Toward a Better Understanding of Return Effectiveness

The deeper the return, the better, right? That, at least, is the basis for many of the flashy graphics we see these days on tennis broadcasts, indicating the location of every return, often separated into “shallow,” “medium,” and “deep” zones.

In general, yes, deep returns are better than shallow ones. But return winners aren’t overwhelmingly deep, since returners can achieve sharper angles if they aim closer to the service line. There are plenty of other complicating factors as well: returns to the sides of the court are more effective than those down the middle, second-serve returns tend to be better than first-serve returns, and topspin returns result in more return points won than chip or slice returns.

While most of this is common sense, quantifying it is an arduous and mind-bending task. When we consider all these variables–first or second serve, deuce or ad court, serve direction, whether the returner is a righty or lefty, forehand or backhand return, topspin or slice, return direction, and return depth–we end up with more than 8,500 permutations. Many are useless (righties don’t hit a lot of forehand chip returns against deuce court serves down the T), but thousands reflect some common-enough scenario.

To get us started, let’s set aside all of the variables but one. When we analyze 600+ ATP matches in the Match Charting Project data, we have roughly 61,000 in-play returns coded in one of nine zones, including at least 2,000 in each.  Here is a look at the impact of return location, showing the server’s winning percentage when a return comes back in play to one of the nine zones:rzones1show

(“Shallow” is defined as anywhere inside the service boxes, while “Medium” and “Deep” each represent half of the area behind the service boxes. The left, center, and right zones are intended to indicate roughly where the return would cross the baseline, so for sharply angled shots, a return might bounce shallow near the middle of the court but be classified as a return to the forehand or backhand side.)

As we would expect, deeper returns work in favor of the returner, as do returns away from the center of the court. A bit surprisingly, returns to the server’s forehand side (if he’s a right-hander) are markedly more effective than those to the backhand. This is probably because right-handed returners are most dangerous when hitting crosscourt forehands, although left-handed returners are also more effective (if not as dramatically) when returning to that side of the court.

Let’s narrow things down just a little and see how the impact of return location differs on first and second serves. Here are the server’s chances of winning the point if a first-serve return comes back in each of the nine zones:

rzones2showF

And the same for second-serve returns:

rzones3showF

It’s worth emphasizing just how much impact a deep return can have. So many points are won with unreturnable serves–even seconds–that simply getting the ball back in play comes close to making the point a 50/50 proposition. A deep second-serve return, especially to a corner, puts the returner in a very favorable position. Consistently hitting returns like that is a big reason why Novak Djokovic essentially turns his opponents’ second serves against them.

The final map makes it clear how valuable it is to move the server away from the middle of the court. Think of it as a tactical first strike, forcing the server to play defensively instead of dictating play with his second shot. Among second-serve returns put in play, any ball placed away from the middle of the court–regardless of depth–gives the returner a better chance of winning the point than does a deep return down the middle.

For today, I’m going to stop here. This is just the tip of the iceberg, as there are so many variables that play some part in the effectiveness of various service returns. Ultimately, understanding the potency of each return location will give us additional insight into what players can achieve with different kinds of serve, which players are deadliest with certain types of returns, and how best to handle different returns with the server’s crucial second shot.

Teymuraz Gabashvili and ATP Quarterfinal Losing Streaks

Yesterday in Moscow, Teymuraz Gabashvili played his 16th career tour-level quarterfinal. Facing 118th-ranked Evgeny Donskoy, it was his best chance yet to reach an ATP semifinal, but just as in each of his previous 15 attempts, he lost.

No other player has contested so many tour-level quarterfinals without ever winning one. But while the streak of 16 consecutive quarterfinal losses is a rarity, it’s not a record. The all-time mark belongs to Gianluca Pozzi, who dropped 18 in a row between 1993 and 2000. Pozzi’s record, depressing as that streak is, might be an inspiration to Gabashvili: At age 35, Pozzi finally broke the streak, defeating Marat Safin, one of the best players he ever faced in a quarterfinal.

Gabashvili and Pozzi are among only twelve players who have strung together more than 10 quarterfinal losses at tour level. Here’s the complete list, including the dates of the first and last loss in each streak:

Player               QFs L Streak     Start       End  
Gianluca Pozzi                 18  19930104  20000501  
Teymuraz Gabashvili            16  20070219         *  
Paul Annacone                  14  19860127  19880704  
Ivan Molina                    12  19751110  19791105  
Mischa Zverev                  11  20060925  20090713  
Diego Perez                    11  19861124  19920810  
Anand Amritraj                 11  19750304  19810706  
Dennis Ralston                 11  19701101  19800602  
Bob Carmichael                 11  19720918  19751231  
Ricardas Berankis              10  20120917         *  
Yen Hsun Lu                    10  20070219  20130923  
Mikhail Youzhny                10  20041101  20060130

Ricardas Berankis is the only other player on this list to have an active streak, and since he’s five years younger than Gabashvili, another few years of mild success and quarterfinal futility could put him in the running for the all-time record. Alas, neither player is likely to repeat the post-streak success of Mikhail Youzhny, who went on to play 63 more tour-level quarterfinals, winning 33 of them.

If there’s a silver lining for Gabashvili, it’s that he’s reached all of those quarterfinals, sparing himself the fate of Rolf Thung, a Dutch player from the 1970s who reached the round of 16 at 18 tour events and lost them all.

Elo-Forecasting the WTA Tour Finals in Singapore

With the field of eight divided into two round-robin groups for the WTA Tour Finals in Singapore, we can play around with some forecasts for this event. I’ve updated my Elo ratings through last week’s tournaments, and the first thing that jumps out is how different they are from the official rankings.

Here’s the Singapore field:

EloRank  Player                Elo  Group  
2        Maria Sharapova      2296    RED  
4        Simona Halep         2181    RED  
6        Garbine Muguruza     2147  WHITE  
8        Petra Kvitova        2136  WHITE  
9        Angelique Kerber     2129  WHITE  
11       Agnieszka Radwanska  2100    RED  
15       Lucie Safarova       2051  WHITE  
21       Flavia Pennetta      2004    RED

Serena Williams (#1 in just about every imaginable ranking system) chose not to play, but if Elo ruled the day, Belinda Bencic, Venus Williams, and Victoria Azarenka would be playing this week in place of Agnieszka Radwanska, Lucie Safarova, and Flavia Pennetta.

Anyway, we’ll work with what we’ve got. Maria Sharapova is, according to Elo, a huge favorite here. The ratings translate into a forecast that looks like this:

Player                  SF  Final  Title  
Maria Sharapova      83.7%  61.1%  43.6%  
Simona Halep         60.8%  35.4%  15.9%  
Garbine Muguruza     59.4%  25.7%  11.3%  
Petra Kvitova        55.2%  23.0%   9.8%  
Angelique Kerber     53.1%  21.7%   8.8%  
Agnieszka Radwanska  37.4%  17.4%   6.1%  
Lucie Safarova       32.3%   9.7%   3.1%  
Flavia Pennetta      18.1%   6.0%   1.4%

If Sharapova is really that good, the loser in today’s draw was Simona Halep. The top seed would typically benefit from having the second seed in the other group, but because Garbine Muguruza recently took over the third spot in the rankings, Pova entered the draw as a dangerous floater.

However, these ratings don’t reflect the fact that Sharapova hasn’t completed a match since Wimbledon. They don’t decline with inactivity, so Pova’s rating is the same as it was the day after she lost to Serena back in July. (My algorithm also excludes retirements, so her attempted return in Wuhan isn’t considered.)

With as little as we know about Sharapova’s health, it’s tough to know how to tweak her rating. For lack of any better ideas, I revised her Elo rating to 2132, right between Petra Kvitova and Angelique Kerber. At her best, Sharapova is better than that, but consider this a way of factoring in the substantial possibility that she’ll play much, much worse–or that she’ll get injured and her matches will be played by Carla Suarez Navarro instead. The revised forecast:

Player                  SF  Final  Title  
Simona Halep         69.9%  40.9%  24.0%  
Garbine Muguruza     59.4%  31.5%  16.5%  
Maria Sharapova      57.6%  29.5%  14.5%  
Petra Kvitova        55.6%  28.4%  14.4%  
Angelique Kerber     52.5%  26.3%  13.2%  
Agnieszka Radwanska  47.9%  22.3%   9.9%  
Lucie Safarova       32.6%  12.9%   4.9%  
Flavia Pennetta      24.7%   8.3%   2.7%

If this is a reasonably accurate estimate of Sharapova’s current ability, the Red group suddenly looks like the right place to be. Because Elo doesn’t give any particular weight to Grand Slams, it suggests that the official rankings far overestimate the current level of Safarova and Pennetta. The weakness of those two makes Halep a very likely semifinalist and also means that, in this forecast, the winner of the tournament is more likely (54% to 46%) to come from the White group.

Without Serena, and with Sharapova’s health in question, there are simply no dominant players in the field this week. If nothing else, these forecasts illustrate that we’d be foolish to take any Singapore predictions too seriously.

Measuring the Effectiveness of Backhand Returns

One-handed backhands can be beautiful, but they aren’t always the best tools for the return of serve. Some of the players with the best one-handers in the game must often resort to slicing backhand returns–Stanislas Wawrinka, for example, slices 68% of backhand first serve returns and 40% of backhand second serve returns, while Andy Murray uses the slice 41% and 3%, respectively.

Using the 650 men’s matches in the Match Charting Database, I looked at various aspects of backhand serve returns to try to get a better sense of the trade-offs involved in using a one-handed backhand. Because the matches in the MCP aren’t completely representative of the ATP tour, the numbers are approximate. But given the size and breadth of the sample, I believe the results are broadly indicative of men’s tennis as a whole.

At the most general level, players with double-handed backhands are slightly better returners, putting roughly the same number of returns in play (about 56%) and winning a bit more often–46.9% to 45.7%–when they do so. The gap is a bit wider when we look at backhand returns put in play: 46.5% of points won to 44.7%. While the favorable two-hander numbers are influenced by the historically great returning of Novak Djokovic, two-handers still have an edge if we reduce his weight in the sample or remove him entirely.

Unsurprisingly, players realize that two-handed backhands are more effective returns, and they serve accordingly. The MCP divides serves into three zones–down the tee, body, and wide–and I’ve re-classified those as “to the forehand,” “to the body,” and “to the backhand” depending on the returner’s dominant hand and whether the point is in the deuce or ad court. While we can’t identify exactly where servers aimed those to-the-body serves, we can determine some of their intent from serves aimed at the corners.

Against returners with two-handed backhands, servers went for the backhand corner on 44.2% of first serves and 34.8% of second serves. Against one-handers, they aimed for the same spot on 47.3% of first serves and 40.9% of second serves. Looking at the same question from another angle, backhands make up 61.7% of the returns in play hit by one-handers compared to 59.0% for double-handers. It seems likely that one-handers more aggressively run around backhands to hit forehand returns, so this last comparison probably understates the degree to which servers aim for single-handed backhands.

When servers do manage to find the backhand side of a single-hander, they’re often rewarded with a slice return. On average, one-handers (excluding Roger Federer, who is overrepresented in this dataset) use the slice on 53.9% of their backhand first-serve returns and 32.3% of their backhand second-serve returns. Two-handers use the slice 20.5% of the time against firsts and only 2.5% of the time against seconds.

For both types of players, against first and second serves, slice returns are less effective than flat or topspin backhand returns. This isn’t surprising, either–defensive shots are often chosen in defensive situations, so the difference in effectiveness is at least partly due to the difference in the quality of the serves themselves. Still, since one-handers choose to go to the slice so much more frequently, it’s valuable to know how the types of returns compare:

Return Type   BH in play W% SL in play W% 
1HBH vs Firsts        43.3%         37.6% 
1HBH vs Seconds       46.0%         44.1% 
                        
2HBH vs Firsts        46.8%         36.2% 
2HBH vs Seconds       48.6%         41.9%

(Again, I’ve excluded Fed from the 1HBH averages.)

In three of the four rows, there’s a difference of several percentage points between the effectiveness of slice returns and flat or topspin returns, as measured by the ultimate outcome of the point. The one exception–second-serve returns by one-handers–reminds us that the slice can be an offensive weapon, even if it’s rarely used as one in the modern game. Some players–including Federer, Feliciano Lopez, Grigor Dimitrov, and Bernard Tomic–are more effective with slice returns than flat or topspin returns against either first or second serves.

However, these players are the exceptions, and in the theoretical world where we can set all else equal, a slice return is the inferior choice. All players have to hit slice returns sometimes, and many of those seem to be forced by powerful serving, but the fact remains: one-handers hit slices much more than two-handers do, and despite the occasional offensive opportunity, slice returns are more likely to hand the point to the server.

These differences are real, but they are still modest. A good returner with a one-handed backhand is considerably better than a bad returner with a two-hander, and it’s even possible to have a decent return game while hitting mostly slices. All that said, in the aggregate, a one-handed backhand is a bit of a liability on the return. It will take further research to determine whether other benefits–such as the sizzling down-the-line winners we’ve come to expect from the likes of Wawrinka and Richard Gasquet–outweigh the costs.

Benoit Paire and Overqualified Challenger Contenders

With three ATP tour-level events on the slate this week, Benoit Paire considered his options and elected to play none of them. Instead, the world #23 is the top seed at the Brest Challenger, making him the highest ranked player to enter a challenger this year–by a wide margin.

Top-50 players may only enter challengers if they are given a wild card, and top-ten players may not enter them at all. Still, since 1990, a top-50 player has played a challenger just over 500 times, at a rate of about 20 per year. (Some of these players didn’t need a wild card, as entry is determined by ranking several weeks before the tournament, during which time rankings rise and fall.)

Many of the high-ranked wild cards fall into one of two categories: Players who lose early in Slams, Indian Wells, or Miami; and clay-court specialists seeking more matches on dirt. Paire’s decision this week–like the Frenchman himself–doesn’t follow one of these common patterns.

Anyway, here are the top-ranked players to contest challengers since 1990, along with their results. A result of “W” means that the player won the title, while any other result indicates the round in which the player lost.

Year  Event           Player               Rank  Result  
2003  Braunschweig    Rainer Schuettler    8     R16     
1991  Johannesburg    Petr Korda           9     SF      
1994  Barcelona       Alberto Berasategui  10    W       
1994  Graz            Alberto Berasategui  11    R16     
2008  Sunrise         Fernando Gonzalez    12    QF      
2004  Luxembourg      Joachim Johansson    12    W       
2011  Prostejov       Mikhail Youzhny      13    QF      
2008  Prostejov       Tomas Berdych        13    QF      
2003  Prague          Sjeng Schalken       13    W       
2005  Zagreb          Ivan Ljubicic        14    W       
2004  Bratislava      Dominik Hrbaty       14    F       
2004  Prostejov       Jiri Novak           14    QF      
2003  Prostejov       Jiri Novak           14    R32     
2007  Dnepropetrovsk  Guillermo Canas      15    SF      
2002  Prostejov       Jiri Novak           15    F       
1998  Segovia         Alberto Berasategui  15    QF      
1997  Braunschweig    Felix Mantilla       15    F       
1997  Zagreb          Alberto Berasategui  15    W

(Schuettler and Korda were outside the top ten a couple of weeks before their respective challengers.)

A look at this list suggests that Alberto Berasategui entered challengers as a top-fifty player more than anyone else. He’s close–with 12 such entries, he’s tied for second with Jordi Arrese. The player who dropped down a level the most times is Dominik Hrbaty, who played 17 challengers while ranked in the top 50. (The active leaders are Jarkko Nieminen with ten and Andreas Seppi with nine.)

Despite all those attempts, Hrbaty wasn’t particularly successful as a high-ranked challenger player. He won only 2 of those 17 events, reaching only one other final. Top-50 players aren’t guaranteed to win these titles, of course, but in general, they have outperformed Hrbaty, winning 18% of possible titles. Here are top-50 players’ results broken down by round:

Result       Frequency  
Title            18.1%  
Loss in F         9.3%  
Loss in SF       11.3%  
Loss in QF       17.1%  
Loss in R16      22.0%  
Loss in R32      22.2%

Paire is a better player than this sample’s average ranking of 37. Combined with a favorable surface, he gets a much more optimistic forecast from my algorithm, with a slightly better than one-in-three chance of winning the title. With a futures title, an ATP trophy, and a pair of challenger triumphs already in the books this year, it seems fitting that Benoit would add another oddity to his wide-ranging season.

Continue reading Benoit Paire and Overqualified Challenger Contenders

Lucky Losers and Familiar Faces

In the final round of qualifying Monday in Moscow, Darya Kasatkina easily defeated Paula Kania. Thanks to a couple of late withdrawals, both players ended up making the main draw … and tomorrow, they’ll play each other again.

This scenario is rare, but not unheard of. Since the mid-1990s, there have been 30 other instances when two women faced each other in qualifying and then again in the main draw. Most recently, Lauren Davis defeated Svetlana Kuznetsova twice at the 2013 Canadian Open. One year earlier, in Sydney, Alexandra Dulgheru beat Sofia Arvidsson in the first round of the main draw despite losing to her in the final round of qualifying.

Tomorrow’s Kasatkina-Kania rematch is far from a sure thing. In those 30 prior matches, barely more than half of the qualifiers–17 of 30–have managed to win both matches.

This sort of rematch is similarly uncommon on the ATP tour. Since 2007 (the earliest year for which I have qualifying results), this has happened a dozen times. Most recently, Albert Ramos-Vinolas defeated Robin Haase in back-to-back rounds in Monte Carlo. Ramos was on the opposite side of things five years ago, when Pablo Cuevas beat him twice in Valencia.

Earlier this year, in a variation on the theme in Auckland, Kenny de Schepper beat Alejandro Falla to qualify, and after both players won their first-round matches, Falla triumphed in the second-round rematch.

Programming note: After watching this sort of ad hoc research disappear into the barely-searchable void that is the Twitter archive, it occurred to me to post occasional brief notes such as this one. It’s not groundbreaking stuff, but at least it’ll be easier to find in the future. These curiosities won’t interfere with or replace my longer, more analytical posts.

The Dreaded Deficit at the Tiebreak Change of Ends

Some of tennis’s conventional wisdom manages to be both blindingly self-evident and obviously wrong. Give pundits a basic fact (winning more points is good), add a dash of perceived momentum, and the results can be toxic.

A great example is the tiebreak change of ends. The typical scenario goes something like this: Serving at 2-3 in a tiebreak, a player loses a point on serve, going down a minibreak to 2-4. As the players change sides, a commentator says, “You really don’t want to go into this change of ends without at least keeping the score even.”

While the full rationale is rarely spelled out, the implication is that losing that one point–going from 2-3 to 2-4–is somehow worse than usual because the point precedes the changeover. Like the belief that the seventh game of the set is particularly important, this has passed, untested, into the canon.

Let’s start with the “blindingly self-evident” part. Yes, it’s better to head into the change of ends at 3-3 than it is at 2-4. In a tiebreak, every point is crucial. Based on a theoretical model and using sample players who each win 65% of service points, here are the odds of winning a tiebreak from various scores at the changeover:

Score  p(Win)  
1*-5     5.4%  
2*-4    21.5%  
3*-3    50.0%  
4*-2    78.5%  
5*-1    94.6%

It’s easy to sum that up: You really want to win that sixth point. (Or, at least, several of the points before the sixth.) On the other hand, compare that to the scenarios after eight points:

Score  p(Win)  
2*-6     2.6%  
3*-5    17.6%  
4*-4    50.0%  
5*-3    82.4%  
6*-2    97.4%

At the risk of belaboring the obvious, when the score is close, points become more important later in the tiebreak. The outcome at 4-4 matters more than at 3-3, which matters more than at 2-2, and so on. If players changed ends after eight points, we’d probably bestow some magical power on that score instead.

Real-life outcomes

So far, I’ve only discussed what the model tells us about win probabilities at various tiebreak scores. If the pundits are right, we should see a gap between the theoretical likelihood of winning a tiebreak from 2-4 and the number of times that players really do win tiebreaks from those scores. The model says that players should win 21.5% of tiebreaks from 2*-4; if the conventional wisdom is correct, we would find that players win even fewer tiebreaks when trying to come back from that deficit.

By analyzing the 20,000-plus tiebreaks in this dataset, we find that the opposite is true. Falling to 2-4 is hugely worse than reaching the change of ends at 3-3, but it isn’t worse than the model predicts–it’s a bit better.

To quantify the effect, I determined the likelihood that the player serving immediately after the changeover would win the tiebreak, based on each player’s service points won throughout the match and the model I’ve referred to above. By aggregating all of those predictions, together with the observed result of each tiebreak, we can see how real life compares to the model.

In this set of tiebreaks, a player serving at 2-4 would be expected to win 20.9% of the time. In fact, these players go to win the tiebreak 22.0% of the time–a small but meaningful difference. We see an even bigger gap for players returning at 2-4. The model predicts that they would win 19.9% of the time, but they end up winning 22.1% of these tiebreaks.

In other words, after six points, the player with more points is heavily favored, but if there’s any momentum–that is, if either player has more of an advantage than the mere score would suggest–the edge belongs the player trailing in the tiebreak.

Sure enough, we see the same effect after eight points. Serving at 3-5, players in this dataset have a 16.3% (theoretical) probability of winning the tiebreak, but they win 19.0% of the time. Returning at 3-5, their paper chance is 17.2%, and they win 19.5%.

There’s nothing special about the first change of ends, and there probably isn’t any other point in a tiebreak that is more crucial than the model suggests. Instead, we’ve discovered that underdogs have a slightly better chance of coming back than their paper probabilities indicate. I suspect we’re seeing the effect of front-runners getting tight and underdogs swinging more freely–an aspect of tennis’s conventional wisdom that has much more to recommend itself than the idea of a magic score after the first six points of a tiebreak.