Economist: A fit Novak Djokovic could dominate tennis’s future

At The Economist’s Game Theory blog, I wrote about Novak Djokovic’s return to the top:

But Mr Djokovic is playing better in his 32nd year than Mr Federer did, and his more rounded game means that he can compete on all surfaces—even with Mr Nadal on clay—in a way that Mr Federer could not.  The odds are against the Serb reaching 20 majors, but another two or three seasons at the top could easily give him a final total of 17 or 18—enough to move Mr Djokovic out of his default position in third place. Fans of Roger and Rafa have long dominated the debate about who is the greatest male player of all time. But by the end of the decade, Mr Djokovic’s trophy cabinet could well be as bulging as those of his legendary rivals.

Read the whole thing.

Eight Slams, Eight Women’s Champions. How About Nine?

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Italian translation at settesei.it

Buried under the din of the Serena-Ramos story is a remarkable fact about parity in women’s tennis right now. Naomi Osaka was the eighth different grand slam champion in eight events, a streak dating back to Serena Williams’s victory at last year’s Australian Open. Since then, it’s been a different face with every trophy: Jelena Ostapenko, Garbine Muguruza, Sloane Stephens, Caroline Wozniacki, Simona Halep, Angelique Kerber, and Osaka. In the same time span, only three different men have won majors.

The women’s field is so deep that the streak could easily keep going. I built a possible Australian Open draw using the current top 128 players in the WTA rankings, then ran a forecast of the tournament based on each player’s current Elo rating. Here are the title chances for each of the last eight slam winners:

Player              Seed  Title Odds  
Simona Halep           1       16.7%  
Caroline Wozniacki     2        7.1%  
Angelique Kerber       3        5.7%  
Serena Williams       16        5.5%  
Naomi Osaka            7        4.9%  
Sloane Stephens        9        2.6%  
Garbine Muguruza      14        1.8%  
Jelena Ostapenko      10        0.5%  
TOTAL                          44.9%

Altogether, they add up to less than 50%! Put another way, there are better than even odds that we get a ninth different woman giving a victory speech in Melbourne. Here are the players with the best chances:

Player              Seed  Title Odds  
Elina Svitolina        6        8.8%  
Aryna Sabalenka       20        6.6%  
Petra Kvitova          5        5.9%  
Karolina Pliskova      8        3.7%  
Ashleigh Barty        17        3.5%  
Caroline Garcia        4        3.3%  
Madison Keys          18        2.6%  
Venus Williams        21        2.6%  
Mihaela Buzarnescu    23        2.3%  
Julia Goerges         11        2.2%

Ok, yes, Mihaela Buzarnescu seems a little out of place here. But of the other nine players, would any of them represent more of a surprise than Ostapenko, Stephens, or Osaka? By the numbers, three of the top five favorites for the Australian Open haven’t won a major in the last two years.

Given the sheer number of plausible contenders, it’s easy to imagine not just nine different slam winners in a row, but twelve, extending through the entire 2019 season. Consider the possibilities:

This is all rather fanciful, I know. But it’s barely even accurate to say there is a “favorite” when only one woman has a double-digit chance of winning the next major, and her odds are a mere one in six. No single player is likely to win any given grand slam, and only Halep has better than a fifty-fifty shot at winning one over the course of the year.

The chances that the streak extends to twelve are small, but not as low as, say, Osaka’s probability of winning the US Open before the tournament began. We’ve seen that the odds of a ninth different winner triumphing in Australia are about 55%. If that person wins, she’ll probably have earned a rosy forecast for Paris, so the probability of a new winner at the French is lower. And so on, after a tenth or eleventh different champion. If we lower the “new-winner” odds by seven percentage points for each slam, the chances of twelve-slam streak are 3.7%, the same as Pliskova’s probability of becoming number nine. Stranger things have happened. In women’s tennis, the unpredictable has become the norm.

Podcast Episode 32: US Open Recap

Episode 32 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, scrupulously skips the Serena-Ramos controversy and goes straight for the tennis. We look at the resurgence of Novak Djokovic and his US Open final victory over Juan Martin del Potro, consider what the future holds for women’s champion Naomi Osaka and how it compares to a few other rising WTA stars, and outline some difficult choices on the horizon for doubles prodigy Jack Sock.

Thanks for listening!

(Note: this week’s episode is about 60 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

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

Gender Differences in Point Penalties

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Italian translation at settesei.it

The officiating in Saturday night’s US Open women’s final has become a hot-button issue, to put it mildly. Many of the complaints about Serena Williams’s treatment at the hands of chair umpire Carlos Ramos come down to a belief that Ramos’s actions were sexist. Most of us have seen players–both men and women–act in ways that seem more objectionable than anything Serena did, and anybody paying attention has seen innumerable coaching violations go unpenalized.

There are a few things we can all agree on. First: Not all umpires are the same. Ramos is more strict than, say, Mohamed Lahyani. Second: Officials have a lot of latitude, so something that triggers a penalty in one match may not have the same result in another match. And third: Umpires usually do everything they can not to call game penalties. A lot of matches have at least one warning, whether for coaching, ball abuse, or a variety of other things, but only a small percentage of them escalate to the loss of a point or game. Of course, players typically proceed with caution as well. Once a warning has been called, you don’t see nearly as many rackets smashed or balls sent sailing out of the stadium.

The differences between umpires, and the latitude granted to them within the rules, makes it easy to point to any given call and accuse the umpire of sexism, racism, favoritism, homerism, Fed-hating, Rafa-hating, or good old-fashioned stupidity. The rarity of point and game penalties makes Saturday night’s decisions all the more glaring, since within each umpire’s range of options, they rarely go nuclear and dock an entire game.

Some numbers

Point penalties–let alone game penalties–are so rare that it’s impossible to draw concrete conclusions. Still, let’s take a look at what we have. As far as I know, none of the ATP, WTA, ITF, or USTA have released any data on penalties, the players who receive them, or the umpires who levy them. (This would be a great time to do so, but I’m not holding my breath.) As an alternative, we can turn to the increasingly sizable dataset of the Match Charting Project (MCP), which now spans over 3,500 matches from the 2010s alone.

MCP data is not random, since matches are chosen by charters in part because of their personal interests. But in a way, that’s good for today’s purposes: MCP matches skew in the direction of notability, with a disproportionate number of finals and substantial data for top players, including over 100 matches for Serena. With those caveats in mind, let’s take a look at penalties in matches from 2010 to the present, not including Saturday’s final. The final column, “P%”, is the percent of matches in which a penalty was levied.

Category        Matches  Penalties     P%  
Women (all)        1895         13  0.69%  
Women (slams)       490          6  1.22%  
Women (finals)      228          2  0.88%
  
Men (all)          1689         16  0.95%  
Men (slams)         234          6  2.56%  
Men (finals)        371          5  1.35%

Men receive more point penalties than women in three separate comparisons: All MCP matches, matches at grand slams*, and finals. The grand slam numbers are particularly pertinent because it is the only category in which the umpires are drawn from the same pool. At other events, the ATP and WTA use separate groups of officials.

(I’m ignoring full-game penalties because there’s almost no data. In these 3,500-plus matches, there was only one instance where things escalated beyond the point penalty stage: Grigor Dimitrov’s meltdown at the 2016 Istanbul final.)

* Update: A number of people have pointed out that the grand slam comparison isn’t exactly apples-to-apples, because men play best-of-five. True. I’m not sure, however, if we should expect proportionally more penalties in longer matches. Coaching, for instance, would continue throughout a match until identified as a code violation, and then (one would hope) stop. That said, it is certainly true that on a per-point or per-set basis, the gender gap at majors is smaller than these numbers suggest, though it still leaves us with more point penalties against men.

These numbers aren’t proof of gender fairness, nor do they establish sexism against either women or men. Aside from the limited number of penalties, we know nothing about the actions that led to them, or about similar instances that didn’t trigger penalties. Perhaps men are generally more abusive to officials, so they should receive half again as many–or even more–penalties than women. I don’t know, and it’s likely that nobody else commenting on the Serena-Ramos incident knows either. Anecdotes are a key ingredient in this sort of vitriol. To firmly settle the issue, we’d need to set up a controlled study, perhaps by instructing a set of male and female players to berate umpires in identical ways and then comparing the results. As entertaining as that would be, it’s not going to happen.

None of this is to say that accusations of sexism require statistical support to be valid. They don’t. But in cases where the data is available, especially when it is possessed by some of the very organizations making accusations, it’s a shame that the numbers get ignored. The limited information available to us via the MCP indicates that men are more frequently penalized by chair umpires than women are. The USTA, ITF, and WTA could go a long way to clear up the issue–whether officials are consistently equitable or there is a pattern of harsher treatment of female players–by releasing details of all matches, including the number and causes of warnings and penalties, as well as the identity of the umpires. Alas, the more likely outcome is a few more weeks of unsubstantiated grandstanding.

Economist: An overzealous chair umpire overshadows Naomi Osaka’s impressive victory

I wrote something for the Economist Game Theory blog on the controversy in the US Open women’s final. Here’s one part I hope people remember:

The tennis world will probably be debating Mr Ramos’s calls until the next major rolls around in January. But one thing should not be in doubt: Ms Osaka didn’t need his help to earn her first grand slam title. Excluding the five penalty-determined points, she won 60 of the 110 points played, good for 64% on her own service and 45% on return. A ratio of that quality almost guarantees victory. In addition, all five of the points Ms Williams was docked would have been played on Ms Osaka’s serve. Given the level that the 20-year-old sustained, the first point penalty increased her chances of winning by less than half a percentage point, from 97.8% to 98.2%. Even if Ms Williams had been able to raise her level to equal her opponent’s, the impact would have been less than two percentage points. The game penalty was worth barely a full percentage point, boosting Ms Osaka’s probability of victory from 98.1% to 99.2%. By the time the New York crowd started booing, the match was virtually in the bag.

Read the whole thing.

The Right Amount of Serve-and-Volley

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Italian translation at settesei.it

In modern tennis, players approach the net at their own peril, especially behind their serve. Technological advances in both strings and rackets have made passing shots faster and more accurate, giving an added edge to the returner. It’s hard to imagine the game changing so that serve-and-volleying would once again become a dominant tactic.

Yet pundits and commentators often suggest that players should approach the net more often, sometimes advocating for more frequent serve-and-volleying. In a recent article at FiveThirtyEight, Amy Lundy brought some numbers to the discussion, pointing out that at the US Open this year, women have won 76% of their serve-and-volley points and men have won 66%. She also provides year-by-year numbers from the women’s Wimbledon draw showing that for more than a decade, the serve-and-volley success rate has hovered around the mid-sixties.

Sounds good, right? Well… not so fast. Through the quarter-finals in New York, men had won roughly 72% of their first-serve points. Most serve-and-volley attempts come on first serves, so a 66% success rate when charging the net doesn’t make for much of a recommendation. The women’s number of 76% is more encouraging, as the overall first-serve win rate in the women’s draw is about 64%. But as we’ll see, WTA players are usually much less successful.

Net game theory

When evaluating a tactic, we have to start by recognizing that players and coaches generally know what they’re doing. Sure, they make mistakes, and they can fall into suboptimal patterns. But it would be a big surprise to find that they’ve left hundreds of points on the table by ignoring a well-known option. If more frequent serve-and-volleying was such a slam dunk, wouldn’t players be doing so?

I dug into Match Charting Project data to get a better idea of how often players are using the serve-and-volley, how successful it has been. and, just as important, how successful they’ve been when they aren’t using it. The results are considerably more mixed than the serve-and-volley cheerleaders would have it.

Let’s start with the women. In close to 2,000 charted matches from 2010 to the present, I found 429 player-matches with at least one serve-and-volley attempt. After excluding aces, regardless of whether the server was intending to approach, those 429 players combined for 1,191 serve-and-volley attempts–95% of them on first serves–of which they won 747. Had those players not serve-and-volleyed on those 1,191 points and won at the same rate as their first- and second-serve baseline points in the same matches, they would have won 725 points. In other words, serve-and-volleying resulted in a winning percentage of 62.7%, and staying back was good for 60.9%. Just to be clear, this is a direct comparison of success rates for the same players against the same opponents, controlling for the differences between first and second serves.

A difference of nearly two percentage points is nothing to sneeze at, but it’s a far cry from the more than ten percent gap we’ve seen on the women’s side at the US Open this year. And it might not be enough of a benefit for many players to overcome their own discomfort or lack of familiarity with the tactic.

When we apply the same analysis to the men, the results are downright baffling. We have more data to work with here: In nearly 1,500 charted matches from 2010 to the present, more than half of the possible player-matches (1,631) tried at least one serve-and-volley. About four in five–once again excluding aces–were first serves. The tour-wide success rate was similar to what we’ve seen at the Open this year, at 66.8%.

Controlling for first and second serves, the same servers, at the same tournaments, facing the same opponents, won points at a 72.2% rate when they weren’t serve-and-volleying. That’s a five percentage point gap* that says men, on average, and serve-and-volleying too much.

* Technical note: These overall rates simply tally all the serve-and-volley attempts and successes for all players. Thus, they may give too much weight to frequent netrushers. I ran the same calculation in two other ways: giving equal weight to each player-match, and weighting each player-match by ln(a+1), where a is the number of serve-and-volley attempts. In both cases the gap shrunk a bit, to four percentage points, which doesn’t change the conclusion.

I was shocked to see this result, and I’m not sure what to make of it. It’s roughly the same for men who serve-and-volley frequently as for those who don’t, so it isn’t just an artifact of, say, the odd points that an Ivo Karlovic or Dustin Brown plays from baseline, or the low-leverage status of the occasional point when a baseliner decides to serve-and-volley. Since I don’t have a good explanation for this, I’m going to settle for a much weaker claim that I can make with more confidence: The evidence doesn’t suggest that men, in general, should serve-and-volley more.

Data from the women’s game is more encouraging for those who would like to see more serve-and-volleying, but it is still rather modest. Certainly, the 76% success rate in Flushing this year is a misleading indicator of what WTA players can expect to reap from the tactic on a regular basis. It’s possible that some women should come in behind their serves more often. But the overall evidence from a couple thousand matches suggests sticking to the baseline is just as good of a bet–if not better.

Juan Martin del Potro’s Daunting Semi-final Assignments

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Italian translation at settesei.it

This afternoon, Juan Martin del Potro will take on Rafael Nadal for a place in the 2018 US Open championship match. Forgive me if this sounds familiar: It’s the third time Delpo and Rafa have squared off in Flushing’s final four. Every time the Argentine has made it this far in New York, it’s been the King of Clay waiting on the other side of the net.

Del Potro could be forgiven for wondering if he was born in the wrong era. Today is his sixth major semi-final, and his fourth against Rafa. The other two weren’t cakewalks either. His first appearance in the last four of a grand slam was at the 2009 French Open against Roger Federer, and his best-ever performance at Wimbledon gave him a semi-final meeting with Novak Djokovic. The only slight positive in all this is that he faced Federer in Paris and Nadal so often in New York. Technically, it could have been worse.

Simply reaching six major semi-finals is an achievement in itself. Since 1977, there have been only 35 players to reach five or more. For each of those players, I calculated the average surface-specific Elo of their opponents, as well as their average chances of winning. Measured by opponent Elo, Delpo has had the fourth most difficult semi-final assignments of any of these players. The table below shows each player’s number of semi-finals, number of wins, average chance of winning those matches (“Avg p(W)”) and the Elo rating of their average opponent (“Avg Opp Elo”):

Player                 SFs  Wins  Avg p(W)  Avg Opp Elo  
David Ferrer             6     1       35%         2202  
Pat Cash                 5     3       22%         2194  
Stan Wawrinka            9     4       35%         2163  
Juan Martin del Potro    6     ?       35%         2161  
Vitas Gerulaitis         7     2       36%         2146  
Mats Wilander           14    11       48%         2122  
Jo Wilfried Tsonga       6     1       31%         2122  
Michael Chang            8     4       46%         2121  
Novak Djokovic          31    22       62%         2115  
Andy Murray             21    11       52%         2114

Like Delpo, many of these guys had one frequent foe. David Ferrer drew Djokovic in three semis. Pat Cash faced Ivan Lendl three times in his five chances. Vitas Gerulaitis kept earning meetings with Bjorn Borg. Stan Wawrinka hasn’t played more than two semis against any particular opponent, but that doesn’t mean his draws have been any easier: He’s faced Djokovic, Federer, and Andy Murray twice each.

Djokovic and Murray pop up at the bottom of the top ten largely because of Federer and Nadal. It’s a tough era, even if you hold a Big Four membership card. Roger and Rafa have had it easier, ranked 24th and 26th in opponent Elo*, in part due to the number of majors they contested before Djokovic and Murray had fully developed–and because they generally avoided playing each other.

* Federer’s average opponent has had an Elo of 2056, and Nadal’s has had a 2045 Elo. Michael Stich is the only player on this list whose opponents’ Elos averaged below 2000.

Today’s match gives Delpo an opportunity to put himself a bit closer to Wawrinka’s category and surpass the likes of Ferrer and Jo Wilfried Tsonga, who reached only one major final each. Based on his own Elo and those of his opponents, del Potro has had about a one-in-three chance of winning his semis. The 2018 US Open represents his sixth, meaning we’d expect two final appearances thus far. Then again, it’s one thing to run the numbers; it’s another thing to beat Rafael Nadal in a major semi-final … twice.

Dominic Thiem In Pressure Service Games

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Dominic Thiem has good reason to be frustrated.

Italian translation at settesei.it

On Tuesday night, Rafael Nadal and Dominic Thiem delivered the match of the 2018 US Open thus far. After nearly five hours of play, nothing separated them as they battled their way to 5-5 in a fifth-set tiebreak. Nadal finally crept ahead by the narrowest of margins, sealing a victory by the unlikely score of 0-6 6-4 7-5 6-7(4) 7-6(5).

Both players had plenty of chances, and while Rafa prepares for a semi-final against Juan Martin del Potro, Thiem will have plenty of time to mull over the opportunities he missed. In the second set, he failed to hold in both of his last two service games, including the final frame of the set, at 4-5. In the third set, he took the lead by breaking Nadal in the seventh game, but failed to follow up his advantage, losing serve when he attempted to serve it out at 5-4. Two games later, he proved unable to hold serve to stay in the set at 5-6, though he forced Rafa to four deuces before finally giving way.

These three missed chances are hardly the entire story of the match, but they stick out in memory. Overall, Thiem served quite well, allowing Nadal only one break per set. That’s 21 holds in 26 service games, an 81% hold rate, a significant achievement compared to the 66% that Nadal’s opponents have averaged against him on hard courts this year, or the paltry 52% that Rafa has allowed overall. The problem isn’t that the Austrian served badly–he didn’t–but that he weakened at the wrong times. Thiem broke Nadal more often than Rafa returned the favor–six to five–but because three of Thiem’s breaks came in the first, 6-0 set [editor’s note: !??!?!?!?] , Nadal’s six proved less costly than Thiem’s five.

Bad day, or just bad?

Is this something Thiem does, or is it just something that he did, perhaps nudged over the edge one of the greatest returners of all time? Too often, viewers–along with many of those paid to talk and write about tennis–see the latter and assume the former. Does Thiem make a habit of serving strong in lower-leverage games and then wilting when the pressure ratchets up?

If he does, it would make him an exception. I looked at “serving for the set” opportunities a few years ago and found that ATP players serve almost exactly as well when a hold would earn them the set than otherwise. The difference is a mere 0.7%, meaning that the “difficulty” of serving for the set translates into one additional break per 143 opportunities. The effect wasn’t any more noticeable when I narrowed the focus to situations in which the player led by only a single break, like Thiem’s dropped service game at 5-4 in the third set last night.

Let’s look again, and pay specific attention to Thiem. My dataset of sequential point-by-point data, spanning most ATP tour matches between late 2011 and a few weeks ago, now covers over 400,000 service games, including 30,000 serving-for-the-set chances, over two-thirds of them with a lead of a single break. Over 1% of them have Thiem serving, so at least our sample size benefits from the Austrian’s strenuous schedule, even if it doesn’t do him any favors on the court. In other words, we’ve got a ton of data here, so if there is an effect, we should be able to find it.

Thiem’s missed chances included chances to both finish a set and stay in a set, so I’ve expanded our view to a variety of pressure situations. For each situation, I’ve calculated the hold rate for players in that position relative to their typical hold rate in those matches. (A player with a lot of serve-to-stay-in opportunities is probably on the losing end, with a lower hold rate than average, but this method should control for that.) A ratio of 1.0 means that the hold rate in the pressure situation is exactly the same as normal. A ratio above 1.0 means the hold rate is higher than usual, and below 1.0 signifies a lower hold rate–the lag many of us expect to see when the stakes get higher. Here are the ratios for a variety of situations, including serving for the set (plus a category one-break leads), serving to stay in the set (also with one-break deficits identified), ties late in the set such as 4-4 and 5-5, and for comparison’s sake, low-pressure situations–“All Else”–which is a catch-all for everything not in the above categories.*

* Yes, it includes the famous seventh game, which I’ve previously shown isn’t particularly important, no matter what Bill Tilden said.

Situation          Examples  Hold% / Avg  
For-Set            5-4; 5-2        0.994  
- For-Set Close    5-3; 6-5        0.989    
To-Stay            4-5; 1-5        0.999  
- To-Stay Close    5-6; 3-5        0.969    
Tied Late          4-4; 5-5        0.953  
All Else           2-3; etc        1.003

The “serving-for-the-set” effect is almost exactly same as what I found three years ago: a drop of a bit more than half a percent. Last year, the impact of serving for the set with a single break lead was a bit greater than I initially found, but it’s still small. We find servers struggling the most when serving to stay in the set while trailing by a a single break–losing serve 3.1% more often than usual–and when serving at 4-4 and 5-5, when they drop serve almost 5% more frequently than expected. These are the most substantial effects I’ve seen, but keep in mind the magnitude–even a 5% difference means it only flips the outcome of one service game in twenty. It certainly matters, but it would be awfully hard to spot with the naked eye.

The one percent

How does Thiem compare? Here is the same set of ratios for him, with separate columns for his career numbers (subject to the limitations of my dataset, which includes few matches before 2012) and for single-season figures from 2016, 2017, and 2018:

Situation        Career   2016   2017   2018  
For-Set           0.996  1.049  1.011  0.966  
- For-Set Close   0.984  1.078  1.008  0.887  
To-Stay           1.030  1.160  1.027  0.940  
- To-Stay Close   0.984  1.148  0.957  0.964  
Tied Late         0.984  0.976  0.991  0.889  
All Else          1.004  0.994  1.009  1.030

Thiem’s career numbers reveal little, just a player who is a tiny bit worse in high-leverage situations, though perhaps a little less affected by the pressure than his peers. The concern is his numbers so far this year, which are way down across the board. Each one of the categories represents a relatively small sample–for example, I have only 42 games in which he was serving for the set with a single break advantage–but taken together, the set of sub-1.0 ratios don’t point in an encouraging direction. We could never have forecast before last night’s match that Thiem would serve so well in general but so much weaker in the clutch, but there were subtle hints lurking in his 2018 performance.

A puzzle

I want to show you the same set of data, but for another player. In one way, it’s the opposite of Thiem’s: many more breaks in pressure situations over the course of the player’s career, but the opposite trend in the last few years, pointing toward more service holds:

Situation        Career   2016   2017   2018  
For-Set           0.929  0.931  1.200  1.077  
- For-Set Close   0.910  0.895  1.333  1.000  
To-Stay           1.026  1.077  1.083  1.061  
- To-Stay Close   0.929  1.100  1.167  1.044  
Tied Late         0.905  1.050  1.000  1.048  
All Else          1.011  1.013  1.024  1.013

Any ideas? It’s a bit of a trick question–you’re looking at the tour serving against Rafa. From 2012-15, Nadal absolutely shut down opposing servers starting at about 4-4. (He wasn’t as good–relative to his average, anyway–late in sets on his own serve.) Very few players or seasons show effects of greater than 5% in either direction, but Rafa’s opponents saw their hold rate dip by more than twice that in some seasons. Yet the story has been different for the last year or two, with Rafa himself becoming the underperformer in his late-set return games.

Again, we shouldn’t read too much into a single year of this data: The sample size is an issue, especially for a top player’s return games, because not many guys find themselves serving for a set against him. But had we looked at Nadal’s return record in pressure situations alongside Thiem’s recent serve performance, it would have made for a more complicated picture, one less likely to predict some of the crucial moments in last night’s match. In any given contest, there are simply too few key games for us to forecast their outcome with any success, especially when a let cord, an untimely distraction, or a missed line call could reverse the result. But that doesn’t mean we shouldn’t try to understand them. Unlucky, unclutch, or whatever else, Thiem could have flipped the outcome of the entire match by holding just one of those three games. The stakes could hardly be higher.

Podcast Episode 31: US Open Week Two

Episode 31 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, features all the stars: Federer’s upset, Sharapova’s loss to the beautiful backhand of Carla Suarez Navarro, Nadal’s upcoming quarter-final against Dominic Thiem, and Djokovic’s chances of racing through the bottom half and winning the title.

We also delve into the current crop of ATP (near-) teenagers, including last week’s hero Alex de Minaur, and speculate wildly about their futures. As always, thank you for listening!

(Note: this week’s episode is about 60 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

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Two Servebots and Zero Tiebreaks

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Isner had energy to burn since he never needed to count to seven.

Italian translation at settesei.it

There have been plenty of upsets at this year’s US Open, but they all pale in comparison with the surprise that John Isner and Milos Raonic delivered Sunday night in their fourth round match. Isner won, 3-6 6-3 6-4 3-6 6-2, failing to hold twice and breaking Raonic’s serve four times. Rarely has a tiebreak seemed so assured, and the two big men didn’t even get close.

In five previous meetings, Isner and Raonic have been more likely to deliver two tiebreaks than only one, and most of their matches were best-of-three, not the grand slam best-of-five format. In 13 previous sets, they had played 9 tiebreaks. In the last year, 45% of Isner’s sets have reached 6-6, while nearly a quarter of the Canadian’s have. One or the other of these guys is responsible for the longest match in history, the longest ever major semi-final, and the longest match in Olympics history. They are really, really good at holding serve, and really not-so-good at breaking.

Great expectations

The likelihood that Isner and Raonic would play a tiebreak depends on some basic assumptions. If Raonic served like he has for the last 52 weeks, that’s a service-point won percentage (SPW) of 72.8%, which is equivalent to holding 93% of the time. If we use Isner’s actual SPW from the match of 74.3%, that translates to a hold rate of 94.4%. If we choose Isner’s SPW from his previous meetings with Raonic of a whopping 76.5%, that gives us an implied hold rate of 96%. Those all sound high but, as we’ll see, the difference between them ends up affecting the probability quite a bit.

I’m going to run the numbers using three sets of assumptions:

  1. The head-to-head. In five matches (four of them on hard courts, the fifth at Wimbledon this year), Isner won 76.5% of service points, while Raonic won 71.4%. That’s equivalent to hold rates of 96.0% and 91.7%, respectively.
  2. The last 52 weeks (adjusted). Across all surfaces, going back to last year’s US Open, Isner has won 73.6% of service points, against Raonic’s 72.8%. Those numbers, however, are against average opponents. Both players, and especially Isner, have below-par return games. If we adjust each SPWs for the other player’s rate of return points won (RPW), we get 75.5% for Isner and 78.5% for Raonic. In game-level terms, those are hold rates of 95.3% and 97.1%.
  3. The match itself. On Sunday night, Isner won 74.3% of service points and Raonic won 68.8%. Using these numbers doesn’t give us a true prediction, since we couldn’t have known them ahead of time. But maybe, if we used every scrap of information available to us and put them all together in a really smart way, we could have gotten close to the true number. Those rates translate to hold percentages of 94.4% for Isner and 88.5% for Raonic.

Not enough tiebreaks

Apparently, the betting odds for at least one tiebreak in the match set the probability around 95%. That turns out to be in line with my predictions, though the specific assumptions affect the result quite a bit.

I’ve calculated a few likelihoods using each set of assumptions. The first, “p(No brk),” is the probability that the two men would simply hold serve for 12 games. It’s not the only way to reach a tiebreak, but it accounts for most of the possibilities. Next, “p(TB)” is the result of a Monte Carlo simulation to show the odds that any given set would result in a tiebreak. “eTB” is the expected number of tiebreaks if we knew that Isner and Raonic would play five sets. Finally, “p(1+ TB)” is the chance that the match would have at least one tiebreak in five sets.

Model   JI Hld  MR Hld  p(No brk)   p(TB)   eTB  p(1+ TB)  
H2H      96.0%   91.7%      46.5%   51.3%   2.6     97.3%  
Last52   95.3%   97.1%      62.8%   65.3%   3.3     99.5%  
Match    94.4%   88.5%      34.0%   41.2%   2.1     93.0%

Given how the big men played on Sunday, it isn’t unthinkable that they never got to 6-6. In large part because Isner’s return game brought Raonic’s SPW under 70%, each set had “only” a 41.2% chance of going to a tiebreak, and there was a 7% chance that a five-setter would have none. The other two sets of assumptions, though, point to the sort of tiebreak certainty reflected in the betting market … and just about anyone who has ever seen these two guys play tennis.

Perhaps the strangest aspect of all of this is that, in six previous matches at this year’s Open, Isner and Raonic combined for seven tiebreaks–at least one in five of their six matches–before their anticlimactic encounter. Knowing Isner, this is a blip, not a trend, and he’s sure to give us a breaker or two in his quarter-final against Juan Martin del Potro. His tournament record will likely show one or two tiebreaks in every match … except for the one against his fellow servebot. This must be why we stick with tennis: Every match has the potential to surprise us, even if we never really wanted to watch it.