at home.

How To Keep Round Robin Matches Interesting, Part Two

Earlier this week, I published a deep dive into the possible outcomes of four-player round robin groups and offered an ideal schedule that would minimize the likelihood of dead rubbers on the final day. I’ve since heard from a few readers who pointed out two things:

  1. You might do better if you determined the schedule for day two after getting the results of the first two matches.
  2. Major tournaments such as the ATP and WTA Tour Finals already do this, pairing the winners of the first two matches and the losers of the first two matches on day two.

This is an appealing idea. You’re guaranteed to end the second day with one undefeated (2-0) player, two competitors at 1-1, and the last at 0-2. The two participants at 1-1 have everything to play for, and depending on day three’s schedule and tiebreak factors, the 0-2 player could still be in the running as well.

Best of all, you avoid the nightmare scenario of two undefeated players and two eliminated players, in which the final two matches are nearly meaningless.

However, this “contingent schedule” approach isn’t perfect.

Surprise, surprise

We learned in my last post that, if we set the entire schedule before play begins, the likelihood of a dead rubber on the final day is 17%, and if we choose the optimal schedule, leaving #4 vs #1 and #3 vs #2 for the final day, we can drop those chances as low as 10.7%.

(These were based on a range of player skill levels equivalent to 200 points on the Elo scale. The bigger the range of player skills–for instance, the ATP finals is likely to have a group with a range well over 300–the more dramatic the differences in these numbers.)

In addition, we discovered that “dead/seed” matches–those in which one player is already eliminated and the other can only affect their semifinal seeding–are even more common. When the schedule is chosen in advance, the probability of a dead rubber or a “dead/seed” match is always near 40%.

If the day two schedule is determined by day one outcomes, the overall likelihood of these “mostly meaningless” (dead or “dead/seed”) matches drops to about 30%. That’s a major step in the right direction.

Yet there is a drawback: The chances of a dead rubber increase! With the contingent day two schedule, there is a roughly 20% chance of a completely meaningless match on day three.

Our intuition should bear this out. After day two, we are guaranteed one 2-0 player and one 0-2 player. It is somewhat likely that these two have faced each other already, but there still remains a reasonable chance they will play on day three. If they do, the 0-2 player is already eliminated–there will be two 2-1 players at the end of day three. The 2-0 player has clinched a place in the semifinals, so the most that could be at stake is a semifinal seeding.

In other words, if the “winner versus winner” schedule results in a 2-0 vs 0-2 matchup on day three, the odds are that it’s meaningless. And this schedule often does just that.

The ideal contingent schedule

If the goal is to avoid dead rubbers at all costs, the contingent schedule is not for you. You can do a better job by properly arranging the schedule in advance. However, a reasonable person might prefer the contingent schedule because it completely avoids the risk of the low-probability “nightmare scenario” that I described above, of two mostly meaningless day three matches.

Within the contingent schedule, there’s still room for optimization. If the day one slate consists of matches setting #1 against #3 and #2 against #4 (sorted by ranking), the probability of a meaningless match on day three is about average. If day one features #1 vs #2 and #3 vs #4, the odds are even higher: about a 21% chance of a dead rubber and another 11% chance of a “dead/seed” match.

That leaves us with the optimal day one schedule of #1 vs #4 and #2 vs #3. It lowers the probability of a dead rubber to 19% and the chances of a “dead/seed” match to 9.7%. Neither number represents a big difference, but given all the eyes on every match at major year-end events, it seems foolish not to make a small change in order to maximize the probability that both day three matches will matter.

How To Keep Round Robin Matches Interesting

Round robins–such as the formats used by the ATP and WTA Tour Finals–have a lot going for them. Fans are guaranteed at least three matches for every player, and competitors can recover from one (or even two) bad outings. Best of all, when compared to a knockout-style draw, it’s twice as much tennis.

On the other hand, round robins have one major drawback: They can result in meaningless matches. It’s fairly common that, after two matches, a player is guaranteed a spot in the semifinals (sometimes even a specific seed) or eliminated from contention altogether. At a high-profile event such as the Tour Finals, with sky-high ticket prices, do we really want to run the risk of dead rubbers?

I don’t claim to have the answer to that question. However, we can take a closer look at the round robin format to answer several relevant questions. What is the probability that the final day of a four-player group will include at least one dead rubber? What about the final match? And most importantly, before the event begins, can we set the schedule in such a way to minimize the likelihood of dead rubbers?

The range of possibilities

As a first step, let’s determine all of the possible outcomes of the first four matches in a four-player round robin group. For convenience, I’ll refer to the players as A, B, C, and D. The first day features two matches, A vs B and C vs D. The second day is A vs C and B vs D, leaving us with a final day of A vs D and B vs C.

Each match has four possible outcomes: the first player wins in two sets, the first player wins in three, the second wins in two, or the second wins in three. (Sets won are important because they are used as a tiebreaker when, for instance, three players win two matches apiece.) Thus, there are 4 x 4 x 4 x 4 = 256 possible arrangements of the group standings entering the final day of round robin play.

Of those 256 permutations, 32 of them (12.5%) include one dead rubber on the final day. In those cases, the other match is played only to decide semifinal seeding between the players who will advance. Another 32 of the 256 permutations involve one “almost-dead” match, between a player who has been eliminated and a player who is competing only to determine semifinal seeding.

In other words, one out of every four possible outcomes of the first two days results in a day three match that is either entirely or mostly meaningless. Later on, we’ll dig into the probability that these outcomes occur, which depends on the relative skill levels of the four players in the group.

Before we do that, let’s take a little detour to define our terms. Because of the importance of semifinal seeding, some dead rubbers are less dead than others. Further, it is frequently the case that one player in a match still has a shot at the semifinals and the other doesn’t. Altogether, from “live” to “dead,” there are six gradations:

  1. live/live — both players are competing to determine whether they survive
  2. live/seed — one player could advance or not; the other will advance, and is playing to try to earn the #1 group seed
  3. live/dead — one player is trying to survive; the other is eliminated
  4. seed/seed — both players will advance; the winner gets the #1 group seed
  5. seed/dead — one player is in the running for the #1 seed; the other is eliminated
  6. dead/dead — both players are eliminated

All else equal, the higher a match lies on that scale, the more engaging its implications for the tournament. For the remainder of this article, I’ll refer only to the “dead/dead” category as “dead rubbers,” though I will occasionally discuss the likelihood of “dead/seed” matches as well. I’ll assume that the #1 seed is always more desirable than #2 and ignore the fascinating but far-too-complex ramifications of situations in which a player might prefer the #2 spot.

The sixth match

As we’ve seen, there are many sequences of wins and losses that result in a dead rubber on day three. Once the fifth match is played, it is even more likely that the seedings have been determined, making the sixth match meaningless.

After five matches, there are 1,024 possible group standings. (256 permutations after the first four matches, multiplied by the four possible outcomes of the fifth match.) Of those, 145 (14.1%) result in a dead sixth rubber, and another 120 (11.7%) give us a “dead/seed” sixth match.

We haven’t yet determined how likely it is that we’ll arrive at the specific standings that result in dead sixth rubbers. So far, the important point is that dead rubbers on day three aren’t just flukes. In a four-player round robin, they are always a real possibility, and if there is way to minimize their likelihood, we should jump at the chance.

Real scenarios, really dead rubbers

To figure out the likelihood of dead rubbers in practical situations, like the ATP and WTA Tour Finals, I used a hypothetical group of four players with Elo ratings spread over a 200-point range.

Why 200? This year’s Singapore field was very tightly packed, within a little bit more than 100 points, implying that the best player, Angelique Kerber, had about a 65% chance of beating the weakest, Svetlana Kuznetsova. By contrast, the ATP finalists in London are likely to be spread out over a 400-point range, giving the strongest competitor, Novak Djokovic, at least a 90% edge over the weakest.

I’ve given our hypothetical best player a rating of 2200, followed by a field of one player at 2130, one at 2060, and one at 2000. Thus, our favorite has a 60% chance of beating the #2 seed, a 69% chance of defeating the #3 seed, and a 76% chance of besting the #4 seed.

For any random arrangement of the schedule, after the first two days of play, this group has a 17% chance of giving us a dead rubber on day three, plus a 23% chance of a “dead/seed” match on day three.

After the fifth match is contested, there is a 16% chance of that the sixth match is meaningless, with an additional 12% chance that the sixth match falls into the “dead/seed” category.

The wider the range of skill levels, the higher the probability of dead rubbers. This is intuitive: The bigger the range between the top and bottom, the more likely that the best player will win their first two matches–and the more likely they will be straight-setters. Similarly, the chances are higher that the weakest player will lose theirs. The higher the probability that players go into day three with 2-0 or 0-2 records, the less likely that day three matches have an impact on the outcome of the group.

How to schedule a round robin group

A 17% chance of a dead rubber on day three is rather sad. But there is a bright spot in my analysis: By rearranging the schedule, you can raise that probability as high as 24.7% … or drop it as low as 10.7%.

Remember that our schedule looks like this:

Day one: A vs B, C vs D

Day two: A vs C, B vs D

Day three: A vs D, B vs C

We get the lowest possible chance of a day three dead rubber if we put the players on the schedule in order from weakest to strongest: A is #4, B is #3, and so on:

Day one: #4 vs #3, #2 vs #1

Day two: #4 vs #2, #3 vs #1

Day three: #4 vs #1, #3 vs #2

There is a small drawback to our optimal arrangement: It increases the odds of a “dead/seed” match. It turns out that you can only optimize so much: No matter what the arrangement of the competitors, the probability of a “dead/dead” or “dead/seed” match on day three stays about the same, between 39.7% and 41.7%. While neither type of match is desirable, we’re stuck with a certain likelihood of one or the other, and it seems safe to assume that a “dead/seed” rubber is better than a totally meaningless one.

Given how much is at stake, I hope that tournament organizers heed this advice and schedule round robin groups in order to minimize the chances of dead rubbers. The math gets a bit hairy, but the conclusions are straightforward and dramatic enough to make it clear that scheduling can make a difference. Over the course of the season, almost every tennis match matters–it would be nice if every match at the Tour Finals did, too.

(I wrote more about this, which you can read here.)

What Would Happen If the WTA Switched to Super-Tiebreaks?

It’s in the news again: Some tennis execs think that matches are too long, fans’ attention spans are too short, and the traditional format of tennis matches needs to change. Since ATP and WTA doubles have already swapped a full third set for a 10-point super-tiebreak, something similar would make for a logical proposal to cap singles match length.

Let’s dig into the numbers and see just how much time would be saved if the WTA switched from a third set to a super-tiebreak. It is tempting to use match times from doubles, but there are two problems. First, match data on doubles is woefully sparse. Second, the factors that influence match length, such as average point length and time between points, are different in doubles and singles.

Using only WTA singles data, here’s what we need to do:

  1. Determine how many matches would be affected by the switch
  2. Figure out how much time is consumed by existed third sets
  3. Estimate the length of singles super-tiebreaks
  4. Calculate the impact (measured in time saved) of the change

The issue: three-setters

Through last week’s tournaments on the WTA tour this year, I have length (in minutes) for 1,915 completed singles matches.  I’ve excluded Grand Slam events, since third sets at three of the four Slams can extend beyond 6-6, skewing the length of a “typical” third set.

The average length of a WTA singles match is about 97 minutes, with a range from 40 minutes up to 225 minutes. Here is a look at the distribution of match times this year:

histo1

The most common lengths are between 70 and 90 minutes. Some executives may wish to shorten all matches–switching to no-ad games (which I’ve considered here) or a more radically different format such as Fast4–but for now, I think it’s fair to assume that those 90-minute matches are safe from tinkering.

If there is a “problem” with long matches–both for fan engagement and scheduling–it arises mostly with three-setters. About one-third of WTA matches go to a third set, and these account for nearly all of the contests that last longer than two hours. 460 matches have passed the two-hour mark this season. Of those, all but 24 required a third set.

Here is the distribution of match lengths for WTA three-setters this season:

histo3

If we simply removed all third sets, nearly all matches would finish within two hours. Of course, if we did that, we’d be left with an awful lot of ties. Instead, we’re talking about replacing third sets with something shorter.

Goodbye, third set

Third sets are a tiny bit shorter than the first and second sets in three-setters. If we count sets that go to tiebreaks as 14 games, the average number of games in a third set is 9.5, while the typical number of games in the first and second sets of a three-setter is 9.7.

Those counts are close enough that we can estimate the length of each set very simply, as one-third the length of the match. There are other considerations, such as the frequency of toilet breaks before third sets and the number of medical timeouts in different sets, but even if we did want to explore those minor issues, there is very little available data to guide us in those areas.

The length of a super-tiebreak

The typical WTA three-setter involves about 189 individual points, so we can roughly estimate that foregoing the third set saves about 63 points. How many points are added back by playing a super-tiebreak?

The math gets rather involved here, so I’ll spare you most of the details. Using the typical rate of service and return points won by each player in three-setters (58% on serve and 46% on return for the better player that day), we can use my tiebreak probability model to determine the distribution of possible outcomes, such as a final score 10-7 or 12-10.

Long story short, the average super-tiebreak would require about 19 points, less than one-third the number needed by the average third-set.

That still doesn’t quite answer our question, though. We’re interested in time savings, not point reduction. The typical WTA third set takes about 44 minutes, or about 42 seconds per point. Would a super-tiebreak be played at the same pace?

Tiebreak speed

While 10-point breakers are largely uncharted territory in singles, 7-point tiebreaks are not, and we have plenty of data on the latter. It seems reasonable to extend conclusions about 7-pointers to their 10-point cousins, and they are played with similar rules–switch servers every two points, switch points every six–and under comparable levels of increased pressure.

Using IBM’s point-by-point data from this year’s Grand Slam women’s draws, we have timestamps on about 700 points from tiebreaks. Even though the 42-seconds-per-point estimate for full sets includes changeovers, tiebreaks are played even more slowly. Including mini-changeovers within tiebreaks, points take about 54 seconds each, almost 30% longer than the traditional-set average.

The bottom line impact of third-set super-tiebreaks

As we’ve seen, the average third-set takes about 44 minutes. A 19-point super-tiebreak, at 54 seconds per point, comes in at about 17 minutes, chopping off more than 60% off the length of the typical third set, or about 20% from the length of the entire match.

If we alter this year’s WTA singles match times accordingly, reducing the length of all three-setters by one-fifth, we get some results that certain tennis executives will love. The average match time falls from 97 minutes to 89 minutes, and more importantly, far fewer matches cross the two-hour threshold.

Of the 460 matches this season over two hours in length, we would expect third-set super-tiebreaks to eliminate more than two-thirds of them, knocking the total down to 147. Here is the revised match length distribution, based on the assumptions I’ve laid out in this post:

histo4

The biggest benefit to switching to a third-set super-tiebreak is probably related to scheduling. By massively cutting down the number of marathon matches, it’s less likely that players and fans will have to wait around for an 11:00 PM start.

Of the various proposals floating around to shorten matches–third-set super-tiebreaks, no-ad scoring, playing service lets, and Fast4–changing the third-set format strikes the best balance of shortening the longest matches without massively changing the nature of the sport.

Personally, I hope none of these changes are ever seen on a WTA or ATP singles court. After all, I like tennis and tend to rankle at proposals that result in less tennis. If something must be done, I’d prefer it involve finding new executives to replace the ones who can’t stop tinkering with the sport. But if some rule needs to be changed to shorten matches and make scheduling more TV-friendly, this is likely the easiest one to stomach.