Serve statistics – Page 6

Measuring the Impact of the Serve in Men’s Tennis

By just about any measure, the serve is the most important shot in tennis. In men’s professional tennis, with its powerful deliveries and short points, the serve is all the more crucial. It is the one shot guaranteed to occur in every rally, and in many points, it is the only shot.

Yet we don’t have a good way of measuring exactly how important it is. It’s easy to determine which players have the best serves–they tend to show up at the top of the leaderboards for aces and service points won–but the available statistics are very limited if we want a more precise picture. The ace stat counts only a subset of those points decided by the serve, and the tally of service points won (or 1st serve points won, or 2nd serve points won) combines the effect of the serve with all of the other shots in a player’s arsenal.

Aces are not the only points in which the serve is decisive, and some service points won are decided long after the serve ceases to have any relevance to the point. What we need is a method to estimate how much impact the serve has on points of various lengths.

It seems like a fair assumption that if a server hits a winner on his second shot, the serve itself deserves some of the credit, even if the returner got it back in play. In any particular instance, the serve might be really important–imagine Roger Federer swatting away a weak return from the service line–or downright counterproductive–think of Rafael Nadal lunging to defend against a good return and hitting a miraculous down-the-line winner. With the wide variety of paths a tennis point can follow, though, all we can do is generalize. And in the aggregate, the serve probably has a lot to do with a 3-shot rally. At the other extreme, a 25-shot rally may start with a great serve or a mediocre one, but by the time by the point is decided, the effect of the serve has been canceled out.

With data from the Match Charting Project, we can quantify the effect. Using about 1,200 tour-level men’s matches from 2000 to the present, I looked at each of the server’s shots grouped by the stage of the rally–that is, his second shot, his third shot, and so on–and calculated how frequently it ended the point. A player’s underlying skills shouldn’t change during a point–his forehand is as good at the end as it is at the beginning, unless fatigue strikes–so if the serve had no effect on the success of subsequent shots, players would end the point equally often with every shot.

Of course, the serve does have an effect, so points won by the server end much more frequently on the few shots just after the serve than they do later on. This graph illustrates how the “point ending rate” changes:

On first serve points (the blue line), if the server has a “makeable” second shot (the third shot of the rally, “3” on the horizontal axis, where “makeable” is defined as a shot that results in an unforced error or is put back in play), there is a 28.1% chance it ends the point in the server’s favor, either with a winner or by inducing an error on the next shot. On the following shot, the rate falls to 25.6%, then 21.8%, and then down into what we’ll call the “base rate” range between 18% and 20%.

The base rate tells us how often players are able to end points in their favor after the serve ceases to provide an advantage. Since the point ending rate stabilizes beginning with the fifth shot (after first serves), we can pinpoint that stage of the rally as the moment–for the average player, anyway–when the serve is no longer an advantage.

As the graph shows, second serve points (shown with a red line) are a very different story. It appears that the serve has no impact once the returner gets the ball back in play. Even that slight blip with the server’s third shot (“5” on the horizontal axis, for the rally’s fifth shot) is no higher than the point ending rate on the 15th shot of first-serve rallies. This tallies with the conclusions of some other research I did six years ago, and it has the added benefit of agreeing with common sense, since ATP servers win only about half of their second serve points.

Of course, some players get plenty of positive after-effects from their second serves: When John Isner hits a second shot on a second-serve point, he finishes the point in his favor 30% of the time, a number that falls to 22% by his fourth shot. His second serve has effects that mirror those of an average player’s first serve.

Removing unforced errors

I wanted to build this metric without resorting to the vagaries of differentiating forced and unforced errors, but it wasn’t to be. The “point-ending” rates shown above include points that ended when the server’s opponent made an unforced error. We can argue about whether, or how much, such errors should be credited to the server, but for our purposes today, the important thing is that unforced errors aren’t affected that much by the stage of the rally.

If we want to isolate the effect of the serve, then, we should remove unforced errors. When we do so, we discover an even sharper effect. The rate at which the server hits winners (or induces forced errors) depends heavily on the stage of the rally. Here’s the same graph as above, only with opponent unforced errors removed:

The two graphs look very similar. Again, the first serve loses its effect around the 9th shot in the rally, and the second serve confers no advantage on later shots in the point. The important difference to notice is the ratio between the peak winner rate and the base rate, which is now just above 10%. When we counted unforced errors, the ratio between peak and base rate was about 3:2. With unforced errors removed, the ratio is close to 2:1, suggesting that when the server hits a winner on his second shot, the serve and the winner contributed roughly equally to the outcome of the point. It seems more appropriate to skip opponent unforced errors when measuring the effect of the serve, and the resulting 2:1 ratio jibes better with my intuition.

Making a metric

Now for the fun part. To narrow our focus, let’s zero in on one particular question: What percentage of service points won can be attributed to the serve? To answer that question, I want to consider only the server’s own efforts. For unreturned serves and unforced errors, we might be tempted to give negative credit to the other player. But for today’s purposes, I want to divvy up the credit among the server’s assets–his serve and his other shots–like separating the contributions of a baseball team’s pitching from its defense.

For unreturned serves, that’s easy. 100% of the credit belongs to the serve.

For second serve points in which the return was put in play, 0% of the credit goes to the serve. As we’ve seen, for the average player, once the return comes back, the server no longer has an advantage.

For first-serve points in which the return was put in play and the server won by his fourth shot, the serve gets some credit, but not all, and the amount of credit depends on how quickly the point ended. The following table shows the exact rates at which players hit winners on each shot, in the “Winner %” column:

Server's…  Winner %  W%/Base  Shot credit  Serve credit  
2nd shot      21.2%     1.96        51.0%         49.0%  
3rd shot      18.1%     1.68        59.6%         40.4%  
4th shot      13.3%     1.23        81.0%         19.0%  
5th+          10.8%     1.00       100.0%          0.0%

Compared to a base rate of 10.8% winners per shot opportunity, we can calculate the approximate value of the serve in points that end on the server’s 2nd, 3rd, and 4th shots. The resulting numbers come out close to round figures, so because these are hardly laws of nature (and the sample of charted matches has its biases), we’ll go with round numbers. We’ll give the serve 50% of the credit when the server needed only two shots, 40% when he needed three shots, and 20% when he needed four shots. After that, the advantage conferred by the serve is usually canceled out, so in longer rallies, the serve gets 0% of the credit.

Tour averages

Finally, we can begin the answer the question, What percentage of service points won can be attributed to the serve? This, I believe, is a good proxy for the slipperier query I started with, How important is the serve?

To do that, we take the same subset of 1,200 or so charted matches, tally the number of unreturned serves and first-serve points that ended with various numbers of shots, and assign credit to the serve based on the multipliers above. Adding up all the credit due to the serve gives us a raw number of “points” that the player won thanks to his serve. When we divide that number by the actual number of service points won, we find out how much of his service success was due to the serve itself. Let’s call the resulting number Serve Impact, or SvI.

Here are the aggregates for the entire tour, as well as for each major surface:

         1st SvI  2nd SvI  Total SvI  
Overall    63.4%    31.0%      53.6%  
Hard       64.6%    31.5%      54.4%  
Clay       56.9%    27.0%      47.8%  
Grass      70.8%    37.3%      61.5%

Bottom line, it appears that just over half of service points won are attributable to the serve itself. As expected, that number is lower on clay and higher on grass.

Since about two-thirds of the points that men win come on their own serves, we can go even one step further: roughly one-third of the points won by a men’s tennis player are due to his serve.

Player by player

These are averages, and the most interesting players rarely hew to the mean. Using the 50/40/20 multipliers, Isner’s SvI is a whopping 70.8% and Diego Schwartzman‘s is a mere 37.7%. As far from the middle as those are, they understate the uniqueness of these players. I hinted above that the same multipliers are not appropriate for everyone; the average player reaps no positive after-effects of his second serve, but Isner certainly does. The standard formula we’ve used so far credits Isner with an outrageous SvI, even without giving him credit for the “second serve plus one” points he racks up.

In other words, to get player-specific results, we need player-specific multipliers. To do that, we start by finding a player-specific base rate, for which we’ll use the winner (and induced forced error) rate for all shots starting with the server’s fifth shot on first-serve points and shots starting with the server’s fourth on second-serve points. Then we check the winner rate on the server’s 2nd, 3rd, and 4th shots on first-serve points and his 2nd and 3rd shots on second-serve points, and if the rate is at least 20% higher than the base rate, we give the player’s serve the corresponding amount of credit.

Here are the resulting multipliers for a quartet of players you might find interesting, with plenty of surprises already:

                   1st serve              2nd serve       
                    2nd shot  3rd  4th     2nd shot  3rd  
Roger Federer            55%  50%  30%           0%   0%  
Rafael Nadal             31%   0%   0%           0%   0%  
John Isner               46%  41%   0%          34%   0%  
Diego Schwartzman        20%  35%   0%           0%  25%  
Average                  50%  30%  20%           0%   0%

Roger Federer gets more positive after-effects from his first serve than average, more even than Isner does. The big American is a tricky case, both because so few of his serves come back and because he is so aggressive at all times, meaning that his base winner rate is very high. At the other extreme, Schwartzman and Rafael Nadal get very little follow-on benefit from their serves. Schwartzman’s multipliers are particularly intriguing, since on both first and second serves, his winner rate on his third shot is higher than on his second shot. Serve plus two, anyone?

Using player-specific multipliers makes Isner’s and Schwartzman’s SvI numbers more extreme. Isner’s ticks up a bit to 72.4% (just behind Ivo Karlovic), while Schwartzman’s drops to 35.0%, the lowest of anyone I’ve looked at. I’ve calculated multipliers and SvI for all 33 players with at least 1,000 tour-level service points in the Match Charting Project database:

Player                 1st SvI  2nd SvI  Total SvI  
Ivo Karlovic             79.2%    56.1%      73.3%  
John Isner               78.3%    54.3%      72.4%  
Andy Roddick             77.8%    51.0%      71.1%  
Feliciano Lopez          83.3%    37.1%      68.9%  
Kevin Anderson           77.7%    42.5%      68.4%  
Milos Raonic             77.4%    36.0%      66.0%  
Marin Cilic              77.1%    34.1%      63.3%  
Nick Kyrgios             70.6%    41.0%      62.5%  
Alexandr Dolgopolov      74.0%    37.8%      61.3%  
Gael Monfils             69.8%    37.7%      60.8%  
Roger Federer            70.6%    32.0%      58.8%  
                                                    
Player                 1st SvI  2nd SvI  Total SvI  
Bernard Tomic            67.6%    28.7%      58.5%  
Tomas Berdych            71.6%    27.0%      57.2%  
Alexander Zverev         65.4%    30.2%      54.9%  
Fernando Verdasco        61.6%    32.9%      54.3%  
Stan Wawrinka            65.4%    33.7%      54.2%  
Lleyton Hewitt           66.7%    32.1%      53.4%  
Juan Martin Del Potro    63.1%    28.2%      53.4%  
Grigor Dimitrov          62.9%    28.6%      53.3%  
Jo Wilfried Tsonga       65.3%    25.9%      52.7%  
Marat Safin              68.4%    22.7%      52.3%  
Andy Murray              63.4%    27.5%      52.0%  
                                                    
Player                 1st SvI  2nd SvI  Total SvI  
Dominic Thiem            60.6%    28.9%      50.8%  
Roberto Bautista Agut    55.9%    32.5%      49.5%  
Pablo Cuevas             57.9%    28.9%      47.8%  
Richard Gasquet          56.0%    29.0%      47.5%  
Novak Djokovic           56.0%    26.8%      47.3%  
Andre Agassi             54.3%    31.4%      47.1%  
Gilles Simon             55.7%    28.4%      46.7%  
Kei Nishikori            52.2%    30.8%      45.2%  
David Ferrer             46.9%    28.2%      41.0%  
Rafael Nadal             42.8%    27.1%      38.8%  
Diego Schwartzman        39.5%    25.8%      35.0%

At the risk of belaboring the point, this table shows just how massive the difference is between the biggest servers and their opposites. Karlovic’s serve accounts for nearly three-quarters of his success on service points, while Schwartzman’s can be credited with barely one-third. Even those numbers don’t tell the whole story: Because Ivo’s game relies so much more on service games than Diego’s does, it means that 54% of Karlovic’s total points won–serve and return–are due to his serve, while only 20% of Schwartzman’s are.

We didn’t need a lengthy analysis to show us that the serve is important in men’s tennis, or that it represents a much bigger chunk of some players’ success than others. But now, instead of asserting a vague truism–the serve is a big deal–we can begin to understand just how much it influences results, and how much weak-serving players need to compensate just to stay even with their more powerful peers.

How Much Does Height Matter in Men’s Tennis?

Italian translation at settesei.it

Clearly, height matters. On average, tall players can serve faster and more effectively than can shorter players. And usually, short players who succeed on tour do so by returning and moving better than their taller colleagues. The conventional wisdom is that height is an advantage, but only up to a point. An inch or two above six feet (a range between 185 and 190 cm) is good, but much more than that is too much. No player above 6’4″ (193 cm, Marat Safin) has ever reached No. 1 in the ATP rankings.

While 5’7″ (170 cm) Diego Schwartzman‘s surprise run to the US Open quarterfinals has brought this issue to the forefront, pundits and fans talk about it all the time. This is a topic crying out for some basic data analysis, yet as is too often the case in tennis, some really simple work is missing from the conversation. Let’s try to fix that.

When I say “basic,” I really mean it. We all know that tall men hit more aces than short men. But how many? How strong is the relationship between height and, say, first serve points won? In this post, I’ll show the relationship between height and each of nine different stats, from overall records to serve- and return-specific numbers.

For my dataset, I took age-25 seasons from 1998 to 2017 in which the player completed at least 30 tour-level matches. (I used only one season per player so that the best players with the longest careers wouldn’t be weighted too heavily.) That gives us 156 player-seasons, from Hicham Arazi and Greg Rusedski in 1998 up to Schwartzman and Jack Sock in 2017. There aren’t very many players at the extremes, so I lumped together everyone 5’8″ (173 cm) and below and did the same with everyone 6’5″ (196 cm) and above. I also grouped players standing 5’10” with those at 5’9″, because there were only four 5’10” guys in the dataset.

That gives us nine “height levels”: one per inch from 5’8″ to 6’5″ with the exception of 5’10”. (The ATP website displays heights in meters, but its database must record and/or store them in inches, because every height translates to something close to an integer height in inches. For example, no player is listed at 174 cm, or 5’8.5″.) Some individual heights are certainly exaggerated, as male athletes and their organizations tend to do, but we have to make do with the information available, and we may assume that the exaggerations are fairly consistent.

Let’s start with the most basic building block of tennis, the match win. There is a reasonably strong relationship here, although the group of players at 6’1″ is nearly as good as the tallest subset. In each of these graphs, height is given on the horizontal axis in centimeters, from 173 (the 5’8″ and below group) up to 196 (the 6’5″ and higher group).

There is a similar, albeit slightly weaker, relationship when we look at the level of single points. Since a small difference in points results in a larger difference in matches won (at the extreme, winning 55% of points translates to nearly a 100% chance of winning the match) this isn’t a surprise. At the match level, r^2 = 0.38, and at the point level, below, r^2 = 0.27:

(If you’re wondering how all of the averages are above 50%, it’s because the sample is limited to player-seasons with at least 30 matches. A fair number of those matches are against players who aren’t tour regulars, and the regulars–the guys in this sample–win a hefty proportion of those matches.)

Serve stats

Now we get to confirm our main assumptions. Taller players are better servers, and the gap is enormous, ranging from 60% of service points won for the shortest players up to nearly 70% for the tallest:

As strong as that relationship is (r^2 = 0.81), the relationship between height and ace rate is stronger still, at r^2 = 0.83:

Aces don’t tell the whole story–the stat with the strongest correlation to height is first serve points won (r^2 = 0.92) as you can see here:

But this is where things start to get interesting. Nearly every inch makes a player more effective on the first serve, but opponents are able to negotiate tall players’ second serves much more successfully. There remains a modest relationship with height (r^2 = 0.18), but it is the weakest of all the stats presented here:

It’s nice to be tall, as anyone who has seen John Isner casually spin a second-serve ace out of the reach of an unlucky opponent. But except in the tallest category, height doesn’t confer much of a second-serve advantage. Players standing 6’4″ (193 cm) win about as many second-serve points as do players at 5’9″ (175 cm). That doesn’t mean that the second serves of the shorter players are just as good–they probably aren’t–but that shorter players tend to possess other skills that they can leverage in second-serve points, which usually last longer. For the purposes of today’s overview, it doesn’t really matter why short players are able to negate the advantage of height on second serve points, just that they are clearly able to do so.

Return stats

We wouldn’t be having this conversation–and David Ferrer wouldn’t be headed to a likely place in the Hall of Fame–if the inverse relationship between height and return effectiveness weren’t nearly as strong as the positive one between height and serving prowess. “Nearly” is the key word here. The relationship between height and overall return points won is almost as strong (r^2 = 0.74) as that of height and overall service points won, but not quite:

Schwartzman is doing more than his part to hold up the left side of that trendline: He is both the shortest player in the top 50 and the best returner. On first serve points, however, there’s only so much the returner can do, so while shorter players still have an advantage, it is less substantial. The relationship here is a bit weaker, at r^2 = 0.63:

It follows, then, that the relationship between height and second-serve return points won must be stronger, at r^2 = 0.77:

The overall and first-serve return point graphs make clear just how much worse the tallest players are than the rest of the pack. The graphs exaggerate it a bit, because I’ve grouped players from 6’5″ all the way up to 6’11”, and the Isners of the sport are considerably less effective than players such as Marin Cilic. Still, we find plenty of confirmation for the conventional wisdom that a height of 6’2″ or 6’3″ (188 cm to 190 cm) allows for players to remain effective on both sides of the ball, while a small increase from there can be a disadvantage.

A note on selection bias

It’s easy to lapse into shorthand and say something like, “shorter players are better returners.” More precisely, what we mean is, “of the players who have become tour regulars, shorter players are better returners.” They have to be, because it is nearly impossible for them to be top-tier servers. If they’ve cracked the top 50, they must have developed a world-class return game. The shorter the player, the more likely this is true.

The same logic is considerably weaker if we descend a couple rungs lower on the ladder of tennis skill. In collegiate tennis, it’s still an advantage to be tall–as Isner can attest–but a player such as 5’10” Benjamin Becker can serve as well as nearly all the competition he will face at that level.

One more note on selection bias

My choice to use each player’s age-25 season might understate the ability of either short or tall players. It is possible that certain playing styles result in earlier or later peaks, meaning that while tall players could be better at age 25, shorter players may be superior at age 28. There are anecdotes that support the argument in both directions, so I don’t think it’s a major issue, but it is one worthy of additional study.

Further reading

A guest post on this blog earlier this year posed the question, Are Taller Players the Future of Tennis?

I didn’t mention serve speed in the above, but here’s a quick study of the fastest serves and their correlation with height.

Second-Strike Tennis: When Returners Dominate

Italian translation at settesei.it

On Wednesday, Diego Schwartzman scored a notable upset, knocking out 12th seed Roberto Bautista Agut in the second round of the Monte Carlo Masters. Even more unusual than Bautista Agut’s first-round exit was the way it happened. Both players won more than half of their return points: 61% for Schwartzman and 52% for Bautista Agut. There were 14 breaks of serve in 21 games.

Players like Schwartzman win more than half of return points fairly regularly. In the last 12 months, including both Challenger and tour-level matches, the Argentine–nicknamed El Peque for his diminutive stature–has done so more than 20 times. What is almost unheard of in the men’s game is for both players to return so well (or serve so poorly) that neither player wins at least half of his service points.

Since 1991–the first year for which ATP match stats are available–there have been fewer than 70 matches in which both players win more than half of their return points. (There are another 25 or so in which one player exceeded 50% and the other hit 50% exactly.) What’s more, these matches have become even less frequent over time: Wednesday’s result was the first instance on the ATP tour since 2014, and there have been fewer than 30 since 2000.

Here are the last 15 such matches, along with the both the winner’s (W RPW) and loser’s (L RPW) rates of return points won. Few of the players or surfaces come as a surprise:

Year  Event            Players                 W RPW  L RPW  
2017  Monte Carlo      Schwartzman d. RBA      61.4%  51.9%  
2014  Rio de Janeiro   Fognini d. Bedene       50.6%  50.6%  
2014  Houston          Hewitt d. Polansky      51.3%  51.5%  
2014  Estoril          Berlocq d. Berdych      51.5%  50.6%  
2013  Monte Carlo      Bautista Agut d. Simon  58.8%  50.6%  
2013  Estoril          Goffin d. P Sousa       55.2%  50.5%  
2011  Casablanca       Fognini d. Kavcic       51.0%  51.9%  
2011  Belgrade         Granollers d. Troicki   61.5%  50.8%  
2008  Barcelona        Chela d. Garcia Lopez   54.3%  50.5%  
2008  Costa Do Sauipe  Coria d. Aldi           58.5%  51.9%  
2007  Rome Masters     Ferrero d. Hrbaty       52.9%  51.7%  
2007  Hamburg          Ferrer d. Bjorkman      50.6%  50.6%  
2006  Monte Carlo      Coria d. Kiefer         53.2%  50.9%  
2006  Hamburg Masters  Gaudio d. A Martin      57.3%  51.1%  
2006  Australian Open  Coria d. Hanescu        53.4%  50.6%

All but 8 of the 69 total matches were on clay. One of the exceptions is at the bottom of this list, from the 2006 Australian Open, and before 2006, there were another five hard-court contests, along with two on grass courts. (The ATP database isn’t completely reliable, but in each of these cases, the high rate of return points won is partially verified by a similarly high number of reported breaks of serve.)

Bautista Agut, who won one of these matches four years ago in Monte Carlo, is one of several players who participated in multiple return-dominated clashes. Guillermo Coria played in five, winning four, and Fabrice Santoro took part in four, winning three. Coria won more than half of his return points in 75 tour-level matches over the course of his career.

Over course, both Schwartzman and Baustista Agut cleared the 50% bar with plenty of room to spare. The Spaniard won 51.9% of return points and Schwartzman comfortably exceeded 60%, putting them in an even more elite category. It was only the 22nd match since 1991 in which both players won at least 51.9% of return points.

As rare as these matches are, Schwartzman is doing everything he can to add to the list. With a ranking now in the top 40, he has entered just about every clay tournament on the schedule, so the most return-oriented competitor in the game is going to play a lot more top-level matches on slow surfaces. If anyone has a chance at equaling Coria’s mark of winning four of these return-dominated matches, my money’s on El Peque.

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.)

https://www.instagram.com/p/BQjI1gJBKgE/

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.

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].

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.

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?

What Happens After an Unsuccessful First Serve Challenge?

Italian translation at settesei.it

A lot of first serves miss, so every player has a well-established routine between the first and second serve. So much so that, traditionally, if something disrupts that routine, the receiver may grant the server another first serve.

Hawkeye has changed all that. If the server doubts the line call, he or she may challenge it. That results in a lengthy wait, usually some crowd noise, and a general wreckage of that between-serves routine.

The conventional wisdom seems to be that the long pause is harmful to the server: that if the challenge fails, the server is less likely to put the second serve in the box. And if the second serve does go in, it’s weaker than average, so the server is less likely to win the point.

My analysis of over 200 first-serve challenges casts doubt on the conventional wisdom. It’s another triumph for the null hypothesis, the only force in tennis as dominant as Novak Djokovic.

As I’ve charted matches for the Match Charting Project, I’ve noted each challenge, the type of challenge, and whether it was successful. I’ve accumulated 116 ATP and 89 WTA instances in which a player unsuccessfully challenged the call on his own first serve. For each of these challenges, I also calculated some match-level stats for that server: how often s/he made the second serve, and how often s/he won second serve points.

Of the 116 unsuccessful ATP challenges, players made 106 of their second serves. Based on their overall rates in those matches, we’d expect them to make 106.6 of them. They won exactly half–58–of those points, and their performance in those matches suggests that they “should” have won 58.2 of them.

In other words, players are recovering from the disruption and performing almost exactly as they normally do.

For WTAers, it’s a similar story. Players made 77 of their 89 second serves. If they landed second serves at the same rate they did in the rest of those matches, they’d have made 77.1. They won 38 of the 89 points, compared to an expected 40 points. That last difference, of five percent, is the only one that is more than a rounding error. Even if the effect is real–which is doubtful, given the conflicting ATP number and the small sample size–it’s a small one.

Of course, the potential benefit of challenging the call on your first serve is big: If you’re right, you either win the point or get another first serve. Of the challenges I’ve tracked, men were successful 38% of the time on their first serves, and women were right 32% of the time.

There’s no evidence here that players are harmed by appealing to Hawkeye on their own first serves. Apart from the small risk of running out of challenges, it’s all upside. Tennis pros adore routine, but in this case, they perform just as well when the routine is disrupted.

First and Second Serves: Another ATP Info-miss

Breaking news, everybody: First serves are better than second serves!

That’s what I learned, anyway, from the latest article in the “Infosys ATP Beyond the Numbers” series:

When you average out the Top 10 players in the 2015 season, they are saving break points 72 per cent of the time when making a first serve. On average, that drops to 53 per cent with second serves. That 19 per cent difference is one of the most important, hidden metrics in our sport.

Is the difference between first and second serves “important?” Definitely. Is it in any way “hidden?” Not so much.

The melodramatic phrasing here suggests that break points are different from regular points, perhaps with a much larger spread between first and second serve winning percentages. But no, that’s not the case.

Last year, top ten players won 75.6% of first-serve points and 55.4% of second-serve points. Combined with the Infosys numbers–which I can’t verify, because the ATP doesn’t make the necessary raw data available–that means that top ten players win 5% less often when making a first serve on break point, and 5% less often when missing their first serve on break point.

At the risk of belaboring this: When it comes to the importance of making your first serve, break points are no different than other points.

Even that 5% difference is less meaningful that it looks. Break points don’t occur at random–better opponents generate more break opportunities. If you play two matches, one against Novak Djokovic and one against Jerzy Janowicz, you’re likely to face far more break points against Novak than against Jerzy … and of course, you’re less likely to win them.

Pundits tend to focus on break points, and in part, they are right to do so, because this small subset of points have an outsized effect on match outcomes. However, because of the small sample, it’s easy–and far too common–to read too much into break point results. My research has repeatedly shown that, once you control for opponent quality, most players win break points about as often as they do non-break points.

The ATP is sitting on a wealth of information. If we’re going to learn anything meaningful when they go “beyond the numbers,” it would be nice if they took advantage of more of their data and offered up more sophisticated analysis.

Are Two First Serves Ever Better Than One?

Italian translation at settesei.it

It’s one of those ideas that never really goes away. Some players have such strong first serves that we often wonder what would happen if they hit only first serves. That is, if a player went all-out on every serve, would his results be any better?

Last year, Carl Bialik answered that question: It’s a reasonably straightforward “no.”

Bialik showed that among ATP tour regulars in 2014, only Ivo Karlovic would benefit from what I’ll call the “double-first” strategy, and his gains would be minimal. When I ran the numbers for 2015–assuming for all players that their rates of making first serves and winning first-serve points would stay the same–I found that Karlovic only breaks even. Going back to 2010, 2014 Ivo was the only player-season with at least 40 matches for whom two first serves would be better than one.

Still, it’s not an open-and-shut case. What struck me is that the disadvantage of a double-first strategy would be so minimal. For Karlovic (and others, mainly big servers, such as Jerzy Janowicz, Milos Raonic,and John Isner), hitting two first serves would only slightly decrease their overall rate of service points won. For Rafael Nadal and Andy Murray, opting for double-first would reduce their rate of service points won by just under two percentage points.

Here’s a visual look at 2015 tour regulars (minimum 30 matches), showing the hypothetical disadvantage of two first serves. The diagonal line is the breakeven level; Ivo, Janowicz, and Isner are the three points nearly on the line.

Since some players are so close to breaking even, I started to wonder if some matchups make the double-first strategy a winning proposition. For example, Novak Djokovic is so dominant against second serves that, perhaps, opponents would be better off letting him see only first serves.

However, it remains a good idea–at least in general–to take the traditional approach against Djokovic. Hypothetically, two first serves would result in Novak raising his rate of return points won by 1.2 percentage points. Gilles Simon and Andy Murray are in similar territory, right around 1 percentage point.

Here’s the same plot, showing the disadvantage of double-first against tour-regular returners this season:

There just aren’t any returners who would cause the strategy to come as close to breaking even as some big servers do.

The match-level tactic

What happens if a nearly-breakeven server, like Karlovic, faces a not-far-from-breakeven returner, like Djokovic? If opting for double-first is almost a good idea for Ivo against the average returner, what happens when he faces someone particularly skilled at attacking second serves?

Sure enough, there are lots of matches in which two first serves would have been better than one. I found about 1300 matches between tour regulars (players with 30+ matches) this season, and for each one, I calculated each player’s actual service points won along with their estimated points won had they hit two first serves. About one-quarter of the time, double-first would have been an improvement.

This finding holds up in longer matches, too, avoiding some of the danger of tiny samples in short matches. In one-quarter of longer-than-average matches, a player would have still benefited from the double-first strategy. Here’s a look at how those matches are distributed:

Finally, some action on the left side of the line! One of those outliers in the far upper right of the graph is, in fact, Ivo’s upset of Djokovic in Doha this year. Karlovic won 85% of first-serve points but only 50% of second-serve points. Had he hit only first serves, he would’ve won about 79% of his service points instead of the 75% that he recorded that day.

Another standout example is Karlovic’s match against Simon in Cincinnati. Ivo won 81% of first-serve points and only 39% of second-serve points. He won the match anyway, but if he had pursued a double-first strategy, Simon could’ve caught an earlier flight home.

Predicting double-first opportunities

Armed with all this data, we would still have a very difficult time identifying opportunities for players to take advantage of the strategy.

For each player in every match, I multiplied his “double-first disadvantage” (the number of percentage points of serve points won he would lose by hitting two first serves) with the returner’s double-first disadvantage. Ranking all matches by the resulting product puts combinations like Karlovic-Djokovic and Murray-Isner together at one extreme. If we are to find instances where we could retroactively predict an advantage from hitting two first serves, they would be here.

When we divide all these matches into quintiles, there is a strong relationship between the double-first results we would predict using season-aggregate numbers and the double-first results we see in individual matches. However, even if the most double-first-friendly quintile–the one filled with Ivo serving and Novak returning–there’s still, on average, a one-percentage-point advantage to the traditional serving tactic.

It is only at the most extreme that we could even consider recommending two first serves. When we take the 2% of matches with the smallest products–that is, the ones we would most expect to benefit from double first–26 of those 50 matches are one in which the server would’ve done better to hit two first serves.

In other words, there’s a ton of variance at the individual match level, and since the margins are so slim, there are almost no situations where it would be sensible for a player to hit two first serves.

A brief coda in the real world

All of this analysis is based on some simplifying assumptions, namely that players would make their first serves at the same rate if they were hitting two instead of one, and that players would win the same number of points behind their first serves even if they were hitting them twice as often.

We can only speculate how much those assumptions mask. I suspect that if a player hit only first serves, he would be more likely to see streaks of both success and failure; without second serves to mix things up, it would be easier to find oneself repeating mechanics, whether perfect or flawed.

The second assumption is probably the more important one. If a server hit only first serves, his ability to mix things up and disguise serving patterns would be hampered. I have no idea how much that would affect the outcome of service points–but it would probably act to the advantage of the returner.

All that said, even if we can’t recommend that players hit two first serves in any but the extreme matchups, it is worth emphasizing that the margins we’re discussing are small. And since they are small, the risk of hitting big second serves isn’t that great. There may be room for players to profitably experiment with more aggressive second serving, especially when a returner starts crushing second serves.

Ceding the advantage on second-serve points to a player like Djokovic must be disheartening. If the risk of a few more double faults is tolerable, we may have stumbled on a way for servers to occasionally stop the bleeding.

Digging Out of the Holes of 0-40 and 15-40

In the men’s professional game, serving at 0-40 isn’t a death sentence, but it isn’t a good place to be. An average player wins about 65% of service points, and at that rate, his chance of coming back from 0-40 is just a little better than one in five.

Some players are better than others at executing this sort of comeback. Tommy Robredo, for instance, has come back from 0-40 nearly 60% more often than we’d expect, while Sam Querrey digs out of the 0-40 hole one-third less often than we would predict.

Measuring a player’s success rate in these scenarios isn’t simply a matter of counting up 0-40 games. That’s what we saw on the ATP official site last week, and it’s woefully inadequate. That article marvels at Ivo Karlovic‘s “clutch” accomplishments from 0-40 and 15-40, when we could easily have guessed that Ivo would lead just about any serving category. Big serving isn’t clutch if it’s what you always do.

Statistics are only valuable in context, and that is particularly true in tennis. Simply counting 0-40 games and reporting the results hides a huge amount of potential insight. Whether a player wins or loses (a game, a set, a match, or a stretch of matches) is only the first question. To deliver any kind of meaningful analysis, we need to adjust those results for the competition and consider what we already know about the players we’re studying.

Rather than tear apart that article, though, let’s do the analysis correctly.

The number of times a player comes back from 0-40 or 15-40 isn’t what’s important. As we’ve seen, big servers will dominate those categories. That doesn’t tell us who is particularly effective (or, dare we say, “clutch”) in such a situation, it only identifies the best servers. What matters is how often players come back compared to how often we would expect them to, taking into consideration their serving ability.

Karlovic is an instructive example. Over the last few years–the time span available in this dataset of point-by-point match records–Ivo has gone down 0-40 56 times, holding 17 of those games, a rate of 30.4%. That’s third-best on tour, behind John Isner and Samuel Groth. But compared to how well we would expect Karlovic to serve, he’s only 7% better than neutral, right in the middle of the ATP pack.

Before diving into the results, a few more notes on methodology. For each 0-40 or 15-40 game, I calculated the server’s rate of service points won in that match. Since we would expect 0-40 games to occur more often in matches with good returners, in-match rates seem more accurate than season-long aggregates. Given the in-match rate of serve points won, I then determined the odds that the server would come back from the 0-40 or 15-40 score. For each game, then, we have a result (came back or didn’t come back) and an estimate of the comeback’s likelihood. Combining both numbers for all of a player’s service games tells us how effective he was at these scores.

For 30 of the players best represented in the dataset, here are their results at 0-40, showing the number of games, the number of successful comebacks, the rate of successful comebacks, and the degree to which the player exceeded expectations from 0-40:

Player                  0-40  0-40 W  0-40 W%  W/Exp  
Tommy Robredo            110      30    27.3%   1.59  
Denis Istomin            114      26    22.8%   1.36  
John Isner                87      31    35.6%   1.34  
Guillermo Garcia-Lopez   161      29    18.0%   1.32  
Kevin Anderson           130      38    29.2%   1.28  
Bernard Tomic            110      24    21.8%   1.25  
Fernando Verdasco        141      30    21.3%   1.17  
Rafael Nadal             140      32    22.9%   1.15  
Kei Nishikori            122      23    18.9%   1.15  
Marin Cilic              125      26    20.8%   1.14  
                                                      
Player                  0-40  0-40 W  0-40 W%  W/Exp  
Jo-Wilfried Tsonga       124      29    23.4%   1.14  
Novak Djokovic           124      34    27.4%   1.12  
Andreas Seppi            145      24    16.6%   1.09  
Grigor Dimitrov          115      22    19.1%   1.08  
Philipp Kohlschreiber    146      28    19.2%   1.08  
Roger Federer            107      26    24.3%   1.07  
Ivo Karlovic              56      17    30.4%   1.07  
Santiago Giraldo         113      18    15.9%   1.06  
Alexandr Dolgopolov      141      25    17.7%   1.03  
Milos Raonic              82      23    28.0%   1.01  
                                                      
Player                  0-40  0-40 W  0-40 W%  W/Exp  
Tomas Berdych            149      30    20.1%   1.01  
Jeremy Chardy            122      21    17.2%   0.98  
Feliciano Lopez          136      26    19.1%   0.97  
Fabio Fognini            211      24    11.4%   0.97  
Mikhail Youzhny          155      18    11.6%   0.92  
David Ferrer             203      32    15.8%   0.89  
Richard Gasquet          152      25    16.4%   0.87  
Andy Murray              164      24    14.6%   0.80  
Gilles Simon             158      16    10.1%   0.72  
Sam Querrey               84      12    14.3%   0.68

As I mentioned above, Robredo has been incredibly effective in these situations, coming back from 0-40 30 times instead of the 19 times we would have expected. Some big servers, such as Isner and Kevin Anderson, are even better than their well-known weapons would leads us to expect, while others, such as Karlovic and Milos Raonic, aren’t noticeably more effective at 0-40 than they are in general.

Many of these extremes don’t hold up when we turn to the results from 15-40. Quite a few more games reach 15-40 than 0-40, so the more limited variation at 15-40 suggests that many of the extreme results from 0-40 can be ascribed to an inadequate sample. For instance, Robredo–our 0-40 hero–falls to neutral at 15-40. Here is the complete list:

Player                  15-40  15-40 W  15-40 W%  W/Exp  
John Isner                238      122     51.3%   1.33  
Milos Raonic              215       98     45.6%   1.18  
Feliciano Lopez           304      108     35.5%   1.17  
Jo-Wilfried Tsonga        301      119     39.5%   1.17  
Denis Istomin             304      101     33.2%   1.17  
Rafael Nadal              320      118     36.9%   1.16  
Ivo Karlovic              148       68     45.9%   1.15  
Kevin Anderson            338      132     39.1%   1.15  
Guillermo Garcia-Lopez    405      106     26.2%   1.14  
Andreas Seppi             396      113     28.5%   1.12  
                                                         
Player                  15-40  15-40 W  15-40 W%  W/Exp  
Bernard Tomic             273       86     31.5%   1.12  
Kei Nishikori             298       96     32.2%   1.10  
Novak Djokovic            348      132     37.9%   1.07  
Richard Gasquet           325      106     32.6%   1.07  
Roger Federer             281      109     38.8%   1.07  
Fernando Verdasco         306       94     30.7%   1.06  
Philipp Kohlschreiber     352      110     31.3%   1.06  
Andy Murray               431      135     31.3%   1.06  
Santiago Giraldo          331       86     26.0%   1.05  
Tomas Berdych             398      131     32.9%   1.05  
                                                         
Player                  15-40  15-40 W  15-40 W%  W/Exp  
Marin Cilic               357      109     30.5%   1.05  
Sam Querrey               244       78     32.0%   1.04  
Jeremy Chardy             300       91     30.3%   1.04  
Fabio Fognini             422       98     23.2%   1.03  
Tommy Robredo             285       78     27.4%   0.99  
Grigor Dimitrov           307       89     29.0%   0.99  
David Ferrer              498      138     27.7%   0.98  
Alexandr Dolgopolov       299       77     25.8%   0.95  
Mikhail Youzhny           339       77     22.7%   0.94  
Gilles Simon              426       93     21.8%   0.91

The big servers are better represented at the top of this ranking. Even though Isner is expected to come back from 15-40 nearly 40% of the time–better than almost anyone on tour–he exceeds that expectation by one-third, far more than anyone else considered here.

Finally, let’s look at comebacks from 0-30:

Player                  0-30  0-30 W  0-30 W%  W/Exp  
John Isner               338     229    67.8%   1.19  
Bernard Tomic            299     146    48.8%   1.15  
Grigor Dimitrov          342     166    48.5%   1.11  
Novak Djokovic           409     235    57.5%   1.10  
Santiago Giraldo         344     142    41.3%   1.10  
Fernando Verdasco        373     175    46.9%   1.10  
Rafael Nadal             376     194    51.6%   1.09  
Tomas Berdych            492     262    53.3%   1.09  
Tommy Robredo            296     132    44.6%   1.08  
Roger Federer            344     193    56.1%   1.08  
                                                      
Player                  0-30  0-30 W  0-30 W%  W/Exp  
Feliciano Lopez          326     161    49.4%   1.07  
Alexandr Dolgopolov      347     154    44.4%   1.07  
Marin Cilic              378     179    47.4%   1.06  
Jo-Wilfried Tsonga       357     185    51.8%   1.06  
Guillermo Garcia-Lopez   380     146    38.4%   1.06  
Ivo Karlovic             186     118    63.4%   1.04  
Philipp Kohlschreiber    395     185    46.8%   1.03  
Denis Istomin            314     135    43.0%   1.03  
Kei Nishikori            341     145    42.5%   1.03  
David Ferrer             529     227    42.9%   1.02  
                                                      
Player                  0-30  0-30 W  0-30 W%  W/Exp  
Kevin Anderson           361     181    50.1%   1.02  
Mikhail Youzhny          390     142    36.4%   1.00  
Andy Murray              419     185    44.2%   1.00  
Andreas Seppi            418     164    39.2%   0.99  
Jeremy Chardy            316     132    41.8%   0.99  
Milos Raonic             246     139    56.5%   0.99  
Fabio Fognini            478     153    32.0%   0.99  
Sam Querrey              292     131    44.9%   0.97  
Gilles Simon             442     155    35.1%   0.96  
Richard Gasquet          370     159    43.0%   0.95

Isner still stands at the top of the leaderboard, while Bernard Tomic and Grigor Dimitrov give us a mild surprise by filling out the top three. Again, as the sample size increases, the variation decreases even further, illustrating that, over the long term, players tend to serve about as well at one score as they do at any other.

The Slow but Steady Erosion of the Server’s Advantage

After a couple of weeks of data-driven skepticism, I can finally confirm a bit of tennis’s conventional wisdom. Over the course of a typical match, breaks of serve are a little easier to come by.

This result–based on tens of thousands of matches from the last few years–is similar for both men and women. After about twelve games (total, not service games for each player), a hold is roughly 2% less likely than it was in the first few games of the match. By the 25th game, a hold is approximately 5% less likely than at the beginning of the match.

To control for the vagaries of surface, opponent, and other conditions, I’ve compared each service game to the server’s hold percentage within that match. Only the closest matches are likely to go very long, so it’s important to compare the last games of those matches to games with similarly even opponents.

It seems that this effect is the result of one or both of two factors: server fatigue (which may have more of an effect on results than an equivalent amount of returner fatigue), and the returner’s increasing familiarity with the server. It would be difficult to separate these two–and with this dataset, probably impossible–so for today, let’s stick with the nature of the effect, not its causes.

The following graph shows the relative probability of a hold of serve based on how much of the match (in games) has been played:

I’ve set the hold probability of the first game at 100%, so all other numbers are relative to that. I’ve excluded tiebreaks from these calculations, though I considered them when counting games–that is, the first game of the second set after a tiebreak is considered the 14th game, not the 13th.

The results get a lot noisier starting around the women’s 25th game and the men’s 35th game, for the simple reason that most matches don’t get that far. For example, while the WTA calculations are based on 11,000 matches, only one-third reached the 25th game and less than one-tenth made it to the 31st.

The general downward trend indicates that the fatigue and/or familiarity effect dwarfs the effect of new balls. I have found that in men’s matches, the age of balls has a very small effect on hold percentage, and in women’s matches, it has no effect. In any case, the steady ebb of the server’s advantage is a stronger effect.

It is likely that some players suffer more from fatigue or familiarity than others. Due to the smaller size of the per-player samples, especially beyond the 20th game or so, I’m reluctant to draw any strong conclusions. Still, there are some intriguing numbers for the players for whom the dataset contains the most matches.

Here, I’ve calculated the hold percentage for several top players at various stages of the match, relative to their hold percentage in the first ten games. Thus, a number below 100% indicates less frequent holds, while a number above 100% means more frequent holds:

Player                 Matches  11 to 20  21 to 30  31 to 50  
Tomas Berdych              337     98.5%     98.3%    101.5%  
David Ferrer               330     97.0%     99.4%    102.4%  
Novak Djokovic             325    100.1%    101.8%    101.7%  
Roger Federer              325    100.2%     99.6%    100.4%  
Andy Murray                295     97.7%     98.7%     97.9%  
Rafael Nadal               293     99.2%    100.3%     93.7%  
Jo-Wilfried Tsonga         255    100.4%    100.9%     99.6%  
Philipp Kohlschreiber      252    101.4%     97.9%     96.7%  
John Isner                 251    100.4%    100.4%    100.3%  
                                                              
Player                 Matches  11 to 20  21 to 30  31 to 50  
Kevin Anderson             247    100.0%     98.1%     97.5%  
Richard Gasquet            246     99.1%     98.4%    105.1%  
Gilles Simon               245    100.1%    103.7%     95.0%  
Milos Raonic               238     97.1%     96.1%     96.7%  
Marin Cilic                238     95.4%     97.5%     94.5%  
Fabio Fognini              235    100.4%     99.6%     98.2%  
Kei Nishikori              233    101.8%    104.1%    107.2%  
Grigor Dimitrov            224    100.9%    100.3%     94.6%  
Andreas Seppi              221    106.4%    100.4%    103.1%  
Feliciano Lopez            221     99.2%     99.7%     98.4%  
                                                              
Total                    23326     98.1%     96.1%     95.1%

While John Isner is steady throughout the stages of the match, other big servers such as Milos Raonic and Marin Cilic are less dominant as the match progresses. The players whose hold percentage improves through the match–such as Novak Djokovic and David Ferrer–tend to be those without big serves, so we may be looking at more of an overall fatigue effect in those cases.

The most extreme number in the table is Rafael Nadal‘s relative hold percentage after the 30th game. Perhaps after that much time on court, his opponents finally figure out how to defend against the ad-court slider.

Here are the same calculations for top WTA players:

Player                Matches  11 to 15  16 to 20  21 to 40  
Agnieszka Radwanska       299    101.0%    104.9%     98.0%  
Sara Errani               279     97.7%     91.2%     92.7%  
Caroline Wozniacki        279    103.1%    102.3%    104.9%  
Serena Williams           266    102.8%    102.4%    104.9%  
Angelique Kerber          265    101.9%    103.0%    101.5%  
Samantha Stosur           253     99.2%    105.0%     97.6%  
Carla Suarez Navarro      252    102.2%    101.8%     93.7%  
Petra Kvitova             251     93.9%    100.4%     95.9%  
Roberta Vinci             250     94.2%     97.9%     95.4%  
Ana Ivanovic              241    100.8%    106.0%     95.2%  
Jelena Jankovic           241    102.2%    108.7%     96.4%  
                                                             
Player                Matches  11 to 15  16 to 20  21 to 40  
Maria Sharapova           236    100.1%    105.9%    104.9%  
Victoria Azarenka         228    100.6%    103.7%     97.8%  
Lucie Safarova            227    102.7%    100.5%     94.4%  
Simona Halep              224     89.2%     95.3%    101.7%  
Dominika Cibulkova        210     98.7%     89.9%     99.9%  
Alize Cornet              210     96.2%    102.8%     96.4%  
Andrea Petkovic           194    101.5%    104.2%    107.5%  
Sloane Stephens           185     97.5%     90.1%     88.7%  
Sabine Lisicki            185     97.4%     97.5%     96.6%  
Ekaterina Makarova        185     96.6%    102.8%     92.8%  
Flavia Pennetta           180    105.1%     92.9%    103.9%  
                                                             
Total                   22406     98.6%     97.2%     95.0%

Here is some confirmation that Serena Williams–at least on serve–gets better as the match progresses. Many of the other players with the strongest serve results late in matches are those known for fitness (like Caroline Wozniacki) or steeliness (Maria Sharapova).

Whether the root cause is fatigue or familiarity, most players are less effective on serve as the match progresses. With further research, I hope we’ll be able to better understand the cause and determine whether there are advantages to serving particularly well at certain stages of the match.

The Effects (and Maybe Even Momentum) of a Long Rally

Italian translation at settesei.it

In yesterday’s quarterfinal between Simona Halep and Victoria Azarenka, a highlight early in the third set was a 25-shot rally that Vika finished off with a forehand winner. It was the longest point of the match, and moved her within a point of holding serve to open the set.

As very long rallies often do, the point seemed like it might represent a momentum shift. Instead, Halep sent the game back to deuce after a 10-stroke rally on the next point. If there was any momentum conferred by these two points, it disappeared as quickly as it arose. It took eight more points before Azarenka finally sealed the hold of serve.

Does a long rally tell us anything at all? Does it have predictive value for the next point, or even the entire game, or is it just highlight-reel fodder that is forgotten as soon as the umpire announces the score?

To answer those questions, I delved into the shot-by-shot data of the Match Charting Project, which now contains point-by-point accounts of nearly 1,100 matches. I identified the longest 1% of points–17 shots or longer for women, 18 shots for men–and analyzed what happened afterwards, looking for both fatigue and momentum effects.

The next point

There’s one clear effect of a long rally: The next point will be shorter than average. The 10-shot rally contested by Vika and Simona yesterday was an outlier: Women average 4.45 shots on the point after a long rally, while the overall average (controlled for server and first or second serve) is 4.85. Men average 4.03 shots on the following point, compared to an average of 4.64.

For women, fatigue is also a factor for the server. Following a long rally, women land only 61.3% of first serves, compared to an average of 64.6%. Men don’t exhibit the same fatigue effect; the equivalent numbers are 62.3% and 62.2%.

There’s more evidence of an immediate fatigue factor for women, as well. The players who win those long rallies are slightly better than their opponents, winning 50.7% of points on average. Immediately after a long rally, however, players win only 49% of points. It’s not obvious to me why this should be the case. Perhaps the player who won the long rally worked a bit harder than her opponent, maybe putting all of her remaining effort into a groundstroke winner, or finishing the point with a couple of athletic shots at the net.

In any case, there’s no equivalent effect for men. After winning a long rally, players win 51.1% of their next points, compared to an expected 50.8%. That’s either a very small momentum effect or, more likely, a bit of statistical noise.

Both men and women double fault more often than usual after a long rally, though the effect is much greater for women. Immediately following these points, women double fault 4.7% of the time, compared to an average of 3.3%. Men double fault 4.5% of the time after a long rally, compared to an expected rate of 4.2%.

Longer-term momentum

Beyond a slightly effect on the characteristics of the next point, does a long rally influence the outcome of the game? The evidence suggests that it doesn’t.

For each long rally, I identified whether the winner of the rally went on to win the game, as Vika did yesterday. I also combined the score after the long rally with the average rate of points won on the appropriate player’s serve to calculate the odds that, from such a score, the player who won the rally would go on to win the game. To use yesterday’s example, when Azarenka held game point at AD-40, her chances of winning the game were 77.6%.

For both men and women, there is no significant effect. Women who won long rallies went on to win 66.2% of those games, while they would have been expected to win 65.7%. Men won 64.4% of those games, compared to an expected rate of 64.1%.

With a much larger dataset, these findings might indicate a very slight momentum effect. But limited to under 1,000 long-rally points for each gender, the differences represent only a few games that went the way of the player who won the long point.

For now, we’ll have to conclude that the aftereffects of a long rally have a very short lifespan: barely one point for women, perhaps not even that long for men. These points may well have a greater effect on fans than they do on the players themselves.