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.

Podcast Episode 15: Return of the Podcast

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

This is a shorter-than usual episode, clocking in at 34 minutes; we hope to return on Friday with another mid-Slam update. Thanks for listening!

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

How Much Does Height Matter in Men’s Tennis?

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.

Sebastian Ofner and ATP Debuts

This is a guest post by Peter Wetz.

Sebastian Ofner, the still relatively young Austrian, received some media attention this June when he qualified for the Wimbledon main draw at his first attempt and even reached the round of 32 by beating Thomaz Bellucci and Jack Sock. Therefore, some people, including me, had an eye on the 21-year-old when he made his ATP tour debut* at Kitzbuhel a few weeks later, where he was awarded a wild card.

Stunningly, Ofner made it into the semifinals despite having drawn top seed Pablo Cuevas in the second round. Cuevas, who admittedly seems to be out of form lately (or possibly is just regressing to his mean), had a 79% chance of reaching the quarterfinal when the draw came out, according to First Ball In’s forecast.

Let’s look at the numbers to contextualize Ofner’s achievement. How deep do players go when making their debut at ATP level? How often would we expect to see what Ofner did in Kitzbuhel?

The following table shows the results of ATP debutantes with different types of entry into the main draw (WC = wild card, Q = qualifier, Direct = direct acceptance, All = WC + Q + Direct). The data considers tournaments starting in 1990.

Round	WC       Q        Direct    All
R16	14.51%	 26.73%   24.46%    21.77%			
QF	 2.39%	  6.39%    4.32%     4.64%
SF	 0.51%	  2.30%    2.16%     1.59%
F	 0.17%	  0.64%    0.72%     0.46%
W	 0.17%	  0.26%    0.72%     0.27%

Since 1990 there have been 1507 ATP debuts: 586 wild cards (39%), 782 qualifiers (52%) and 139 direct acceptances (9%). Given these numbers, we would expect a wild card debutante to get to the semifinal (or further) every 9 years. In other words, it is a once in a decade feat. In fact, in the 28 years of data, only Lleyton Hewitt (Adelaide 1998), Michael Ryderstedt (Stockholm 2004) and Ernests Gulbis (St. Petersburg 2006) accomplished what Ofner did. Only Hewitt went on to win the tournament.

More than half of the players of all entry types who reached the final won the tournament. Speaking in absolute terms, 4 of 7 finalists (of ATP debutantes) won the tournament. (Due to the small sample size, it is perfectly possible that this is just noise in the data.)

If we exclude rounds starting from the semifinals because of small sample sizes, qualifiers outperform direct acceptances. This may be the result of qualifiers having already played two or three matches and having already become accustomed to the conditions, making it easier for them than it is for debutantes who got accepted directly into the main draw. But to really prove this, more investigation is needed.

For now we know that what Sebastian Ofner has achieved rarely happens. We should also know that by no means is his feat a predictor of future greatness.

* I define Kitzbuhel as Ofner’s ATP tour debut because Grand Slam events are run by the ITF. However, Grand Slam statistics, such as match wins, are included in ATP statistics.

Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.

Putting the Antalya Draw Into Perspective

This is a guest post by Peter Wetz.

When the pre-Wimbledon grass court tournament in Antalya was announced by the ATP in May 2016, some people were scratching their heads: Which top players will be willing to play in Antalya, Turkey one week ahead of Wimbledon? Even more so, because one week earlier two events are played in London and Halle, the latter being considerably closer to London. If a player wanted to participate in Antalya, he would have to fly from Halle (or London) to Antalya and then back to London for Wimbledon, not an ideal itinerary.

Taking a glance at the entry list, the doubts are verified: After Dominic Thiem, the only top 10 player entered in the event, there were just three other men (Paolo Lorenzi, Viktor Troicki and Fernando Verdasco) ranked within the top 40. Only three (Thiem, Verdasco, and Lorenzi) of the 28 players who were directly accepted to the main draw of the event, will be seeded at Wimbledon.

But how weak is the field really compared to others? Of course there are countless ways to measure the strength of a draw, but for a quick and dirty approach we will simply look at two measures, that is, the last direct acceptance (LDA) and the mean rank of quarterfinalists.

The LDA is the rank of the last player who gained direct entrance into a tournament’s main draw excluding lucky losers, qualifiers and special exempts. Comparing the last direct acceptance of the Antalya draw (86, Radu Albot) to all other ATP Tour level events with a draw size of 32 or 28 players, it turns out that Antalya is at the 39th percentile. This means that 39% of the other tournaments have a better/lower (or equal) LDA and that 61% have a worse/higher LDA, respectively. The following image shows a percentile plot of LDAs of tournaments since 2012, highlighting this week’s event in Antalya:

The fact that the LDA compares well against the other tournaments tells us that despite the lack of top ranked seeds, the field seems to be more dense at the bottom. Not that bad after all?

Let us take a look at the mean rank of the eight players who made it into the quarterfinals. Choosing quarterfinalists limits the calculation to the players who were able to perform well at the event, winning at least one, and usually two, matches. This should reduce some of the noise in the data that would be otherwise included due to lucky first round wins.

The mean rank of the quarterfinalists at the Antalya Open 2017 is 109. Out of the 726 tournaments since 2000 with 32 or 28 player draws which were considered in this analysis, only 35 tournaments had a higher mean rank of players at the quarterfinal stage. With nine out of those 35 tournaments, the Hall of Fame Tennis Championships at Newport–which takes place each year after Wimbledon–stands out from the pack. As the following plot shows, the Antalya Open is at the 95th percentile in this category. This seems to be more aligned with what we would have expected.

To provide some context, the following table lists the top 10 tournaments with links to the draws having the worst mean rank of quarterfinalists.

#  Tournament           Mean QF Rank
1  Newport '10          240
2  Newport '01          197
3  Delray Beach '16     191
4  Moscow '13           166
5  Newport '11          166
6  Newport '07          165
7  s-Hertogenbosch '09  164
8  Newport '08          163
9  Gstaad '14           156
10 Amsterdam '01        152
...
36 Antalya '17          109

The seeds are to blame for this: Of the eight seeds, only Verdasco managed to win a match. The other seven went winless. We have to go back as far as 1983’s Tel Aviv tournament to find a draw where only one seed won a match. In Tel Aviv, however, the third seed Colin Dowdeswell won three matches all in all, whereas Fernando Verdasco crashed out in the second round. By the way, Tel Aviv 1983 marks the first title of the then 16 years and 2 months old Aaron Krickstein, still the youngest player to win a singles title on the ATP Tour. That only two out of eight seeds win their first match happens about once per year. The last time this happened at the 2016 Brasil Open, where only Pablo Cuevas and Federico Delbonis won matches as seeds.

Despite the presence of only one top 30 player in this year’s Antalya draw, the middle and bottom of the field looked surprisingly solid, as we saw when considering the last direct acceptance. However, if we take into account the development of the tournament and calculate the mean rank of quarterfinalists, it becomes clear that the field got progressively weaker. Still, there have been worse draws in the past and there will doubtless be worse draws in future. Maybe even in the not too distant future, if we take a glance at this year’s Newport entry list.

Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.

Podcast Episode 14: Wimbledon Preview

Episode 14 of the Tennis Abstract Podcast is Carl Bialik’s and my Wimbledon preview! We highlight the favorites, the overrated, and the underrated, along with a look at some of the most intriguing matchups. Along the way, we talk about the difficult of making grass court forecasts, and speculate about how players’ consistency changes with age.  Enjoy!

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The Men Are Old, and The Best Men Are Even Older

It’s been one of the main talking points in men’s tennis for years now: The sport is getting older. Every year, a bigger slice of Grand Slam draws are taken up by thirty-somethings, and now, the entire big four has entered their fourth decades.

I don’t want to belabor the point. But my interest was piqued by an observation from commentator Chris Fowler this week:

When we talk about the sport getting older, this is what we really mean — the best guys are getting up in years.

When we calculate the average age of a draw, or the number of 30-somethings, we weight every player equally. Democratic as it is, it gives most of the weight to guys who are looking for flights home before middle Sunday. As substantial as the overall age shift has been over the last decade, the shift at the top of the game has been even more dramatic.

To quantify the shift, I calculated what I’ll call the “projected winner age” (PWA) of every Wimbledon men’s field from 1991 to 2017. This captures in one number the notion that Fowler is hinting at. We take a weighted average of all 128 men in the main draw, weighted by their chances of winning the tournament, as determined by grass-court Elos at the start of the event.

For example, last year’s Wimbledon men’s draw had an average age of 28.5 years, but a projected winner age of 30.0. We don’t yet know the exact average age of this year’s draw (it looks to be about the same, maybe a tiny bit younger), but we can already say that the PWA is 31.4.

An observer a decade ago would’ve thought such a number was insane. Here are the average ages and PWAs for the last 27 Wimbledons men’s events:

As recently as 2011, there wasn’t much difference between average age and PWA. Until 2015, the difference had never been greater than two years. Now, the difference is almost three years, and the point of comparison–average age–is nearly its own all-time high.

A lot of this, of course, is thanks to the big four. Even as the aging curve has shifted, allowing for late bloomers such as Stan Wawrinka, the biggest stars of the late ’00s–Roger Federer and Rafael Nadal–have declined even less than the revised aging curve would imply. In a sport hungry for new winners, we might have to settle for winners who are newly in their 30s.