## 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
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.

## Dominic Thiem played Davis Cup in Barcelona. Sort of…

This is a guest post by Peter Wetz.

Last week Dominic Thiem fought his way into the finals of the Barcelona Open by winning against Kyle Edmund, Daniel Evans, Yuichi Sugita, and Andy Murray. Three of these four players play for the same flag and Thiem won against each of them. Thiem is not exactly a champion of the current Davis Cup format–he has opted out of playing for Austria several times and has a rather poor record of 2-3 when he does compete–but in Barcelona he has, at least, shown that he can beat several players from the same country over a short amount of time. And that’s what Davis Cup is about, right?

In this post my goal is to put this statistical hiccup into some context. It is not the first time the Austrian defeated three players of the same nationality at one event: In 2016 at Buenos Aires Thiem already beat three players from Spain. However, given that Spanish players appear much more frequently in draws than Britons do, I will take a closer look.

Since 1990, there have only been three tournaments where a single player faced three players from Great Britain. And only one of these players who faced three Britons won each encounter. The following table shows the three tournaments and each of the matches where a player from Great Britain was faced by the same player. Wally Masur is the only player since 1990 who defeated three players from Great Britain in a single tournament. Thiem remains the only player who achieved this in a tournament outside of the island.

```Tournament     Round Winner        Loser           Score
'93 Manchester R32   Wally Masur   Ross Matheson   6-4 6-4
'93 Manchester R16   Wally Masur   Chris Wilkinson 6-3 6-7(4) 6-3
'93 Manchester QF    Wally Masur   Jeremy Bates    6-4 6-3

'97 Nottingham R32   Karol Kucera  Martin Lee      6-1 6-1
'97 Nottingham SF    Karol Kucera  Tim Henman      6-4 2-6 6-4
'97 Nottingham F     Greg Rusedski Karol Kucera    6-4 7-5

'01 Nottingham R32   Martin Lee    Lee Childs      6-4 5-7 6-0
'01 Nottingham R16   Martin Lee    Arvind Parmar   6-4 6-3
'01 Nottingham QF    Greg Rusedski Martin Lee      6-3 6-2
```

Obviously, there are not many chances to face three Britons in a single tournament. And when one of those opponents is likely to be Andy Murray, a player’s chances of beating all three are even slimmer.

Let’s broaden the perspective a bit and take a look at how often a player defeated three (or more) players from the same country without looking only at Great Britain. The following table displays the results of this analysis. The first column contains the country, the second column (3W) shows how often a player defeated three players of this country, the third column (3WL) shows how often a player defeated two players of this country and then lost to a player of the same country, and so on.

```Country  3W  3WL  4W  4WL  5W  5WL
USA      119 179  19  30   1   4
ESP      98  157  17  18   3   2
FRA      28  45   5   2    1   0
ARG      22  26   5   3    0   0
GER      15  18   1   1    0   0
AUS      13  9    0   0    0   0
SWE      9   16   1   0    0   0
CZE      4   5    0   0    0   0
NED      4   4    0   0    0   0
RUS      4   3    0   0    0   0
ITA      2   3    1   0    0   0
BRA      1   3    1   0    0   0
GBR      1   2    0   0    0   0
CHI      1   1    0   0    0   0
SUI      1   1    0   0    0   0
```

As we could have imagined, USA, ESP, and FRA come out on top here, simply, because for years they have had the highest density of players in the rankings. These are also the only countries of which a player was faced five times at a single tournament. Facing a player of the same country six or more times never happened according to the data at hand. The following table shows the most recent occasions of the entries printed in bold in the above table (5W).

```Tournament    Round Winner        Loser             Score
'91 Charlotte R32   Jaime Yzaga   Chris Garner      7-6 6-3
'91 Charlotte R16   Jaime Yzaga   Jimmy Brown       6-4 6-4
'91 Charlotte QF    Jaime Yzaga   Michael Chang     7-6 6-1
'91 Charlotte SF    Jaime Yzaga   M. Washington     7-5 6-2
'91 Charlotte F     Jaime Yzaga   Jimmy Arias       6-3 7-5

'07 Lyon      R32   Sebastien Gr. Rodolphe Cadart   6-3 6-2
'07 Lyon      R16   Sebastien Gr. Fabrice Santoro   4-6 6-1 6-2
'07 Lyon      QF    Sebastien Gr. Julien Benneteau  6-7 6-2 7-6
'07 Lyon      SF    Sebastien Gr. Jo Tsonga         6-1 6-2
'07 Lyon      F     Sebastien Gr. Marc Gicquel      7-6 6-4

'08 Valencia  R32   David Ferrer  Ivan Navarro      6-3 6-4
'08 Valencia  R16   David Ferrer  Pablo Andujar     6-3 6-4
'08 Valencia  QF    David Ferrer  Fernando Verdasco 6-3 1-6 7-5
'08 Valencia  SF    David Ferrer  Tommy Robredo     2-6 6-2 6-3
'08 Valencia  F     David Ferrer  Nicolas Almagro   4-6 6-2 7-6
```

Finally, we take a look at the big four. Did they ever eliminate three or more players from the same country in a single tournament? Yes, they did. In 2014 Roger Federer beat three Czech players in Dubai. In 2005, 2008, and 2013 he beat three German players in Halle. In 2009 Andy Murray beat three Spanish players in Valencia. In 2007 Novak Djokovic beat three Spanish players in Estoril. In 2013 Rafael Nadal beat three Argentinian players both in Acapulco and Sao Paolo. In 2015 he even beat four Argentinian players in Buenos Aires. And there are many other examples where Rafa beat three of his countrymen at the same tournament.

We can see that this happens fairly often, specifically for countries where the tournament is organized, because more players of this country appear in the draw due to wild cards and qualifications. If we exclude these cases, Federer’s streak in Dubai stands out, as does Thiem’s streak in Barcelona.

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

## Little Data, Big Potential

This is a guest post by Carl Bialik.

I had more data on my last 30 minutes of playing tennis than I’d gotten in my first 10 years of playing tennis  — and it just made me want so much more.

Ben Rothenberg and I had just played four supertiebreakers, after 10 minutes of warmup and before a forehand drill. And for most of that time — all but a brief break while PlaySight staff showed the WTA’s Micky Lawler the system — 10 PlaySight cameras were recording our every move and every shot: speed, spin, trajectory and whether it landed in or out. Immediately after every point, we could walk over to the kiosk right next to the net to watch video replays and get our stats. The tennis sure didn’t look professional-grade, but the stats did: spin rate, net clearance, winners, unforced errors, net points won.

Later that night, we could go online and watch and laugh with friends and family. If you’re as good as Ben and I are, laugh you will: As bad as we knew the tennis was by glancing over to Dominic Thiem and Jordan Thompson on the next practice court, it was so much worse when viewed on video, from the kind of camera angle that usually yields footage of uberfit tennis-playing pros, not uberslow tennis-writing bros.

This wasn’t the first time I’d seen video evidence of my take on tennis, an affront to aesthetes everyone. Though my first decade and a half of awkward swings and shoddy footwork went thankfully unrecorded, in the last five years I’d started to quantify my tennis self. First there was the time my friend Alex, a techie, mounted a camera on a smartphone during our match in a London park. Then in Paris a few years later, I roped him into joining me for a test of Mojjo, a PlaySight competitor that used just one camera — enough to record video later published online, with our consent and to our shame. Last year, Tennis Abstract proprietor Jeff Sackmann and I demo-ed a PlaySight court with Gordon Uehling, founder of the company.

With PlaySight and Mojjo still only in a handful of courts available to civilians, that probably puts me — and Alex, Jeff and Ben — in the top 5 or 10 percent of players at our level for access to advanced data on our games. (Jeff may object to being included in this playing level, but our USPS Tennis Abstract Head2Head suggests he belongs.) So as a member of the upper echelon of stats-aware casual players, what’s left once I’m done geeking out on the video replays and RPM stats? What actionable information is there about how I should change my game?

Little data, modest lessons

After reviewing my footage and data, I’m still looking for answers. Just a little bit of tennis data isn’t much more useful than none.

Take the serve, the most common shot in tennis. In any one set, I might hit a few dozen. But what can I learn from them? Half are to the deuce court, and half are to the ad court. And almost half of the ones that land in are second serves. Even with my limited repertoire, some are flat while others have slice. Some are out wide, some down the T and some to the body — usually, for me, a euphemism for, I missed my target.

If I hit only five slice first serves out wide to the deuce court, three went in, one was unreturned and I won one of the two ensuing rallies, what the hell does that mean? It doesn’t tell me a whole lot about what would’ve happened if I’d gotten a chance to I try that serve once more that day against Ben — let alone what would happen the next time we played, when he had his own racquet, when we weren’t hitting alongside pros and in front of confused fans, with different balls on a different surface without the desert sun above us, at a different time of day when we’re in different frames of mind. And the data says even less about how that serve would have done against a different opponent.

That’s the serve, a shot I’ll hit at least once on about half of points in any match. The story’s even tougher for rarer shots, like a backhand drop half volley or a forehand crosscourt defensive lob, shots so rare they might come up once or twice every 10 matches.

More eyes on the court

It’s cool to know that my spinniest forehand had 1,010 RPM (I hit pretty flat compared to Jack Sock’s 3,337 rpm), but the real value I see is in the kind of data collected on that London court: the video. PlaySight doesn’t yet know enough about me to know that my footwork was sloppier than usual on that forehand, but I do, and it’s a good reminder to get moving quickly and take small steps. And if I were focusing on the ball and my own feet, I might have missed that Ben leans to his backhand side instead of truly split-stepping, but if I catch him on video I can use that tendency to attack his forehand side next time.

Video is especially useful for players who are most focused on technique. As you might have gathered, I’m not, but I can still get tactical edge from studying patterns that PlaySight doesn’t yet identify.

Where PlaySight and its ilk could really drive breakthroughs is by combining all of the data at its disposal. The company’s software knows about only one of the thousands of hours I’ve spent playing tennis in the last five years. But it has tens of thousands of hours of tennis in its database. Even a player as idiosyncratic as me should have a doppelganger or two in a data set that big. And some of them must’ve faced an opponent like Ben. Then there are partial doppelgangers: women who serve like me even though all of our other shots are different; or juniors whose backhands resemble mine (and hopefully are being coached into a new one).  Start grouping those videos together — I’m thinking of machine learning, clustering and classifying — and you can start building a sample of some meaningful size. PlaySight is already thinking this way, looking to add features that can tell a player, say, “Your backhand percentage in matches is 11 percent below other PlaySight users of a similar age/ability,” according to Jeff Angus, marketing manager for the company, who ran the demo for Ben and me.

The hardware side of PlaySight is tricky. It needs to install cameras and kiosks, weatherproofing them when the court is outdoors, and protect them from human error and carelessness. It’s in a handful of clubs, and the number probably won’t expand much: The company is focusing more on the college game. Even when Alex and I, two players at the very center of PlaySight’s target audience among casual players, happened to book a PlaySight court recently in San Francisco, we decided it wasn’t worth the few minutes it would have taken at the kiosk to register — or, in my case, remember my password. The cameras stood watch, but the footage was forever lost.

Bigger data, big questions

I’m more excited by PlaySight’s software side. I probably will never play enough points on PlaySight courts for the company to tell me how to play better or smarter — unless I pay to install the system at my home courts. But if it gets cheaper and easier to collect decent video of my own matches — really a matter of a decent mount and protector for a smartphone and enough storage space — why couldn’t I upload my video to the company? And why couldn’t it find video of enough Bizarro Carls and Bizarro Carl opponents around the world to make a decent guess about where I should be hitting forehands?

There are bigger, deeper tennis mysteries waiting to be solved. As memorably argued by John McPhee in Levels of the Game, tennis isn’t so much as one sport as dozens of different ones, each a different level of play united only by common rules and equipment. And a match between two players even from adjacent levels in his hierarchy typically is a rout. Yet tactically my matches aren’t so different from the ones I see on TV, or even from the practice set played by Thiem and Thompson a few feet from us. Hit to the backhand, disguise your shots, attack short balls and approach the net, hit drop shots if your opponent is playing too far back. And always, make your first serve and get your returns in.

So can a tactic from one level of the game even to one much lower? I’m no Radwanska and Ben is no Cibulkova, but could our class of play share enough similarity — mathematically, is Carl : Ben :: Aga : Pome — that what works for the pros works for me? If so, then medium-sized data on my style is just a subset of big data from analogous styles at every level of the game, and I might even find out if that backhand drop half volley is a good idea. (Probably not.)

PlaySight was the prompt, but it’s not the company’s job to fulfill product features only I care about. It doesn’t have to be PlaySight. Maybe it’s Mojjo, maybe Cizr. Or maybe it’s some college student who likes tennis and is looking for a machine-learning class. Hawk-Eye, the higher-tech, higher-priced, older competitor to PlaySight, has been slow to share its data with researchers and journalists. If PlaySight has figured out that most coaches value the video and don’t care much for stats, why not release the raw footage and stats to researchers, anonymized, who might get cracking on the tennis classification question or any of a dozen other tennis analysis questions I’ve never thought to ask? (Here’s a list of some Jeff and I have brainstormed, and here are his six big ones.) I hear all the time from people who like tennis and data and want to marry the two, not for money but to practice, to learn, to discover, and to share their findings. And other than what Jeff’s made available on GitHub, there’s not much data to share. (Just the other week, an MIT grad asked for tennis data to start analyzing.)

Sharing data with outside researchers “isn’t currently in the road map for our product team, but that could change,” Angus said, if sharing data can help the company make its data “actionable” for users to improve to their games.

Maybe there aren’t enough rec players who’d want the data with enough cash to make such ventures worthwhile. But college teams could use every edge. Rising juniors have the most plastic games and the biggest upside. And where a few inches can change a pro career, surely some of the top women and men could also benefit from PlaySight-driven insights.

Yet even the multimillionaire ruling class of the sport is subject to the same limitations driven by the fractured nature of the sport: Each event has its own data and own systems. Even at Indian Wells, where Hawk-Eye exists on every match court, just two practice courts have PlaySight; the company was hoping to install four more for this year’s tournament and is still aiming to install them soon. Realistically, unless pros pay to install PlaySight on their own practice courts and play lots of practice matches there, few will get enough data to be actionable. But if PlaySight, Hawk-Eye or a rival can make sense of all the collective video out there, maybe the most tactical players can turn smarts and stats into competitive advantages on par with big serves and wicked topspin forehands.

PlaySight has already done lots of cool stuff with its tennis data, but the real analytics breakthroughs in the sport are ahead of us.

Carl Bialik has written about tennis for fivethirtyeight.com and The Wall Street Journal. He lives and plays tennis in New York City and has a Tennis Abstract page.

## Cool Down Tennis

This is a guest post by Carl Bialik.

Imagine you’re named boss of tennis. Right after being sworn in by Rod Laver and Martina Navratilova, you’re handed an empty wall calendar. You make the schedule for 2018. What’s your first move?

Mine would be to move Indian Wells and Miami earlier in the calendar, and the Australian Open later, after the two U.S. Masters tournaments.

I never wanted this more than while sweating my way around the Indian Wells grounds in search of shade last month. I wasn’t alone. The only full sections of the main stadium during day sessions were the ones protected from the sun. Around the fan-friendly venue, there are plenty of seats in the shade — under tents, or in Adirondack chairs that shade-seeking people push ever closer to the screen as the sun shifts. The players can only wait for shade to slowly descend on the court. Jack Sock needed a towel holding 50 ice cubes to cool down.

Sure, it was unusually hot at this year’s Indian Wells tournament. But the climatological averages are clear: It’s hot in the California desert and in the Florida sunshine in March, and in the antipodean summer in January. It’d be cooler in Indian Wells, Miami and Melbourne if the two Masters events moved two months earlier and led up to the year’s first Grand Slam in March. Each of the two-week events would be, on average, 4 to 10 degrees Fahrenheit cooler each year. (The precipitation would be about the same, so Miami men’s finalist Rafael Nadal might continue to bemoan humidity, request sawdust and show more than he’d planned beneath his shorts; while women’s champ Johanna Konta might keep having to change clothes midmatch because they’ve accumulated approximately five kilograms of sweat.)

I’m using the averages because I don’t want to make too much of an unseasonably hot Indian Wells, or too little of an unusually cold March in Miami. But the averages might understate the problem because it’s precisely the outliers we’re worried about. A nudge downward of a few degrees, on average, could translate into a big drop in the probability of an unbearably hot fortnight — say, from 25 percent to 5 percent.

Changing the tennis calendar would also mean less daylight. That wouldn’t be so good for the nickname Sunshine Double, but it’d be good for tennis. Until more tennis stadiums adopt overhanging partial roofs — but for sun, not for rain — shorter days means less sun for fans to contend with and more reason to fill the seats. Plus, night tennis is exciting. The venues already have plenty of lights and evening sessions.

Scrambling the schedule would do more than cool down tennis. The three midyear majors’ proximity to each other helps the sport carry some momentum and mainstream buzz from one to the next. The Australian Open squanders all that in the four-month gap between its end and the start of the French Open. There’s even a month between the Aussie Open and the next big event.

The other three majors also get opening acts, to help players build up familiarity with the surface and for fans to build anticipation. The Australian Open gets two weeks at the start of the season — without so much as a 500 event on the men’s side.

The lack of buffer between the offseason and Melbourne also means it loses some players still recovering from the end of the previous season. That was the case this year with Juan Martin del Potro, who skipped this year’s first major after winning the Davis Cup with Argentina in November.

Imagine instead starting the season with Indian Wells and Miami — or Miami, then Indian Wells, while we’re scrambling things, for the convenience of travel from the sport’s power center of Europe — using the same courts and balls as Melbourne. Follow that month — or less, if one or both of the U.S. early-year Masters succumbs to the reality that they could be just a week — by Doha and Dubai, then Brisbane, Sydney and the like, before the main event in Melbourne at the start of March. We’d start the season with a real hard-court swing, ending with the first major.

From Australia, the tour could stay in the southern hemisphere. The swing through South America has a long history and a terrible spot on the current calendar. It was traditionally played on clay but some of its biggest events are moving to hard courts — first (North American) Acapulco, now, maybe, Rio, in search of Masters status — to the chagrin of Nadal and others. Too many players simply don’t think it’s worth it to compete on clay for a few weeks if that’s followed by a month of hard-court events. But move Indian Wells and Miami, and South American clay could move a month later in the calendar — while slightly tempering what Nadal bemoans as “too extreme” weather conditions by an average of 1 degree. The swing would give way seamlessly to Houston, Charleston and the European clay spell — which, by the way, would absorb Bucharest, Hamburg, Umag, Bastad and Gstaad from their awkward post-Wimbledon calendar slots. And no one would suggest Miami move to green clay.

We’d be left with a coherent calendar with five seasons of roughly equal length and importance, four with a major and one with the year-end finals: (1) Outdoor hard courts in the U.S., the Middle East and Oceania, followed by (2) clay in the Americas and Europe, (3) English and German grass (with Newport for those who want to visit the sport’s hall of fame), (4) North American and Asian outdoor hard courts, and (5) European indoor hard courts (absorbing the current winter events such as St. Petersburg and Rotterdam) culminating in wherever the tours’ multiplying year-end finals are calling home that year. And let’s play Davis Cup and Fed Cup at the same time — the tours acting in sync; what a concept! — on weekends at the edge of the five new seasons, giving hosts a wider range of sensible surfaces to choose from, and creating the option for combined venues if men and women from the same country are hosting the same round. (Prague in 2012 would’ve been tennis nirvana.) Or, hell, consider merging the events.

Could all this happen? Sure — if tennis power were centralized in a person or people who prioritize the overall good of the global game. Without a radical transformation of tennis, though, it’ll be slow going: It took years for the idea of lengthening the grass-court season by a week to become reality.

Carl Bialik has written about tennis for fivethirtyeight.com and The Wall Street Journal. He lives and plays tennis in New York City and has a Tennis Abstract page.

## 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.)

A post shared by New York Open (@nyopentennis) on

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.

## Measuring the Performance of Tennis Prediction Models

With the recent buzz about Elo rankings in tennis, both at FiveThirtyEight and here at Tennis Abstract, comes the ability to forecast the results of tennis matches. It’s not far fetched to ask yourself, which of these different models perform better and, even more interesting, how they fare compared to other ‘models’, such as the ATP ranking system or betting markets.

For this, admittedly limited, investigation, we collected the (implied) forecasts of five models, that is, FiveThirtyEight, Tennis Abstract, Riles, the official ATP rankings, and the Pinnacle betting market for the US Open 2016. The first three models are based on Elo. For inferring forecasts from the ATP ranking, we use a specific formula1 and for Pinnacle, which is one of the biggest tennis bookmakers, we calculate the implied probabilities based on the provided odds (minus the overround)2.

Next, we simply compare forecasts with reality for each model asking If player A was predicted to be the winner ($P(a) > 0.5$), did he really win the match? When we do that for each match and each model (ignoring retirements or walkovers) we come up with the following results.

```Model		% correct
Pinnacle	76.92%
538		75.21%
TA		74.36%
ATP		72.65%
Riles		70.09%
```

What we see here is how many percent of the predictions were actually right. The betting model (based on the odds of Pinnacle) comes out on top followed by the Elo models of FiveThirtyEight and Tennis Abstract. Interestingly, the Elo model of Riles is outperformed by the predictions inferred from the ATP ranking. Since there are several parameters that can be used to tweak an Elo model, Riles may still have some room left for improvement.

However, just looking at the percentage of correctly called matches does not tell the whole story. In fact, there are more granular metrics to investigate the performance of a prediction model: Calibration, for instance, captures the ability of a model to provide forecast probabilities that are close to the true probabilities. In other words, in an ideal model, we want 70% forecasts to be true exactly in 70% of the cases. Resolution measures how much the forecasts differ from the overall average. The rationale here is, that just using the expected average values for forecasting will lead to a reasonably well-calibrated set of predictions, however, it will not be as useful as a method that manages the same calibration while taking current circumstances into account. In other words, the more extreme (and still correct) forecasts are, the better.

In the following table we categorize the set of predictions into bins of different probabilities and show how many percent of the predictions were correct per bin. This also enables us to calculate Calibration and Resolution measures for each model.

```Model    50-59%  60-69%  70-79%  80-89%  90-100% Cal  Res   Brier
538      53%     61%     85%     80%     91%     .003 .082  .171
TA       56%     75%     78%     74%     90%     .003 .072  .182
Riles    56%     86%     81%     63%     67%     .017 .056  .211
ATP      50%     73%     77%     84%     100%    .003 .068  .185
Pinnacle 52%     91%     71%     77%     95%     .015 .093  .172
```

As we can see, the predictions are not always perfectly in line with what the corresponding bin would suggest. Some of these deviations, for instance the fact that for the Riles model only 67% of the 90-100% forecasts were correct, can be explained by small sample size (only three in that case). However, there are still two interesting cases (marked in bold) where sample size is better and which raised my interest. Both the Riles and Pinnacle models seem to be strongly underconfident (statistically significant) with their 60-69% predictions. In other words, these probabilities should have been higher, because, in reality, these forecasts were actually true 86% and 91% percent of the times.3 For the betting aficionados, the fact that Pinnacle underestimates the favorites here may be really interesting, because it could reveal some value as punters would say. For the Riles model, this would maybe be a starting point to tweak the model.

In the last three columns Calibration (the lower the better), Resolution (the higher the better), and the Brier score (the lower the better) are shown. The Brier score combines Calibration and Resolution (and the uncertainty of the outcomes) into a single score for measuring the accuracy of predictions. The models of FiveThirtyEight and Pinnacle (for the used subset of data) essentially perform equally good. Then there is a slight gap until the model of Tennis Abstract and the ATP ranking model come in third and fourth, respectively. The Riles model performs worst in terms of both Calibration and Resolution, hence, ranking fifth in this analysis.

To conclude, I would like to show a common visual representation that is used to graphically display a set of predictions. The reliability diagram compares the observed rate of forecasts with the forecast probability (similar to the above table).

The closer one of the colored lines is to the black line, the more reliable the forecasts are. If the forecast lines are above the black line, it means that forecasts are underconfident, in the opposite case, forecasts are overconfident. Given that we only investigated one tournament and therefore had to work with a low sample size (117 predictions), the big swings in the graph are somewhat expected. Still, we can see that the model based on ATP rankings does a really good job in preventing overestimations even though it is known to be outperformed by Elo in terms of prediction accuracy.

To sum up, this analysis shows how different predictive models for tennis can be compared among each other in a meaningful way. Moreover, I hope I could exhibit some of the areas where a model is good and where it’s bad. Obviously, this investigation could go into much more detail by, for example, comparing the models in how well they do for different kinds of players (e.g., based on ranking), different surfaces, etc. This is something I will spare for later. For now, I’ll try to get my sleeping patterns accustomed to the schedule of play for the Australian Open, and I hope, you can do the same.

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

#### Footnotes

1. $P(a) = a^e / (a^e + b^e)$ where $a$ are player A’s ranking points, $b$ are player B’s ranking points, and $e$ is a constant. We use $e = 0.85$ for ATP men’s singles.

2. The betting market in itself is not really a model, that is, the goal of the bookmakers is simply to balance their book. This means that the odds, more or less, reflect the wisdom of the crowd, making it a very good predictor.

3. As an example, one instance, where Pinnacle was underconfident and all other models were more confident is the R32 encounter between Ivo Karlovic and Jared Donaldson. Pinnacle’s implied probability for Karlovic to win was 64%. The other models (except the also underconfident Riles model) gave 72% (ATP ranking), 75% (FiveThirtyEight), and 82% (Tennis Abstract). Turns out, Karlovic won in straight sets. One factor at play here might be that these were the US Open where more US citizens are likely to be confident about the US player Jared Donaldson and hence place a bet on him. As a consequence, to balance the book, Pinnacle will lower the odds on Donaldson, which results in higher odds (and a lower implied probability) for Karlovic.