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:


And the same for second-serve returns:


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.

Is Kevin Anderson Developing Into an Elite Player?

With his upset win over Andy Murray on Monday, Kevin Anderson reached his first career Grand Slam quarterfinal. At age 29, he’ll ascend to a new peak ranking, and with a bit of cooperation from the rest of the draw, one more win could put him in the top ten for the first time.

Anderson has been a stalwart in the top 20 for two years now, but this additional step comes as a bit of a surprise. Despite the overall aging of the ATP tour and the emergence of Stan Wawrinka as a multi-Slam champion, it’s still a bit difficult to imagine a player in his late twenties taking major steps forward in his career.

What’s more, Anderson’s game is very serve-dependent. With an excellent backhand, he isn’t as one-dimensional a player as John Isner, Ivo Karlovic, or perhaps even Milos Raonic, but it’s much easier to categorize him with those players than with more baseline-oriented peers.

In today’s game, it is very difficult to reach the very top ranks without a quality return game. Tiebreaks are too much of a lottery to depend on in the long-term; you have to consistently break serve to win matches. As I wrote in a post about Nick Kyrgios earlier this year, almost no players have finished a season in the top ten without winning at least 37% of return points. Anderson has achieved that mark only once, in 2010. Entering the US Open this year, he was winning only 34.2% of return points.

The only top-ten player this year with a lower rate of return points won is Raonic, at 30.2%. Raonic is a historical anomaly, and as his tiebreak winning percentage has tumbled, from a near-record 75% last year to a more typical 51% this year, his place in the top ten is in jeopardy as well. In other words, the only servebot in the top ten has to rely on plenty of luck–or outstanding, perhaps one-of-a-kind skills in the clutch–to remain among the game’s elite.

Anderson is a more well-rounded player than Raonic, and he wins more return points than that. But he still falls well short of the next-worst return game in the top ten, Wawrinka’s 36.7%. The 2.5 percentage points between Anderson and Wawrinka represent a big gap, almost one-fifth of the entire range between the game’s best and worst returners.

The less effective a player’s return game, the more he must rely on tiebreaks to win sets, and that’s one explanation for Anderson’s success this season. His 62%(26-16) tiebreak winning percentage in 2015 is the best of his career, and considerably higher than his career tiebreak winning percentage of 54%. Again, it sounds like a small difference, but take away three or four of the tiebreaks he’s won this year, and he no longer reached the final at Queen’s Club … or might not be preparing for a quarterfinal in New York.

Very few players have managed to spend meaningful time in the top ten while depending so heavily on winning tiebreaks. Another metric to help us see this is the percentage of sets won that are won in tiebreaks. Entering the US Open, just over 25% of Anderson’s sets won were won in tiebreaks. Only four times since 1991 has a player sustained a rate that high and ended the year in the top ten: Raonic last year, Andy Roddick in 2007 and 2009, and Greg Rusedski in 1998.

In fact, between 1991 and 2014, only 17 times did a player finish a season in the top ten with this rate above 20%. Roddick represents five of those times, and almost all, except for Roddick at his peak, were players who finished outside the top five. Wawrinka’s and Raonic’s 2014 seasons were the only occurrences in the last decade.

The one ray of light in Anderson’s statistical profile this season is a significantly improved first serve. His 2015 ace rate is over 18%, compared to the 2014 (and career average) rate of 14%. His percentage of first-serve points won is up to 78.8%, from last season’s 75.4% and a career average of 75.8%.

This is a major improvement, and is the reason why he is one of only five players on tour (along with Isner, Karlovic, Roger Federer, and Novak Djokovic) winning more than 69% of service points this year. In many ways, Anderson’s stats are similar to those of Feliciano Lopez, but the Spaniard–another player who has long stood on the fringes on the top ten–has never topped 68% of service points won for a full season.

If Anderson can sustain this new level of first-serve effectiveness, he will–at the very least–continue to see a bit more success in tiebreaks. A tiebreak winning percentage higher than his career average of 54% (though still probably below his 2015 rate of 62%) will help keep him in the top 15. However, even for the best servers, tiebreaks are often little more than coin flips, and players don’t join the game’s elite by relying on coin flips.

As his quarterfinal appearance at the Open shows, Anderson is moving in the right direction. It’s easy to see a path for him that involves ending the season in the top ten. But to move up to the level above that, following the path of someone like Wawrinka, he’ll need to start serving like peak Andy Roddick, or–perhaps just as difficult–significantly improve his return game.

Break Point Persistence: Why Venus is Better Than Her Ranking

Some points matter a lot more than others. A couple of clutch break point conversions or a well-played tiebreak make it possible to win a match despite winning fewer than half of the points. Even when such statistical anomalies don’t occur, one point won at the right time can erase the damage done by several other points lost.

Break points are among the most important points, and because tennis’s governing bodies track them, we can easily study them. I’ve previously looked at break point stats, with a special emphasis on Federer, here and here. Today we’ll focus on break points in the women’s game.

The first step is to put break points in context. Rather than simply looking at a percentage saved or converted, we need to compare those rates to a player’s serve or return points won in general. Serena Williams is always going to save a higher percentage of break points than Sara Errani does, but that has much more to do with her excellent service game than any special skills on break points.

Once we do that, we have two results for each player: How much better (or worse) she is when facing break point on serve, and how much better (or worse) she is with a break point on return.

For instance, this year Serena has won 2.8% more service points than average when facing break point, and 7.5% more return points than average with a break point opportunity. The latter number is particularly good–not only compared to other players, but compared to Serena’s own record over the last ten years, when she’s converted break points exactly as often as she has won other break points.

Serena’s experience isn’t unusual. From one year to the next, these rates aren’t persistent, meaning that most players don’t consistently win or lose many more break points than expected. Since 2006, Maria Sharapova has converted 1% fewer break points than expected. Caroline Wozniacki has recorded exactly the same rate, while Victoria Azarenka has converted 2% fewer break points than expected.

On serve, the story is similar, with a slight twist. Inexperienced players seem to perform a little worse when trying to convert a break point against a more experienced opponent, so most top players save break points about 4% more often than they win other service points. Serena, Sharapova, Wozniacki, Azarenka, and Petra Kvitova all have career rates at about this level.

Unlike in the men’s game, there’s little evidence that left-handers have a special advantage saving break points on serve. Angelique Kerber is a few percentage points above average, but Kvitova, Lucie Safarova, and Ekaterina Makarova are all within one percentage point of neutral.

While a few marginal players are as much as ten percentage points away from neutral saving break points or converting them, the main takeaway here is that no one is building a great career on the back of consistent clutch performances on break points. Among women with at least 250 tour-level matches in the last decade, only Barbora Strycova has won more than 3% more break points (serve and return combined) than expected. Maria Kirilenko is the only player more than 3% below expected.

This analysis doesn’t tell us anything very interesting about the intrinsic skills of our favorite players, but that doesn’t mean it’s without value. If we can count on almost all players posting average numbers over the long term, we can identify short-term extremes and predict that certain players will return to normal.

And that (finally) brings us to Venus Williams. Since 2006, Venus has played break points a little bit worse than average, saving 2% more break points than typical serve points (compared to +4% for most stars) and winning break points on return 3% less often than other return points.

But this year, Venus has saved break points 17% less often than typical service points, the lowest single-season number from someone who played more than 20 tour-level matches. That’s roughly once per match this year that Venus has failed to save a break point that–in an average year–she would’ve saved.

There’s no guarantee that saving those additional break points would’ve changed many of Venus’s results this year, but given the usual strength of her service game, holding serve even a little bit more would make a difference.

This type of analysis can’t say whether a rough patch like Venus’s is due to bad luck, mental lapses, or something else entirely, but it does suggest very strongly than she will bounce back. In fact, she already has. In her successful US Open run, she’s won about 66% of service points while saving 63% of break points. That’s not nearly as good as Serena’s performance this year, but it’s much closer to her own career average.

Like so many tennis stats that fluctuate from match to match or year to year, this is another one that evens out in the end. A particularly good or bad number probably isn’t a sign of a long-term trend. Instead, it’s a signal that the short-term streak is unlikely to last.

Sabr Metrics: The Case For the Hyper-Aggressive Return

Roger Federer has made waves the last few weeks by occasionally moving way up the court to return second serves. While the old-school tactic was nearly extinct in today’s game of baseline attrition, it seems to be working for Fed.

At least in one sense, it’s too early to say whether the kamikaze return is an effective tactic. Federer has used it sparingly for only a handful of matches, and in that tiny sample, he’s missed plenty of returns. But in the view of many pundits, the hyper-aggressive return gets in his opponents’ heads, making the tactic more valuable than simply changing the result of a few points. Presumably Roger agrees, since he keeps using it.

I agree that the tactic is a good one, though for a different reason. By taking greater risks, Fed is generating more unpredictability, or streakiness, on his opponents’ service games, which is valuable even if he doesn’t win any more return points.

Watching and waiting

To win a match, a player usually needs to break serve, and in the contemporary men’s game, that’s not an easy thing to do. On average, servers win about 64% of points and hold about 80% of service games. On hard courts, the equivalent numbers are even higher. Against a good server–let alone John Isner, Fed’s opponent tonight–they are higher still.

Returners who stand well behind the baseline and try only to put the ball back in play are basically crossing their fingers and hoping for the best. Maybe their opponent will miss several first serves, or the server will make a couple of errors against those weak returns. It can work, and for a brilliant returner such as Novak Djokovic, hitting moderately aggressive returns and winning some of the ensuing rallies is usually good enough for several breaks per match.

For most players, however, breaks of serve rely more on the server’s occasional lapses. To put it in numerical terms: A passive returner is playing the lottery in every return game–a lottery with only a 10% to 20% chance of winning.

Generating the coin flip

The best way to earn more breaks of serve, of course, is to win more return points. But unless you’re spending the offseason at Djokovic’s training camp, that’s unlikely.

The alternative is to change the rules of the lottery. Instead of accepting a steady rate of 35% of return points, a hyper-aggressive strategy is more likely to make the point-by-point results more streaky, even if the overall rate doesn’t change.

To see why this is effective, we need to oversimplify a bit. A player who wins 35% of return points will, on average, break in 17% of his return games. If we introduce a slight variation in the rate of return points won, we see a slight improvement in break rate, as well. If that same player wins 30% of return points in half of his games and 40% of return points in the other half, he’ll break serve 18% of the time.

That one percent improvement is barely noticeable. It probably represents what’s already going on in most matches, often because servers are a bit streaky already. The more volatility we introduce, though, the more the odds tilt toward the returner.

Double the variation and say that the returner wins 25% of return points half the time and 45% the other half. Now he’ll break serve in 21% of games, or one extra break per 25 return games. Still not overwhelming, but that’s one extra break in a five-setter.

The real magic happens when we expand the variation to an even split between 20% of return points and 50% of return points. In that scenario–when, remember, our returner is still winning 35% of points–the break rate improves to 26%, almost one more break per ten return games. On average, that’s an extra break per best-of-three match, and closer to two extra breaks in a typical best-of-five match.

Back to reality

A hyper-aggressive return game is going to result in more return errors as well as more return winners. That’s true regardless of return position: Mikhail Kukushkin managed to break Marin Cilic four times on Friday by going for return winners, even if he stayed in the general area of the baseline.

So a new return tactic is unlikely to make a player much better in general. And of course, it’s unlikely to generate anything like the neat, theoretical examples shown above, when one game is better and one game is worse.

However, I suspect that higher-risk shots are more likely to be streaky, which would result in something like those neat examples. And if the pundits are right, that Fed’s kamikaze return unnerves his opponents, that ought to make his return games even streakier still, as his opponents deal with a new challenge mid-match.

Whenever there’s an opportunity to change the nature of the game and make it less predictable, the underdog should take it. Odd as it is to think of Federer as the underdog, he–like everyone else on the men’s tour–is in fact fighting an uphill battle in every return game. Hyper-aggressive tactics are a small step toward leveling the field.

Nick Kyrgios and the Minimum Viable Return Game

No matter how well a player serves, he still needs to win some return points. While one-dimensional ATPers such as Ivo Karlovic and John Isner have demonstrated that an unbreakable serve alone can get you a steady paycheck and some quality time in the top 20, their playing style has never translated into a prolonged stay in the top ten.

Nick Kyrgios isn’t quite as tall as Isner or Karlovic, but his numbers are similar. In the last year, he has won 31.7% of return points, third-worst among the top 50, ahead of only those two players. In fact, since 1991, only five players have lasted a full season at tour-level while winning a lower percentage of return points. To make an impact in the upper echelon of the men’s game, the Australian will need to improve his return game in a big way.

To win matches, you need to break serve or win tiebreaks, and most players don’t demonstrate any particular tiebreak skill. That leaves breaks of serve, and to break serve, you need to win return points. Almost all ATP tour regulars win between 29% and 43% of return points, so a single percentage point or two is a meaningful distinction. While Milos Raonic‘s rate of return points won over the last 52 weeks is a Kyrgios-comparable 32.1%, no other top-ten player is below 36%.

If Kyrgios is to crack the top ten without any substantial improvement in his return game, Raonic is the model. Last year, Milos finished the season at #8 in the rankings despite having won only 33.7% of return points. That’s the lowest rate on record for a player with a year-end ranking in the top ten, and only the seventh time since 1991 that a RPW% below 35% earned someone a spot in the top ten.

Even at 33.7%–two percentage points higher than Kyrgios’s current rate–it took a remarkable run of tiebreak success for Raonic to win as many matches as he did. Milos won 75% of tiebreaks last year, a rate that almost no one has ever sustained beyond a single season. In other words, if Raonic is to continue winning matches at the same pace, he’ll probably need to post better return-game results.

To earn a place in the elite of the top five, the return-game threshold is even higher. Only two players–Pete Sampras and Goran Ivanisevic–have finished a season in the top five with a RPW% below 36%, and only two more–Andy Roddick and Stanislas Wawrinka–have done so with a sub-37% RPW%. Roger Federer, the most serve-oriented of the big four, hasn’t posted a RPW% below 38% in fifteen years.

The difference between 32% and 36% is enormous. To use a baseball analogy, a similar gap in batting average would be, roughly, from .240 to .280. The effects are equally meaningful. At 32%, a player is breaking serve roughly once per eight return games–considerably less than once per set. At 36%, he’s breaking serve almost once per five return games. Improve a few more percentage points to 39%, and he’s breaking every fourth game, almost twice as often as Kyrgios is now.

Those break rates are simply a way of quantifying what we already know at a general level: Players with strong return games have the power to decide matches. The more one-dimensional the playing style, the more likely a match is decided by just a few key points. And the smaller that number of points, the more that luck plays a part.

Of course, luck cuts both ways. It’s what makes players like Isner and Kyrgios so dangerous. Someone like Novak Djokovic or Rafael Nadal can usually dictate play, but against an unbreakable opponent, it all comes down to a few points in a couple of tiebreaks. So big servers tend to rocket into the top 30 or 40. A fifty-fifty winning percentage, especially coupled with a big upset and an occasional deep run at a big tournament, is plenty good enough to earn a spot that high in the rankings.

But without at least a mediocre return game, it’s tough for a big server to get beyond that level. Isner has managed it by winning tiebreaks at one of the best rates of all time, and even he has barely dipped his toe in the top ten. Raonic is a substantially better returner than the American, and it remains to be seen whether he can sustain his impressive tiebreak winning percentage and keep a spot among the game’s best.

Fortunately, Kyrgios has plenty of time to improve and break out of the mold of a one-dimensional big server. If he hopes to make a mark beyond the occasional upset and a home at the fringes of the top 20, that’s exactly what he’ll need to do.

The Unaceables

Last night, Florian Mayer solved the John Isner serve, breaking the American three times en route to a straight-set victory.  Mayer is known as a tricky opponent, but not as a particularly good returner.  He had never played Isner before, though he beat Ivo Karlovic in Miami last year.

One element of his success is that he got his racquet on the Isner serve.  Over the last 52 weeks, Isner has amassed a 17.1% ace rate, meaning that about one in six of his serves are untouchable.  Last night, he barely managed 10%, as Mayer allowed him only six aces.

We might wonder: Is this is a skill of Mayer’s that we’ve failed to notice before?  At first glance, it doesn’t appear to be.  While Mayer often holds his opponents to low ace numbers, he’s had some horrible performances in that department, allowing Feliciano Lopez a 20.4% ace rate in Shanghai last year, Thomaz Bellucci 15.5% in Madrid on clay, and while playing injured, he ignominiously allowed Ivo Karlovic a 50% ace rate at last year’s Cincinnati Masters.

We can answer this question not just for Mayer, but for every regular on the ATP tour.  While some servers hit far more aces than others, ace rate is influenced by both the server and the returner.  Mayer himself is a good example.  In the last 52 weeks, he’s had eight matches in which at least one in ten serves went for an ace.  But in five other matches, he didn’t hit a single one!  Some of the variation is due to good and bad serving performances, but a substantial part can be explained by the man on the other side of the net.

As  it turns out, last night was an aberration for the German.  Mayer is below-average at ace prevention, allowing 8% more aces than an average player, ranking 80th among the 139 active players whose results I analyzed.

I looked at every 2011 and 2012 match, using only those matches in which both players racked up 10 matches in the last fifteen months.  After calculating each player’s ace rate, I generated an “expected” number of aces for each returner.  Simply tallying how many aces a player allowed isn’t good enough–this way, we adjust for the quality of the server.

Mayer, for instance, played 70 matches in that span against opponents who also played at least 10 matches.  (I excluded guys who played fewer than 10 because their ace rate in such a small number of matches may say more about their opponents than themselves.)  In his 4812 return points, he allowed 345 aces.  But based on the serving abilities of his opponents, he should have allowed only 321.  Those numbers will look a little better after last night, but not enough to move him up very much in the rankings.

By contrast, the best returners get their racquets on just about everything.  Atop the list is Gael Monfils, who allows barely half the aces that we would expect him to.  The top eight returners all reduce expected ace rates by at least a third.

In the table below, I’ve shown these stats for the ten players who appear to be the best at avoiding aces, along with 20 other players of interest.

Player                 Rank  Matches  vAce%  expAce%    Diff  
Gael Monfils              1       62   3.5%     6.8%    -48%  
Benoit Paire              2       23   3.8%     6.3%    -40%  
Andy Murray               3       81   4.4%     7.3%    -39%  
Stanislas Wawrinka        4       61   4.2%     7.0%    -39%  
Cedrik Marcel Stebe       5       12   3.2%     5.2%    -38%  
Viktor Troicki            6       70   4.3%     7.0%    -38%  
Gilles Simon              7       77   4.7%     7.3%    -36%  
David Ferrer              8       90   5.1%     7.8%    -35%  
Carlos Berlocq            9       53   4.7%     7.0%    -32%  
Mardy Fish               10       71   5.7%     8.3%    -31%  

Jo Wilfried Tsonga       14       89   5.7%     7.9%    -28%  
Roger Federer            20       92   6.0%     7.9%    -24%  
Novak Djokovic           22       89   6.4%     8.4%    -24%  
Kei Nishikori            32       63   5.8%     7.0%    -17%  
Rafael Nadal             34       91   7.4%     8.8%    -16%  
Nikolay Davydenko        38       60   5.8%     6.7%    -14%  
Sam Querrey              39       35   6.7%     7.8%    -14%  
Milos Raonic             40       60   6.7%     7.6%    -12%  
Kevin Anderson           53       74   7.5%     8.0%     -6%  
John Isner               59       68   7.6%     7.8%     -2%  

Radek Stepanek           73       62   8.6%     8.0%      6%  
Lukasz Kubot             74       44   8.5%     8.0%      7%  
Ivo Karlovic             78       45   7.9%     7.3%      7%  
Juan Martin Del Potro    81       84   8.8%     8.1%      9%  
Tomas Berdych            91       87   8.5%     7.6%     12%  
David Nalbandian        102       43   9.4%     7.9%     20%  
Arnaud Clement          120       17   9.3%     7.2%     29%  
Andy Roddick            130       55  11.8%     8.3%     42%  
Bernard Tomic           135       38  12.8%     8.5%     50%  
Olivier Rochus          139       36  14.7%     7.2%    103%

Before we go anointing Monfils and Benoit Paire the greatest returners in the game, it’s important to remember the serious limitations of the ace stat.  Much more important is getting the return in play.  But except for Grand Slam matches, we don’t have those numbers. In the meantime, we can use ace rate and return points won as proxies for return skills.