Qinwen Zheng’s Serve Under Construction

Also today: The odds of a 42-point tiebreak; January 19, 1974

Qinwen Zheng in 2023. Credit: Hameltion

Qinwen Zheng is one of the top prospects in the women’s game, up to 14th on the WTA ranking list at age 21. She won her first tour-level title in Palermo last summer, then upset Ons Jabeur en route to a quarter-final showing at the US Open. After topping Barbora Krejcikova for a second title in Zhengzhou, she reached the final at the WTA Elite Trophy, falling in a two hour, 52-minute final to Beatriz Haddad Maia.

With yesterday’s upsets of Elena Rybakina and Jessica Pegula at the Australian Open, Zheng’s draw opened up. With only one other seed in the second quarter, she’s the heavy favorite to earn a semi-final date with Iga Swiatek. Potential is poised to become reality.

It’s never been difficult to dream big on the Chinese woman’s behalf. Her service motion–once she gets past a hitchy toss–is a photographer’s dream, and she takes advantage of her five-foot, ten-inch frame to send first serve after first serve into the corners. When she hits a target out wide, returners are lucky to get a racket on the ball, let alone put it back in play. Her forehand is equally powerful.

The results bear out the devastation wreaked by her first delivery. Here are last year’s WTA top ten in first-serve percentage:

Player               1stWon%  
Qinwen Zheng           73.7%  
Elena Rybakina         73.6%  
Aryna Sabalenka        72.8%  
Caroline Garcia        72.5%  
Liudmila Samsonova     71.5%  
Iga Swiatek            70.0%  
Petra Kvitova          69.8%  
Belinda Bencic         69.5%  
Petra Martic           69.5%  
Ekaterina Alexandrova  69.4%

Pretty good company, huh? Her forehand grades well, too. According to Match Charting Data, Zheng hits more winners, induces more forced errors, and commits fewer unforced errors with that shot than the average player on tour. Her forehand potency (FHP) per match over the last 52 weeks is 10.8, placing her in the top ten among tour regulars, just behind Haddad Maia and Madison Keys.

That’s the good news. If you’re going to have just two world-class weapons, those are the ones to pick. They’ve served her well so far: If she justifies her seed and reaches the final four in Melbourne, she could crack the top ten.

The rest of Zheng’s game is–let’s be optimistic here–a work in progress. Today I want to look specifically at her serve as a whole; we’ll save her not-as-problematic backhand for another day.

When the 21-year-old lands her first serve, as we’ve seen, good things happen. She hits more aces than almost anyone on tour, and about half of her first-serve points end with either an unreturned first serve or a plus-one winner. The problem is, she doesn’t make many first serves, and when she misses, her second serve is as erratic as her first serve is imposing.

The average top-50 player on the WTA tour makes about 62% of her first serves. In 2023, Zheng succeeded just 51.8% of the time, almost three full percentage points below anyone else.

Making matters worse, her second-serve results are nearly as bad. The average top-50 WTAer wins 47% of her second-serve points. Zheng won 45.5%, a mark that places her in the bottom third of that group. Among the current top 20, only Jelena Ostapenko and Daria Kasatkina win fewer second-serve points. It’s even worse against a strong opponent. She hung onto just 20% of second-serve points against Swiatek in the United Cup this month, 24% versus Rybakina in Beijing, and a mere 26% against Liudmila Samsonova in Montreal. Zheng’s primary weapon makes her look like an elite server, but the overall picture is more mundane. Her first serve sets her on a level with Rybakina, but she barely holds serve as often as Petra Martic.

What is to be done?

This seems like it should be fixable, especially in so young a player. It’s certainly easy to dream. Imagine the seemingly-modest scenario in which Zheng manages to land her first serves and win second-serve points at the rates of an average top-50 player while maintaining her dominance on firsts. She would then win 63.5% of her service points. Only Swiatek and Sabalenka do better.

Easier said than done, of course. A good first serve is no guarantee of a strong second. On the women’s tour, there almost zero correlation between first-serve and second-points won.

Still, this seems like partly a tactical failure, not entirely a gap in her skillset. If Zheng can win nearly 74% of her first-serve points when she misses almost half of the time, what would happen if she served a bit more conservatively? Perhaps she could make 57% of her first serves and still win 72% of them? If so, that would be a bit better. Could she make 62% of first serves–the tour average rate–and win 70% of them? That would be better still.

Once we assume that these tradeoffs are feasible, the whole thing starts to sound like less of a tactical question and more of a pure math problem. I’m not sure that it is: Players practice various types of “first serves” and “second serves,” not every theoretical delivery on the continuum between them. Maybe a thoughtful veteran could tweak things to increase or decrease her first-in percentage at will, but I’m skeptical that a young player could do th esame. At the very least, it’s a project that would take some time.

Still, it’s worth working out whether Zheng could get more bang for her serve-talent buck. In 2009, Dutch researchers Franc Klaassen and Jan R. Magnus (henceforth K&M) published a paper in the Journal of Econometrics that proposed to answer this sort of question. They worked out the usual relationship between serving risk (how many first serves in, how many double faults) and reward (rate of first- and second-serve points won). My friend Jeff McFarland converted their rather complex algorithm to a spreadsheet, which is why I’m able to publish this today, and not in March. Thanks Jeff!

The following table shows Zheng’s actual 2023 results along with her model-optimized rates:

         1stIn%  1stWon%    DF%  2ndWon%   SPW%  
Actual    51.8%    73.7%   6.0%    45.5%  60.1%  
Optimal   60.5%    70.9%   8.8%    47.5%  61.7%

K&M’s formula estimates that Zheng could get close to a tour-average level of first serves in and still win about 71% of them, a success rate that would keep her in the top five. The more surprising output is that she could do better by taking more chances on her second serve. (This is a kind of light version of the oft-discussed argument that a player should just hit two first serves. The algorithm recommends some degree of this for most pros.) By adopting the more risky second-serve approach, she would in theory win 47.5% of those points despite the increase in double faults.

Altogether, those changes would increase her total service points won from 60.1%–12th among the current top 50–to 61.7%, which would rank her fifth.

Another way of looking at the potential gain is in points per thousand. For every thousand service points played, the fully-optimized version of Zheng would win about 16 more than she does now. If her return game remained the same, that’s an improvement of eight points per thousand overall. A few years ago I stumbled on a neat rule of thumb, that an improvement of one point per thousand translates into a gain of one place in the rankings, except near the very top. If that held in this case, the re-imagined Zheng would be on the cusp on the top five.

Again, this is all theoretical. I have no idea whether a big server could consciously execute a decision to take slightly fewer chances on the first and more on the second, or whether her results would follow the model if she did.

But! This is a potential route to a jump up the rankings without reworking groundstrokes, getting fitter or stronger, or even gaining experience. It’s probably not easy, but it’s likely simpler than the alternatives. As it stands now, Zheng’s second serve–and the frequency she’s forced to hit it–is going to hold her back. Solve that problem, and much of her obvious potential is unlocked.

* * *

The odds of a 42-point tiebreak

“10-point tiebreak, my ***.” Credit: @hardpicstennis

Yesterday, Elena Rybakina and Anna Blinkova played a 42-point tiebreak. It’s the longest breaker in grand slam singles history. Blinkova won it, 22-20.

What are the odds?

Let’s start with simply getting to 9-all. We’ll assume that Rybakina and Blinkova were playing at the same level. Yes, Rybakina was a heavy favorite entering the match, and she won a few more points than Blinkova to get to 6-4, 4-6, 6-all. But the margin was narrow, and the math is simpler if we assume they are equal. They won serve points throughout the match at about a 59% rate. Since players tend to be more conservative during tiebreaks, returners fare better, so we’ll say that whoever is serving had a 55% chance of winning the point.

I ran a Monte Carlo simulation to find the odds of reaching 9-all. Here are those probabilities, along with odds at various other levels of serve dominance:

SPW   Reach 9-all  
55%         10.0%  
60%         10.3%  
65%         11.2%  
70%         12.5%  
80%         17.0%

Roughly speaking, there was a one-in-ten chance that yesterday’s breaker would reach 9-all.

From there, the math is simpler. There are two ways to get from 9-all to 10-all: both women could win their service points, or both could win their return points. Serving at 55%, the chances that one or the other occurs are 50.5%. The same logic applies to the step from 10-all to 11-all, 11-all to 12-all, and so on. So for Rybakina and Blinkova, getting from 9-all to 20-all was roughly equivalent to flipping a coin eleven times and getting heads every time–a one-in-two-thousand shot.

To reach 20-all, then, players need to get to 9-all, then trade points another eleven times. For servers at 55%, that’s a one-in-ten shot followed by a one-in-two-thousand shot, or one in twenty thousand–a 0.005% likelihood–altogether.

Here are the equivalent numbers for servers at various levels:

SPW   Reach 9-all  Reach 20-all  that's 1 in…  
55%         10.0%        0.005%         18357  
60%         10.3%        0.008%         12916  
65%         11.2%        0.014%          7086  
70%         12.5%        0.031%          3201  
80%         17.0%        0.244%           409 

You might remember the 24-22 tiebreak that Reilly Opelka won against John Isner in Dallas a couple of years ago. The probabilities are dramatically different depending on how serve-dominant the players are, so the Rybakina-Blinkova result was considerably more far-fetched than what Opelka and Isner produced. Adjusting for the fact that the Dallas tiebreak was first-to-seven and assuming that both players won 80% of serve points (an estimate on the low side), this method gives us a one-in-2,192 chance of that tiebreak reaching 22-all.

There are various ways to tweak the numbers. It might be the case that players perform better facing match point; if so, it’s a bit more likely that they’d reach this sort of outrageous score. Maybe it’s appropriate to give Rybakina a modest edge over Blinkova; if we did that, the odds of drawing even so long would be lower. One-in-18,357 isn’t exactly right, but it gives us a rough idea of just how unusual yesterday’s feat truly was.

* * *

January 19, 1974: Sanctioned

Four months from its proposed opening day, things finally started to look up for World Team Tennis. On January 18th, the USLTA officially sanctioned the league in exchange for a $144,000 fee. Another chip fell the next day, when American co-number one Jimmy Connors signed with the Baltimore Banners.

WTT still had several hurdles to clear. The British LTA continued to object to the league’s attempted takeover of so many weeks of the summer calendar. The ILTF, as well, had yet to give their okay. The ATP, still a nascent players’ union, also held back. A few top men–John Newcombe, Ken Rosewall, and now Connors–had thrown in their lot with the upstarts, but until the union made its stance clearer, the WTT ranks remained dominated by women stars.

Across the country, those women were making the case that they’d be able to draw sufficient crowds on their own. Also on January 19th, the first event of the 1974 Virginia Slims circuit came to a close. 6,000 fans packed San Francisco’s Civic Auditorium to watch Chris Evert take on Billie Jean King for the title. Another 2,000 were turned away at the gates. Traffic was jammed for blocks in every direction, and ticket scalpers worked the rows of stalled motorists.

The Slims tour had been dominated by Margaret Court in 1973, with Billie Jean hampered by injury and Evert competing on a separate tour sponsored by the USLTA. This year, Court was absent, pregnant with her second child. If San Francisco was any indication, the Australian would hardly be missed. The federation had made peace with the one-time rebels of the Slims tour, and now Gladys Heldman’s women-only circuit was the only game in town. Billie Jean was healthy (and the ultimate marquee draw, after defeating Bobby Riggs), and Evert provided new blood.

Chrissie also provided fresh motivation for the Old Lady. King had hinted that she would dial back her tournament commitments in 1974, but she wasn’t one to back down from a challenge. Playing no-ad games for the San Francisco title, Billie Jean kept her younger opponent under constant pressure. Five times Evert reached sudden-death point on her serve; five times she saved it. King finally pulled ahead to take the first set, winning the tiebreak, 5-2. Evert mounted a comeback from 0-4 in the second, but Billie Jean halted her momentum when she chased down a drop shot that Chris didn’t think she could touch.

“She was very gutsy and I once thought I had no chance,” King said after the match. “And thank God for giving me a pretty good pair of wheels on that particular shot.”

Billie Jean was thrilled at both the result and the sellout crowd. Nothing pleased her more than a successful women’s tour–except, of course, for a successful women’s tour with herself on top.

* * *

Subscribe to the blog to receive each new post by email:

 

March 24, 1973: Plimpton Falls Short

George Plimpton in 1977

We’re lucky that it was a bit of a slow news day for tennis on March 24, 1973. A few newspapers had room for this:

PHILADELPHIA–The local team of James L. Van Alen 2d and Jimmy Dunn won the United States amateur-professional handicap court tennis doubles championship today by defeating George Plimpton and Eddie Noll of New York, 6-5, 6-5, 3-6, 6-4, at the Racquet Club.

Yes, that Jimmy Van Alen. And yes–oh yes!–that George Plimpton.

Van Alen was, depending on your perspective, somewhere between a gadfly and a visionary. He invented the tiebreak and spent more than a decade badgering the rest of the US tennis establishment. Even when his brainchild became standard, he wasn’t satisfied. His ideal was a nine-point breaker: first to five, sudden death. As the first-to-seven, win-by-two variation gained popularity, he got steadily crankier about it.

Details aside, the man loved tiebreaks. He proposed that once a set reached 6-all, a special red flag would be flown above the stadium to indicate that a tiebreak was underway. He convinced the officials at the US Open to go for it, and when he attended other events, he brought along a spare flag of his own.

A Van Alen “Sudden Death” flag flying above Forest Hills in 1971

In 1973, Van Alen was 70 years old. He was far past his prime as a lawn tennis player, and he had never been a particularly great one. (He did win a match at the 1931 US National Championships.) His pastime of choice was court tennis, the ancient sport on which lawn tennis was based. Court tennis is a more strategic game that relies less on power. Van Alen won national singles and doubles titles in his niche pursuit.

Van Alen’s prestige gave him another advantage. This was an “amateur-professional” doubles championship–that is, one of each. Van Alen the amateur chose to team up with Jimmy Dunn, the head pro at the Philadelphia host club. It always helps to choose the right partner: It was Dunn’s tenth title at this event.

* * *

Van Alen was not, however, the most interesting man on the court that day. Few characters could compete with George Plimpton in that category.

Plimpton was a journalist and occasional actor. By 1973, he was 46 years old and a minor celebrity. Despite a patrician background that could be traced back to the Mayflower, Plimpton got closer to the action than any sportswriter before him. He pitched to major-league all-stars, traded punches with Sugar Ray Robinson, and manned the net for hockey’s Boston Bruins.

He achieved his fame through dalliances in football and golf, yet when he wasn’t on assignment, tennis was his sport of choice. The writer was known as an excellent lawn tennis player, and he occasionally turned up in pro-am exhibitions. When he got married in 1968, the New York Times went with the standard line for a racket-wielder: “Plimpton Drops Singles for Doubles.” A decade later, he played alongside Vitas Gerulaitis as a headliner at a Rockefeller Center benefit match–on ice.

A 1971 New Yorker cartoon

Among his many stunts, he once faced off against Richard González at the Los Angeles Tennis Club. Gorgo wasn’t one to show mercy on an amateur, and the fact Plimpton was a journalist probably didn’t help either. González destroyed him.

Like Van Alen, Plimpton found a home in the small world of court tennis. He had competed at national events since at least 1961. He merged his profession and his passion in 1971 when he edited Pierre’s Book, the instructional guide written by French court tennis great Pierre Etchebaster.

Despite an advantage of more than two decades, Plimpton doesn’t seem to have been Van Alen’s equal at the royal game. In that 1973 championship match, his pro partner, Eddie Noll, had to handle three-quarters of his team’s shots.

Unfortunately for us, Plimpton never wrote much about the sport he pursued so avidly. He covered lawn tennis just once for Sports Illustrated, the publication that backed him on some of his wilder adventures. For that 1967 story, he was drawn to a series of unusual matches at Southampton and Newport–early-round tilts that refused to end, extending to 32-30, 48-46, and 49-47. Naturally, he checked in with the tournament director at the Newport Casino, Jimmy Van Alen.

“That’s nonsense out there,” said the inventor of the tiebreak. “Just nonsense.”

* * *

This is the second installment in what I fear will be an ongoing series about 1973, perhaps the most consequential season in modern tennis history. Check back throughout the year for the latest news from, uh, fifty years ago.

A Closer Look at Tiebreak Tactics

Italian translation at settesei.it

In theory, tiebreaks are a showcase for big serving, the skill that generates enough holds of serve to push a set to 6-6. But no matter how two players get there, the tiebreak itself doesn’t always work out that way.

Two examples suffice from Wednesday’s Australian Open action. Roger Federer’s second-round match against Daniel Evans opened with twelve straight service holds, threatened by only one break point. Yet in the tiebreak, which Federer won 7-5, the returner claimed 9 of 12 points. Across the grounds in front of a much smaller crowd, Thomas Fabbiano and Reilly Opelka forced a fifth-set super-tiebreak. Through 52 games and 319 points, Opelka hit 67 aces and the pair averaged 2.9 shots per “rally.” In the match-deciding tiebreak, Opelka hit no aces, Fabbiano got all but one of his serves back in play, and they averaged 5.5 shots per point.

When I started researching tiebreaks several years ago, I found that the balance of power shifts away from the server: returners win more points in tiebreaks than at other points during the set. It’s not a huge effect, accounting for about a 6% drop in server winning percentage, possibly due to the fact that players almost always give 100% on each point, unlike weak returners facing 40-0 in the middle of the set. Sure, Federer-Evans and Fabbiano-Opelka are outliers: even if servers suffer a bit in the typical tiebreak, the whole sport doesn’t usually turn upside down. Still, the effect is worth a deeper dive.

Isner isn’t the only conservative

Let’s start with some overall trends. Filtering for men’s matches from 2010-19, I found 831 tiebreaks with shot-by-shot data from the Match Charting Project. For each set that ended in a tiebreak, I tallied several stats for both tiebreak points and non-tiebreak points, calculated the single-set ratio for each stat, and then aggregated all 831 breakers to get some tour-wide numbers. Here’s what happens to stats in tiebreaks:

  • Service points won: -6.5%
  • Aces: -6.1%
  • First serve in: +1.3%
  • Returns in play: +8.5%
  • Rally length: +18.9%

(Technical note: When aggregating the ratios from all 831 tiebreaks, I weighted by the number of points in each tiebreak, but only up to a maximum of 11. Longer tiebreaks tend to be the ones if which servers are the strongest, like the 17-15 marathon in the first set of Fabbiano-Opelka. If those were weighted for their true length, we’d bias the results towards the best serving performances.)

Judging by the increase in successful first offerings, it looks like servers are a bit more conservative in tiebreaks. The large drop in aces and even bigger increase in returns in play provide additional evidence. Focused returners may be able to erase a small number of aces, but not that many, and they wouldn’t be able to convert so many into successful returns. The nearly 20% increase in rally length can be explained in part by the drop in aces (those one-shot rallies are replaced with more-shot exchanges), but the magnitude of the rally length effect suggests that players are more conservative on both sides of the ball.

More than one way

Not every player handles breakers the same way. Several men, including Federer, serve about as well as usual in these high-pressure situations. Certain others, like Rafael Nadal, appear to be more conservative, but make up for it by feasting on the toned-down offerings of opposing servers. Still others, like the impossible-to-write-about-tiebreaks-without-bringing-up Ivo Karlovic, underperform on both sides of the ball.

Here are the 20 players with the most tiebreaks recorded by the Match Charting Project since 2010. For each one, you can see how their rates of service points and return points won in tiebreaks compare to non-tiebreak situations. For instance, Jo Wilfried Tsonga wins 5.4% more service points in tiebreaks than otherwise, compared to the usual shift of 6.5% in the opposite direction. But Tsonga’s rate of return points won falls 3.4%, while the typical player increases his haul on return by 6.5%.

Player                    SPW    RPW  
Jo Wilfried Tsonga       5.4%  -3.4%  
Roger Federer            0.4%   3.2%  
Stan Wawrinka           -0.1%   4.2%  
John Isner              -0.6%   6.4%  
Novak Djokovic          -0.8%  11.8%  
Andy Murray             -2.2%   8.7%  
Alexander Zverev        -2.7%  18.7%  
Juan Martin del Potro   -3.3%   5.3%  
Nick Kyrgios            -4.1%  10.5%  
Dominic Thiem           -4.6%  12.1%  
----ATP AVERAGE----     -6.5%   6.5%  
Kevin Anderson          -7.1%   8.9%  
Gilles Simon            -8.0%  16.3%  
Tomas Berdych           -8.4%   6.8%  
Milos Raonic            -9.2%   9.1%  
Rafael Nadal            -9.4%  13.6%  
Marin Cilic            -10.2%   5.8%  
Bernard Tomic          -11.3%   4.5%  
Ivo Karlovic           -12.6%  -0.9%  
Grigor Dimitrov        -13.8%   5.1%  
Karen Khachanov        -25.1%  -5.4%

For most players, the goal appears to be to win enough extra return points to counteract the drop in service success. Nadal is the most extreme example, winning almost 10% fewer service points than usual, but doing even more damage to his opponents. Alexander Zverev is the most impressive of the bunch, dropping his serve level only a bit, while converting himself into a Rafa-like returner. As you might expect, his tiebreak record is outstanding, winning far more than expected last season. We’ll see whether his eye-popping numbers persist.

A winning strategy

Ideally, I would wrap up a post like this with a recommendation. You know, analyzing the various approaches, based on these numbers, we can confidently say that players should….

It’s not that easy. It’s hard enough to identify which players are good at tiebreaks, let alone why. As I’ve written many times before, tiebreak results are closely related to overall tennis-playing skill, but not to serving prowess or excellence in the clutch. In any given season, some players amass outstanding tiebreak records, but their success one year rarely translates to the next. At various times in the past, I’ve highlighted Federer, Isner, Nadal, and Andy Murray as players who defy the odds and consistently outperform expectations in tiebreaks, but even they don’t always manage it. Isner, the poster boy for triumph via tiebreak, won slightly fewer breakers than expected in both 2016 and 2018.

Still, let’s look at these four guys in the light of the shot-by-shot data I’ve shared so far. Federer, Isner, and Murray are in the minority of players who hit more aces in tiebreaks than otherwise. However, it it doesn’t necessarily mean they are much more aggressive; of the the three, only Federer makes fewer first serves than usual. Isner manages to reduce the number of returns in play by 10%, compared to non-tiebreak situations, while the other two do not. Nadal breaks the mold entirely, making 6% more first serves than usual and hitting barely half as many aces.

In other words, there’s no single path to success. Federer and Isner maintain their superlative serving while taking advantage of their opponents’ nerves or conservative tactics. (I’ve previously suggested that the difference in serve points won comes from players like Isner upping their return game in pressure situations. He does, but not any more than the average player.) Nadal plays to his own strengths, forcing players into rallies from both sides of the ball. There may be some quality that ties these four men together (like focus), but we’re not going to find it here.

The Effect of Tiebreak Luck

I’ve written several things over the years about players who win more or fewer tiebreaks than expected. (Interested readers should start here.) Fans and commentators tend to think that certain players are particularly good or bad at tiebreaks. For instance, they might explain that a big serve is uncommonly valuable at the end of a set, or that mental weakness is more harmful than ever at such times.

My research has shown that, for the vast majority of players, tiebreak results are indistinguishable from luck. Let me qualify that just a bit: Tiebreak results are dependent on each player’s overall skill, so better players tend to win more tiebreaks. But there’s no additional factor to consider. While players tend to win service points at a slightly lower rate in tiebreaks, the effect is similar for everyone. There’s no magical tiebreak factor.

However, a single season is short enough that some players will always have glittering tiebreak records, tricking us into thinking that they have some special skill. In 2017, John Isner won 42 of his 68 tiebreaks, a 62% success rate. Based on his rate of service points won and return points won against the opponents he faced in tiebreaks, we’d expect him to win only 34–exactly half. Whether by skill or by luck, he exceeded expectations by 8 tiebreaks. Armed with a monster serve and a steady emotional presence on court, Isner is the kind of guy who makes us think that he has hacked the game of tennis, that he has figured out how to win tiebreaks. But while he has beaten expectations several times throughout his career, even Big John can’t sustain such a level. In 2018, he played 73 tiebreaks, and the simple model predicts that he would win 41. He managed only 39.

For additional examples, name whichever player you’d like. Roger Federer has built a career on unshakeable service performances, yet his tiebreak performances have been roughly neutral for the last four years. In other words, he wins tiebreak serve and return points at almost exactly the same rate as he does non-tiebreak points. Robin Haase, infamous for his record streak of 17 consecutive tiebreak losses, has paralleled Federer’s tiebreak performance for the last four years. 2018 was particuarly good for his high-pressure record, as he won two more breakers than expected, putting him in the top quartile of ATP players for the season.

Meaning from randomness

In short, season-by-season tiebreak performance resembles a spreadsheet full of random numbers. A player with a good tiebreak record last year may well sustain it this year, but only if it’s based on good overall play. If there is an additional secret to tiebreak excellence (beyond being good at tennis), no one has told the players about it.

But in sports statistics, every negative result has a silver lining. We might be disappointed if a stat is not predictive of future results. However, the very lack of predictiveness allows us to make a different kind of prediction. If a player has a great tiebreak year, beating expectations in that category, the odds are he just got lucky. Therefore, he’s probably not going to get similarly lucky this year, and his overall record will regress accordingly.

The player to watch in 2019 in this department is Taylor Fritz, who recorded a sterling 20-8 record in tiebreaks last season. Based on his performance in the whole of those matches, we would have expected him to win only 13 of 28. His Tiebreaks Over Expectations (TBOE) of +7 exceeded that of any other tour player last season, even though many of his peers contested far more breakers. It’s always possible that Fritz really does have the magical mix of steely nerves and impeccable tactics that translates into tiebreak wins, but it’s far more likely that he’ll post a neutral tiebreak record in 2019. In 2017, the player after Isner on the TBOE list was Jack Sock, and it’s fair to say that his 2018 campaign didn’t exactly continue in the same vein.

With that regression to the mean in mind, here are the TBOE leaders and laggards from the 2018 ATP season. The TBExp column shows the number of tiebreaks that the simple model would have predicted, and TBOR is a rate-stat version of TBOE, reflecting the percentage of tiebreaks won above or below average. Rate stats like TBOR are usually more valuable than counting stats like TBOE, but in this case the counting stat may have more to tell us, since it takes into account which players contest the most tiebreaks. Sam Querrey’s rate of underperformance isn’t quite as bad as Cameron Norrie’s, but the number of tiebreaks he plays is a result of his game style, justifying his place at the bottom of this list.

Player                 TBs  TBWon  TBExp  TBOE   TBOR  
Taylor Fritz            28     20   13.3   6.7   0.24  
Bradley Klahn           22     16   10.6   5.4   0.24  
Martin Klizan           16     13    8.1   4.9   0.31  
Kei Nishikori           22     17   12.5   4.5   0.20  
Bernard Tomic           18     14    9.6   4.4   0.24  
Alexander Zverev        23     17   13.2   3.8   0.17  
Albert Ramos            22     15   11.2   3.8   0.17  
Adrian Mannarino        25     16   12.3   3.7   0.15  
Stan Wawrinka           21     13    9.6   3.4   0.16  
Juan Martin Del Potro   32     22   18.7   3.3   0.10  
                                                       
Borna Coric             21      8   10.8  -2.8  -0.13  
Denis Shapovalov        30     12   15.0  -3.0  -0.10  
Karen Khachanov         42     20   23.4  -3.4  -0.08  
Ivo Karlovic            47     19   22.6  -3.6  -0.08  
Denis Istomin           31     13   16.7  -3.7  -0.12  
Ricardas Berankis       22      7   10.9  -3.9  -0.18  
Pablo Cuevas            21      7   11.3  -4.3  -0.20  
Andrey Rublev           18      5    9.6  -4.6  -0.26  
Fernando Verdasco       25      8   12.8  -4.8  -0.19  
Roberto Bautista Agut   26     10   14.8  -4.8  -0.19  
Cameron Norrie          22      5    9.9  -4.9  -0.22  
Sam Querrey             36     12   18.5  -6.5  -0.18

The guys at the top of this list can expect to see their tiebreak records drift back to normalcy in 2019, while the guys at the bottom have reason to hope for an improvement in their overall results this year.

Converting tiebreaks to wins

I’m sure we all agree that tiebreaks are really important, but what’s the real impact of the over- and underperformance I’m talking about here? In other words, given that Kei Nishikori won 4.5 more tiebreaks last season than expected (than he “should” have won), how did that effect his overall won-loss record? And by extension, what might it mean for his match record in 2019?

The math gets hairy*, but in the end, two additional tiebreak wins are roughly equal to one additional match win. Nishikori’s 4.5 bonus tiebreaks are equivalent to about 2.25 additional match wins. He was 48-22 last year, so with neutral tiebreak luck, he would’ve gone 46-24. Of course, that still leaves some unanswered questions; translating match record to ranking points and titles is much messier, and I won’t attempt anything of the sort. His lucky tiebreaks might have converted should-have-been-losses into wins, or they might have turned gut-busting three-setters into more routine straight-set victories. But blending all the possibilities together, each player’s TBOE has a concrete value we can convert to wins.

The exact numbers aren’t important here, but the concept is. When you see an extremely good or bad tiebreak record, you don’t need to whip out a spreadsheet and calculate the precise number of breakers the player should have won. Given neutral luck, every ATP regular should have a tiebreak record between 40% and 60%–40% for the guys at the fringe, 60% for the elites. (In 2018, Federer’s expected rate was 60.1%, and Sock’s was 40.9%.) Any number out of that range, like Richard Gasquet’s 13-of-16 in 2016, is bound to come crashing back to earth, though rarely so catastrophically as the Frenchman’s did, falling to a mere 5 wins in 17 tries.

Any given tiebreak might be determined by superlative serving, daring return tactics, or sheer mental fortitude. But over time, those effects even out, meaning that no player is consistently good or bad in breakers. The better player is more likely to win, but luck has a huge say in the outcome. In the long term, that luck usually cancels itself out.

* A quick overview of the math: In a best-of-three match, there are three possible times that the tiebreak can take place. Flipping the result of a tiebreak could change the result of the first set, the second set, or the third set. The win probability impact of flipping the first set is 50%–assuming equal players, the winner has a 75% chance of winning the match and the loser has a 25% chance. The win probability effect of reversing the second set is also 50%. Either the winner takes the match (100%) instead of forcing a third set (50%), or the winner forces a third set (50%) instead of losing the match (0%). Changing the result of the third set directly flips the outcome of the match, so the win probability effect is 100%.

Every completed match has a first and second set, but fewer than 40% of ATP matches have third sets. The weighted average of 50%, 50%, and 100% is about 58%, which would be our answer if ATPers played only best-of-three matches. The math for five-setters is more involved, but the most important thing is that best-of-five gives each of the first four sets less leverage, and by extension, it does the same to tiebreaks in the first four sets. Weighing that effect combined with the frequency of best-of-five set matches would give us a precise value to convert TBOE to wins. Rather than going further down that rabbit hole, I’m happy with the user-friendly andapproximately correct figure of 50%.

Ivo Karlovic and the Odds-On Tiebreak

Italian translation at settesei.it

Ivo Karlovic is on track to accomplish something that no player has ever done before. Over the course of his career, Karlovic, along with John Isner, has set a new standard for one-dimensional tennis playing. The big men win so many service points that they are almost impossible to break, making their own service-return limitations manageable. With a player on court who maximizes the likelihood of service holds, tiebreaks seem inevitable.

This season, Karlovic has taken tiebreak-playing to a new level. Through last night’s semi-final at the Calgary Challenger (final score: 7-6, 7-6), the 6-11 Croatian has played 42 matches, including 115 sets and 61 tiebreaks. In percentage terms, that’s a tiebreak in 53% of all sets. Among player-seasons with at least 30 matches across the ATP, ATP qualifying, and ATP Challenger levels since 1990, no one has ever before topped 50%.

Even approaching the 50% threshold marks someone as very unusual. Less than 20% of tour-level sets reach 6-6, and it’s rare for any single player to top 30%. This year, only Isner and Nick Kyrgios have joined Karlovic in the 30%-plus club. Even Reilly Opelka, the seven-foot American prospect, has tallied only 31 tiebreaks in 109 sets this season, good for a more modest rate of 28.4%.

Karlovic is in truly uncharted territory. Isner came very close in his breakthrough 2007 season on the Challenger tour, playing 51 tiebreaks in 102 sets. The rest of the all-time top ten list starts to get a little repetitive:

Rank  Year  Player        Sets  TBs    TB%  
1     2018  Ivo Karlovic   115   61  53.0%  
2     2007  John Isner     102   51  50.0%  
3     2005  Ivo Karlovic   118   56  47.5%  
4     2016  Ivo Karlovic   146   68  46.6%  
5     2017  Ivo Karlovic    91   42  46.2%  
6     2006  Ivo Karlovic   106   48  45.3%  
7     2015  Ivo Karlovic   168   76  45.2%  
8     2018  John Isner     149   65  43.6%  
9     2001  Ivo Karlovic    78   34  43.6%  
10    2004  Ivo Karlovic   140   61  43.6%

* Karlovic’s and Isner’s 2018 totals are through matches of October 20th. 

For more variety, here are the 15 different players with the highest single-season tiebreak rates:

Rank  Year  Player           Sets  TBs    TB%  
1     2018  Ivo Karlovic      115   61  53.0%  
2     2007  John Isner        102   51  50.0%  
3     2004  Amer Delic         95   37  38.9%  
4     2008  Michael Llodra    117   45  38.5%  
5     2008  Chris Guccione    173   65  37.6%  
6     2002  Alexander Waske   109   40  36.7%  
7     1993  Greg Rusedski      99   35  35.4%  
8     2017  Reilly Opelka     115   40  34.8%  
9     2005  Wayne Arthurs      95   33  34.7%  
10    2004  Dick Norman        97   33  34.0%  
11    2001  Ivan Ljubicic     148   50  33.8%  
12    2004  Max Mirnyi        137   46  33.6%  
13    2014  Samuel Groth      172   57  33.1%  
14    2005  Gregory Carraz     98   32  32.7%  
15    2007  Fritz Wolmarans    80   26  32.5%

Karlovic is truly in a class by himself. He’ll turn 40 next February, but age has had little impact on the effectiveness of his serve. While he reached his career peak ranking of No. 14 back in 2008, it was more recently that his serve was at its best. In 2015, he won more than three-quarters of his service points and held 95.5% of his serve games. Both of those marks were career highs. His recent serve stats have remained among his career bests, winning 73.5% of service points in 2018, though as his ranking has tumbled, these feats have come against weaker competition, in ATP qualifying and Challenger matches.

Age has taken its toll, however, and Ivo’s return game is the victim. From 2008-12, he broke serve in more than one out of ten chances, while in 2016-18, it has fallen below 8%. Neither mark is particularly impressive–Isner and Kyrgios are the only tour regulars to break in less than 17% of games this season–but the difference, from a peak of 12.0% in 2011 to a low of 7.1% this year, helps explain why the Croatian is playing more tiebreaks than ever.

Karlovic has long been one of the most unique players on tour, thanks to his height, his extreme statistical profile, and his willingness (or maybe his need) to approach the net. As he gets older and his game becomes even more one-dimensional, it’s only fitting that he breaks some of his own records, continuing past the age when most of his peers retire in order to hit even more aces and play even more tiebreaks.

Two Servebots and Zero Tiebreaks

Embed from Getty Images

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.

The Victims of Tiebreak Pressure

The conventional wisdom is that tiebreaks are all about two things: serves and mental strength. Despite my previous efforts, pundits continue to promote the idea that big servers have an edge in the first-to-seven shootout. Less contestably, experts remind us that a lot is at stake in a tiebreak, and the player who can withstand the pressure will prevail.

Back in 2012, I wrote a few articles about tiebreaks, using a year’s worth of data from men’s matches at grand slams to discover that servers hold less of an advantage during shootouts. On average, more points go the direction of the returner. I also found that very few players exceeded expectations in tiebreaks–that is, a player’s performance in non-tiebreak situations did a very good job of predicting his chances of winning tiebreaks. Last, I determined that big servers were not any more likely than their weaker-serving peers to be among the small group of players who boasted stronger-than-expected results in shootouts.

I’ve dug into a much larger dataset to revisit the first of these conclusions. My collection of sequential point-by-point data allows us to look at over 15,000 tiebreaks from the ATP tour alone, compared to fewer than 400 that I used in my earlier study. The broader and deeper sample will allow us go beyond general statements about serve or return advantages and look at how particular players fare in the jeu décisif.

Serving under pressure

First, the basics. In these 15,000 tour-level breakers, servers won 3.4% fewer points than they did in non-tiebreak situations. This is an apples-to-apples comparison: For each player in each match, I used his rate of service points won (SPW) on non-tiebreak points and his SPW on tiebreak points. To get the aggregate figure, I calculated the average of all player-matches, weighted by the number of tiebreaks in the match.*

* Initially, I weighted by the number of tiebreak points, thinking that, say, a 16-point tiebreak should be weighted more than an 8-point breaker. That gave me results that pointed to a huge improvement in SPW in tiebreaks … because of selection bias. When a tiebreak goes beyond 12 points, it often means that both players are serving well. Thus, when two servers are hot, they must play more points, increasing their weight in this calculation. It’s always possible that an extra-long tiebreak results from a lot of return points won, but in the serve-leaning men’s game, it is the much less likely scenario.

The 3.4% decrease in serve points won means that, for instance, a server who wins 65% on his own deal in the twelve games before the tiebreak will fall to 62.8% in the breaker. Fortunately for him, his opponent probably suffers the same drop. Benefits only accrue to those players who either maintain or increase their SPW after the twelfth game of the set.

It makes sense that servers suffer a bit under the pressure. In the men’s game, at least, the returner has little to lose. Since tiebreaks are thought to be serve-dominated, every return point won seems like a lucky break. Perhaps if players knew the real numbers, the mental game would shift back in their favor. They wouldn’t have to focus on becoming superhuman, unbreakable servers; they would need only to maintain the level that got them into the tiebreak in the first place.

The less-breakables

When we split things up by player, the dataset conveniently spits out 50 players with at least 100 tiebreaks. (Well, 49, but Nicolas Mahut was next on the list, so we’ll include him also.) The guys who play the most tiebreaks are either good, lucky, or both, because they’ve managed to stick around and play so many tour matches, so the average player on this list is a little better than the average player in general.

Here are the top and bottom ten in our group of the 50 most prolific tiebreak players. The first stat, “SPW Ratio,” is the ratio between tiebreak SPW and non-tiebreak SPW, so a higher number means that the player wins more serve points in tiebreaks than otherwise. Because that stat awkwardly centers on 0.966 (the 3.4% decrease), I’ve shown another stat, called here “Ratio+,” with all numbers normalized so the average is 1.0. Again, a higher number means more serve points won in tiebreaks. The 1.09 held by John Isner at the top of the list means that the big man wins 9% more breakers than expected, where “expected” is defined as the tour-average 3.4% drop.

Player               TBs  SPW Ratio  Ratio+  
Andy Murray          141       1.05    1.09  
John Isner           368       1.05    1.09  
Nick Kyrgios         109       1.05    1.08  
David Ferrer         132       1.01    1.05  
Alexandr Dolgopolov  116       1.01    1.05  
Lukas Rosol          100       1.01    1.05  
Jo-Wilfried Tsonga   188       1.01    1.04  
Roger Federer        175       1.01    1.04  
Nicolas Mahut         94       1.01    1.04  
Benoit Paire         139       1.00    1.04  
…                                            
Denis Istomin        120       0.94    0.98  
Viktor Troicki       104       0.94    0.97  
Tomas Berdych        181       0.93    0.96  
Nicolas Almagro      118       0.93    0.96  
Fernando Verdasco    156       0.93    0.96  
Robin Haase          123       0.93    0.96  
Adrian Mannarino     101       0.91    0.95  
Jiri Vesely          105       0.90    0.93  
Ryan Harrison        100       0.89    0.92  
Pablo Cuevas         100       0.87    0.90

Most of the big names who aren’t shown above (Rafael Nadal, Novak Djokovic, Juan Martin del Potro, Milos Raonic) are a bit better than average, with a Ratio+ stat around 1.02. I’m not surprised to see Isner or Roger Federer near the top, as those two have traditionally won more tiebreaks than expected. Less predictable is the chart-topping Andy Murray, who apparently manages to raise his serve game in breakers as well as anyone else.

Warning: Negative result ahead

Murray, Isner, and Federer have consistently served well in tiebreaks over the last seven years, the time span of this dataset. But even they have had seasons where they just barely edged out the tour average: Murray was 9% better than his peers in 2013 and 10% better in 2016, serving better in tiebreaks than non-tiebreaks by a 5% and 6% margin, resepectively, but in between, he was merely average. Isner, who was at least 10% better than tour average in each season from 2012 to 2015, served slightly worse in tiebreaks than in non-tiebreaks in 2016, and is just barely better than average in his first fifty shootouts of 2018.

These are small margins, and most players do not sustain positive or negative trends from year to year. To take another example, from 2014 to 2017, Raonic recorded single-season Ratio+ numbers of 1.11, 0.92, 1.00, and 0.98. I wouldn’t recommend putting any money on Milos’s full-season 2018 figure, let alone his tiebreak serve success in 2019.

Despite the evocative appearance of Isner, Federer, and Murray at the top of the list and some players considered to be mentally weaker near the bottom, there is no evidence that this is a skill, something that players will predictably repeat, rather than luck. As I did in my match point study earlier this week, I divided each player’s tiebreaks randomly into two groups. If tiebreak serve prowess were a skill, a player’s SPW Ratio in one random group would be reasonably predictive of his corresponding number in the other group. It is not to be: No matter where we set the minimum number of tiebreaks for inclusion, there is no correlation between the two groups.

If you’ve gone through many of my posts, you’ve read something like this before. Handling the pressure and serving well in tiebreaks seems like something that certain players will do well and others will not. This overall finding isn’t sufficient proof to say that no players have tendencies in either direction–most tour pros simply don’t contest enough tiebreaks over their entire careers to know that for sure. But with possible exceptions like Isner, Murray, Federer, and the unfortunate Pablo Cuevas, players converge around the tour average, which means their service game becomes a little less effective in breakers. If someone posts a particularly high or low SPW Ratio for a season, it probably means luck figured heavily in their results. If you’re going to bet on something using these numbers, the smart money suggests that most players will revert to the mean.

Winning Return Points When It Matters

In my post last week about players who have performed better than expected in tiebreaks (temporarily, anyway), I speculated that big servers may try harder in tiebreaks than in return games.

If we interpret “try harder” as “win points more frequently,” we can test it. With my point-by-point dataset, we can look at every top player in the men’s game and compare their return-point performance in tiebreaks to their return-point performance earlier in the set.

As it turns out, top players post better return numbers in tiebreaks than they do earlier in the set. I looked at every match in my dataset (most tour-level matches from the last few seasons) for the ATP top 50, and found that these players, on average, won 5.2% more return points than they did earlier in those sets.

That same group of players saw their serve performance decline slightly, by 1.1%. Since the top 50 frequently play each other, it’s no surprise that the serve and return numbers point in different directions. However, the return point increase and the serve point decrease don’t cancel each other out, suggesting that the top 50 is winning a particularly large number of tiebreaks against the rest of the pack, mostly by improving their return game once the tiebreak begins.

(There’s a little bit of confirmation bias here, since some of the players on the edge of the top 50 got there thanks to good luck in recent tiebreaks. However, most of top 50–especially those players who make up the largest part of this dataset–have been part of this sample of players for years, so the bias remains only minor.)

My initial speculation concerned big servers–the players who might reasonably relax during return games, knowing that they probably won’t break anyway. However, big servers aren’t any more likely than others to return better in tiebreaks. (Or, put another way, to return worse before tiebreaks.) John Isner, Ivo Karlovic, Kevin Anderson, and Roger Federer all win slightly more return points in tiebreaks than they do earlier in sets, but don’t improve as much as the 5.2% average. What’s more, Isner and Anderson improve their serve performance for tiebreaks slightly more than they do their return performance.

There are a few players who may be relaxing in return games. Bernard Tomic improves his return points won by a whopping 27% in tiebreaks, Marin Cilic improves by 16%, and Milos Raonic improves by 11%. Tomic and Raonic, in particular, are particularly ineffective in return games when they have a break advantage in the set (more on that in a moment), so it’s plausible they are saving their effort for more important moments.

Despite these examples, this is hardly a clear-cut phenomenon. Kei Nishikori, for example, ups his return game in tiebreaks almost as much as Cilic does, and we would never think of him as a big server, nor do I think he often shows signs of tactically relaxing in return games. We have plenty of data for most of these players, so many of these trends are more than just statistical noise, but the results for individual players don’t coalesce into any simple, overarching narratives about tiebreak tendencies.

There is one nearly universal tendency that turned up in this research. When leading a set by one break or more, almost every player returns worse. (Conversely, when down a break, almost every player serves better.) The typical top 50 player’s return game declines by almost 5%, meaning that a player winning 35% of return points falls to 33.4%.

Almost every player fits this pattern. 48 of the top 50–everyone except for David Ferrer and Aljaz Bedene–win fewer return points when up a break, and 46 of 50 win more service points when down a break.

Pinning down exactly why this is the case is–as usual–more difficult than establishing that the phenomenon exists. It may be that players are relaxing on return. A one-break advantage, especially late, is often enough to win the set, so it may make sense for players to conserve their energy for their own service games. Looking at it from the server’s perspective, that one-break disadvantage might remove some pressure.

What’s clear is this: Players return worse than usual when up a break, and better than usual in tiebreaks. The changes are much more pronounced for some ATPers than others, but there’s no clear relationship with big serving. As ever, tiebreaks remain fascinating and more than a little inscrutable.

The Luck of the Tiebreak, 2015 in Review

Tiebreak outcomes are influenced by luck a lot more than most people think. All else equal, big servers aren’t any more successful than weak servers, and one season’s tiebreak king is often the next season’s tiebreak chump.

I’ve written a lot about this in the past, so I won’t repeat myself too much. (If you want to read more, here’s a good place to start.) In short, the data shows this: Good players win more tiebreaks than bad players do, but only because they’re better in general, not because they have special tiebreak skills. Very few players perform better or worse than they usually do in tiebreaks.

In the past, I’ve found that three players–Roger Federer, Rafael Nadal, and John Isner–consistently increase their level in tiebreaks. In other words, when you calculate how many tiebreaks Federer (or Nadal, or Isner) should win based on his overall rate of serve and return points won, you discover than he wins even more tiebreaks than that.

In any given year, some players score very high or very low–winning or losing far more tiebreaks than their overall level of play would suggest that they should. But the vast majority of those players regress back to the mean in subsequent years.

Here’s a look at which players outperformed the most in 2015 (minimum 20 tiebreaks). TBExp is the number of tiebreaks we would expect them to win, given their usual rate of serve and return points won. TBOE (Tie Breaks Over Expectations) is the difference between the number they won and the number we’d expect them to win, and TBOR is that difference divided by total tiebreaks.

Player              TBs  TBWon  TBExp  TBOE   TBOR  
Stan Wawrinka        46     34   24.9   9.1  19.8%  
Martin Klizan        25     17   12.2   4.8  19.0%  
Marin Cilic          35     26   21.0   5.0  14.2%  
Tomas Berdych        34     24   20.0   4.0  11.7%  
John Isner           64     39   31.7   7.3  11.3%  
Feliciano Lopez      42     27   22.4   4.6  11.0%  
Jiri Vesely          28     16   13.2   2.8  10.1%  
Sam Groth            31     18   14.9   3.1  10.1%  
Gilles Muller        45     27   22.7   4.3   9.5%  
Gael Monfils         28     18   15.4   2.6   9.4%

There are a lot of big servers here (more on that later) and a lot of new faces. Federer and Nadal were roughly neutral in 2015, winning exactly as many tiebreaks as we’d expect. Of the tiebreak masters, only Isner remained among the leaders. He has never posted a season below +5% TBOR, and only twice has he been below +11% TBOR. Just from this leaderboard, you can tell how elite that is.

Along with Isner, we have Marin Cilic, Feliciano Lopez, Sam Groth, and Gilles Muller, all players one would reasonably consider to be big servers. As I mentioned above, big serving doesn’t typically correlate with exceeding tiebreak expectations. It may just be a fluke: Lopez was roughly neutral in 2013 and 2014, and -15% in 2012; Groth doesn’t have much of a tour-level track record, but was -5% in 2014; Muller has been up and down throughout his career; and Cilic almost always underperformed until 2013.

Adding to the “fluke” argument is the case of Ivo Karlovic. His -14% TBOR this year was one of the worst among players who contested 20 or more tiebreaks, and he’s been exactly neutral over the last decade.

Let’s take a closer look at a few players.

Stan Wawrinka: For the second year in a row, he won at least 15% more tiebreaks than expected. Whether it’s clutch, focus, or dumb luck, the shift in his tiebreak fortunes dovetails nicely with his upward career trajectory. From 2006-13, he only posted one season at neutral or better, and his overall TBOR of -9% was one of the worst in the game for that span.

Cilic’s story is similar. Before 2013, he posted only one season above expectations. Since then, he’s won 19%, 16%, and 14% more tiebreaks than expected.

While only anecdotes, these two cases contradict an idea I’ve heard quite a bit, that players weaken in the clutch as they get older. The subject often comes up in the context of Karlovic’s tiebreak futility or Federer’s break point frustrations. It’s tough to prove one way or the other, in part because there’s no generally accepted measure of clutch in tennis. (If indeed there is any persistent clutch skill.) Using a measure like TBOR is dangerous, both because it is so noisy, and because of survivorship bias–players who get worse as they get older are more likely to fall in the rankings and play fewer tour matches as a result.

Another complicating factor is worthy of further study. To estimate how many tiebreaks a player should win, we need to take our expectation from somewhere. I’m using each player’s overall rates of serve and return points won. But if a player is trying harder in tiebreaks (assuming more effort translates into better results), we would expect that he would win more points in tiebreaks.

Isner has admitted to coasting on unimportant points, and for someone with his game style, a whole lot of return points can be classified as unimportant. Very generally speaking, the more one-dimensional the player, the more reason he has to take it easy during return games, and the more he does so, the more we would observe that he outperforms expectations in tiebreaks–simply because he sets expectations artificially low.

That might be an explanation for Isner’s consistent appearance on these leaderboards. And if we assume that players become more strategically sound as they age–or simply better at tactically conserving energy–we might have a reason why older players score higher in this metric.

Two more players worth mentioning are Milos Raonic and Kei Nishikori. They were 5th and 6th on the 2014 leaderboard, outperforming expectations by 15% and 14%, respectively. In 2015, Raonic fell to neutral, and Nishikori (in far fewer tiebreaks) dropped to -14%, nearly the bottom of the rankings. Taken together, it’s a good reminder of the volatility of these numbers. In Raonic’s case, it’s a warning that relying too much on winning tiebreaks (which, by extension, implies relying too little on one’s return game) is a poor recipe for long-term success.

Finally, some notes on the big four. Novak Djokovic and Andy Murray have never figured heavily in these discussions, both because they don’t play a ton of tiebreaks, and because they don’t persistently out- or underperform expectations. Federer and Nadal, however, were long among the best. Both have returned to the middle of the pack: Federer hasn’t posted a TBOR above 5% since 2011, and Nadal underperformed by 8.5% in 2014 before bouncing back to neutral last season.

Whatever tiebreak skill Roger and Rafa once had now eludes them. On the other hand, ten months of good tiebreak luck can happen to anyone, even a legend. If either player can recapture that tiebreak magic–even if it’s mere luck that allows them to do so–it might translate into a few more wins as they try to reclaim the top spot in the rankings.

The Dreaded Deficit at the Tiebreak Change of Ends

Italian translation at settesei.it

Some of tennis’s conventional wisdom manages to be both blindingly self-evident and obviously wrong. Give pundits a basic fact (winning more points is good), add a dash of perceived momentum, and the results can be toxic.

A great example is the tiebreak change of ends. The typical scenario goes something like this: Serving at 2-3 in a tiebreak, a player loses a point on serve, going down a minibreak to 2-4. As the players change sides, a commentator says, “You really don’t want to go into this change of ends without at least keeping the score even.”

While the full rationale is rarely spelled out, the implication is that losing that one point–going from 2-3 to 2-4–is somehow worse than usual because the point precedes the changeover. Like the belief that the seventh game of the set is particularly important, this has passed, untested, into the canon.

Let’s start with the “blindingly self-evident” part. Yes, it’s better to head into the change of ends at 3-3 than it is at 2-4. In a tiebreak, every point is crucial. Based on a theoretical model and using sample players who each win 65% of service points, here are the odds of winning a tiebreak from various scores at the changeover:

Score  p(Win)  
1*-5     5.4%  
2*-4    21.5%  
3*-3    50.0%  
4*-2    78.5%  
5*-1    94.6%

It’s easy to sum that up: You really want to win that sixth point. (Or, at least, several of the points before the sixth.) On the other hand, compare that to the scenarios after eight points:

Score  p(Win)  
2*-6     2.6%  
3*-5    17.6%  
4*-4    50.0%  
5*-3    82.4%  
6*-2    97.4%

At the risk of belaboring the obvious, when the score is close, points become more important later in the tiebreak. The outcome at 4-4 matters more than at 3-3, which matters more than at 2-2, and so on. If players changed ends after eight points, we’d probably bestow some magical power on that score instead.

Real-life outcomes

So far, I’ve only discussed what the model tells us about win probabilities at various tiebreak scores. If the pundits are right, we should see a gap between the theoretical likelihood of winning a tiebreak from 2-4 and the number of times that players really do win tiebreaks from those scores. The model says that players should win 21.5% of tiebreaks from 2*-4; if the conventional wisdom is correct, we would find that players win even fewer tiebreaks when trying to come back from that deficit.

By analyzing the 20,000-plus tiebreaks in this dataset, we find that the opposite is true. Falling to 2-4 is hugely worse than reaching the change of ends at 3-3, but it isn’t worse than the model predicts–it’s a bit better.

To quantify the effect, I determined the likelihood that the player serving immediately after the changeover would win the tiebreak, based on each player’s service points won throughout the match and the model I’ve referred to above. By aggregating all of those predictions, together with the observed result of each tiebreak, we can see how real life compares to the model.

In this set of tiebreaks, a player serving at 2-4 would be expected to win 20.9% of the time. In fact, these players go to win the tiebreak 22.0% of the time–a small but meaningful difference. We see an even bigger gap for players returning at 2-4. The model predicts that they would win 19.9% of the time, but they end up winning 22.1% of these tiebreaks.

In other words, after six points, the player with more points is heavily favored, but if there’s any momentum–that is, if either player has more of an advantage than the mere score would suggest–the edge belongs the player trailing in the tiebreak.

Sure enough, we see the same effect after eight points. Serving at 3-5, players in this dataset have a 16.3% (theoretical) probability of winning the tiebreak, but they win 19.0% of the time. Returning at 3-5, their paper chance is 17.2%, and they win 19.5%.

There’s nothing special about the first change of ends, and there probably isn’t any other point in a tiebreak that is more crucial than the model suggests. Instead, we’ve discovered that underdogs have a slightly better chance of coming back than their paper probabilities indicate. I suspect we’re seeing the effect of front-runners getting tight and underdogs swinging more freely–an aspect of tennis’s conventional wisdom that has much more to recommend itself than the idea of a magic score after the first six points of a tiebreak.