Measuring the Impact of Break Points

Yesterday I dove deep into tiebreak luck. I explained that while better players tend to win more tiebreaks, there’s no special tiebreak skill that causes certain players to perform better at the end of sets than they do at other stages of the match. Therefore, if a player has a long stretch of excellent or dismal tiebreak results, we should discard the tempting hypothesis that he or she possesses some special tiebreak talent and assume that he or she will post more average results in the future.

The same is true of break points. In any given season, you can find players who win or lose a disproportionate number of break points, and it’s tempting to point to mental strength by way of explanation. Yet more often that not, the unusual results disappear, along with any convincing case that we’ve identified a notably steely or flimsy tennis brain.

To quantify those over- and underachievements, I’ve attempted to measure the number of break points converted compared to the “expected” number, where the expectation is defined by how often the player wins return points. (It’s a bit more complicated than looking up a player’s single season return-points-won (RPW) rate. Instead, we consider their RPW for each match, and weight the matches according to how many break point opportunities occurred in the match.) For example, Gael Monfils converted 146 of his 317 break point chances last year, good for a 46.1% win rate. That far outstrips his weighted RPW of 38.7%. He claimed 23 more break points than expected, or an excess of 19%. Parallel to my approach with tiebreaks, I’ve named those stats, so the counting stat is Break Points Over Expectation (BPOE) and the rate stat is Break Points Overperformance Rate (BPOR).

(On average, returners win slightly fewer break points than non-break points. I’ve adjusted the “expected” level downward by 1.4% to account for this.)

Monfils was an outlier, the only player in 2018 to exceed +20 BPOE, and the only player with 40-plus matches to post a BPOR of more than 15%. Yet there was little in his past performance that would have told us what was coming. From 2009 to 2017, he had three negative seasons, two years indistinguishable from neutral, and four above average. Over the entire span, he won break points less than one percent more often than expected. The Frenchman’s pressure-point success in 2018 could be thanks to some newfound mental strength, but if history is any guide, he won’t continue to display whatever mix of luck and nerves led him to post his circuit-leading figures.

Here are the best and worst break point performances, by BPOE, posted by ATPers with at least 20 tour-level matches last year:

Player                 Chances  Won   BPOE  BPOR  
Gael Monfils               317  146   23.4  1.19  
Mackenzie Mcdonald         252  116   19.0  1.20  
Michael Mmoh               129   63   16.9  1.37  
Malek Jaziri               298  134   16.2  1.14  
Pierre Hugues Herbert      297  126   16.1  1.15  
Adrian Mannarino           318  136   14.1  1.12  
Ricardas Berankis          235  103   13.8  1.15  
Sam Querrey                290  118   13.8  1.13  
Martin Klizan              313  139   13.5  1.11  
Jan Lennard Struff         272  118   13.4  1.13  
                                                  
Marton Fucsovics           414  162  -11.5  0.93  
Filip Krajinovic           238   86  -11.8  0.88  
Evgeny Donskoy             239   79  -11.9  0.87  
Stan Wawrinka              217   66  -11.9  0.85  
Aljaz Bedene               303  108  -12.9  0.89  
John Isner                 308   85  -13.0  0.87  
Mischa Zverev              347  123  -14.1  0.90  
Marin Cilic                568  209  -18.1  0.92  
Joao Sousa                 484  176  -21.6  0.89  
Novak Djokovic             617  246  -21.7  0.92

It’s striking to see Novak Djokovic at the bottom of the list, nearly as bad or unlucky as Monfils was good or fortunate. Yet Novak’s story is surprisingly similar to Gael’s. From 2009 to 2017, his overall BPOR was 0.997–almost precisely neutral–and he posted nearly as many positive seasons as negative ones.

Yep, it’s random

To give more player-specific examples would only belabor the point: A player’s performance on break points (independent of his overall return-point skill) has no relationship from one year to the next. I found 700 pairs of consecutive player-seasons between 2009 and 2018 (for example, Djokovic’s 2017 and 2018) and found that the correlation between the two seasons was effectively zero. (r^2 = 0.002)

Here’s one more illustration of the point. This table shows the ten players who recorded the highest 2017 BPOR figures of those men who played at least 20 ATP matches in both 2017 and 2018. The right-most column shows what they did the following year:

Player             2017 BPOR  2018 BPOR  
Damir Dzumhur           1.16       1.05  
Alexander Zverev        1.15       1.02  
Nicolas Kicker          1.15       1.04  
Peter Gojowczyk         1.14       0.92  
Dusan Lajovic           1.13       1.04  
Mikhail Kukushkin       1.13       0.94  
Mischa Zverev           1.13       0.90  
John Isner              1.12       0.87  
Andrey Rublev           1.12       0.96  
Thiago Monteiro         1.12       1.17  
AVERAGE                 1.14       0.99

Only Thiago Monteiro continued to be successful enough to maintain a place amid the tour leaders; John Isner’s follow-up campaign was so different that he registered as one of the tour’s worst in 2018. Taken together, five of 2017’s top ten ended 2018 below average, and the ten men combined for a BPOR just a bit worse than neutral. This is all just another way of saying we’re looking at something indistinguishable from chance.

Putting a price tag on good fortune

We’ve established that break point performance in the present has nothing to tell us about break point performance in the future. But as I pointed out in yesterday’s post about tiebreaks, that very lack of predictiveness has value.

Monfils’s BPOE of +23 helped his overall cause, helping him rack up more victories in 2018 than he otherwise would have. His break point results probably boosted his ranking and prize money tally. Reverting to neutral break point performance won’t knock him off tour, but assuming he continues to serve and return at the same level he did last year, a more pedestrian BPOE could hurt his cause. But how much?

Yesterday I suggested that two additional tiebreaks are equal to one additional win. Break points are a bit more complicated–clearly a single break point is not as valuable as an entire tiebreak, both because it is a single point and because it rarely offers the player a chance to finish off an entire set or match. On the other hand, break points are more numerous, and figures Monfils’s +23 and Djokovic’s -21 are more extreme than the most unexpected tiebreak performances.

Measuring high-leverage points

The key to measuring the impact of break points is the general concept of win probability, and the more specific notion of leverage. (Leverage is often referred to as volatility or importance; these are all the same basic idea.) Win probability is simply a measure of each player’s chances of winning the match at any given stage. Leverage is an index of how much a single point can affect that probability. Say two equal players embark on a new match. Before the first ball is struck, each have a 50% chance of emerging victorious. If winning the first point increases the server’s chance of winning to 51% while losing it decreases his probability to 49%, we would say that the leverage of the first point is 2%–the difference between the win probabilities that would result from winning or losing the point.

The more crucial the point, the higher the leverage. The typical point is well below 5%, but a truly high-pressure moment, like 5-6 in a third-set tiebreak, can be as high as 50%.

Win probability stats depend a great deal on the inputs you choose, so there’s no single mathematically correct leverage measurement at any given moment. If you think two players are equal, your estimate of the win probability at the start of the match is very different than if you think one of the competitors is a heavy favorite. Those judgements affect the leverage of every point as well. Still, for aggregates of large numbers of matches–say, an entire season–we can get a general idea of the value of break points.

Necessary assumptions

If we make the simple but clearly wrong assumption that all players are equal, the leverage of the average point on the ATP tour last year was 4.6%, and the leverage of the average break point on tour last year was 10.5%. Those numbers are useful as a starting point, but they are clearly too high; when we accept that most matches are not contested between players of equal skill, we realize that any given break point isn’t quite that important–if Djokovic fails to convert one against Monteiro, he’ll remain almost certain to win the match.

One alternative approach is to assume that each player’s skill level is represented exactly by their performance in a given match. So if Djokovic plays Monteiro and wins 80% of service points, while Monteiro wins only 60%, we could calculate the win probability and leverage of every point using those numbers. Using that method, we get a leverage of 2.9% on the average point and 6.5% on the average break point.

The second assumption is also not exactly right, but it probably gets closer to the truth than the first. Keeping in mind that it’s an approximation, let’s use a break point leverage of 7.5%. That figure means that, on average, changing the result of a single break point affects the win probability of a single match by 7.5%. Another of way of thinking about it–the one most relevant to the task at hand–is that winning a break point instead of losing it is equivalent to winning 7.5% (or about one-thirteenth) of a match.

Break points are (fractions of) wins

Returning to the concept of BPOE, we can now say that 13 additional break points is equivalent to one additional win. Monfils’s 2018 tally of +23 was good for almost two extra victories over the course of the season, and Djokovic’s count of -21 would, on average, cost him 1.5 matches. Given the multitude of other factors influencing each man’s performance, it’s unreasonable to expect either player’s won-loss record in 2019 to bounce back so predictably and precisely. (Especially since it’s impossible to win 1.5 matches.) But in the unlikely event that all else is equal, we should expect those advantages and disadvantages to disappear in the new season.

The range of minus-21 to plus-23 break points is a decent representation of how extreme break point luck can be. Since 2009, only four players have posted single-season numbers above +23, including the most extreme BPOE of +34, accumulated by Damir Dzumhur in 2017. (Dzumhur was hit hard by the ensuing reverse in fortune: His 2017 tour-level record was 37-24, but in 2018, when his BPOE fell to a still-lucky +8, his record dropped to 25-31.) At the opposite extreme, Dominic Thiem suffered from a tally of 28 break points below expectations in 2015. A year later, he bounced back to minus-5, and his ranking improved from 19th to 9th. Despite the roller-coaster descents and climbs of Dzumhur and Thiem, the range of the break-point-luck effect appears to be about five wins, from about minus-2 wins at the low end to plus-3 for the players most favored by fortune.

For most players in most seasons, however, break point luck is little more than a rouding error. And while it’s easy to get sucked into the measurements I’ve laid out, that’s the most important point of all: Just like there’s no special tiebreak factor, there’s no reason to think that certain players are somehow better at break points than others. The better a player’s return game, the more break points he’ll convert. Anything beyond that will eventually regress to the mean. And for players with extremely strong or weak break point performances, that regression is likely to have effects that extend to the overall won-loss record, ranking, and beyond.

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%.

Podcast Episode 42: 2019 Season Preview

Episode 42 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, rings in 2019 with a discussion of the players we’re most looking forward to watching in the new year. The WTA offers us a wealth of promising future stars, and the ATP continues to provide a generation of potential contenders who may finally break through.

We also delve into the ATP Cup and the possible demise of Hopman Cup, as well as the complexities and implications of the new structure of the ITF rankings and transition tour.

Thanks for listening!

(Note: this week’s episode is about 55 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.

Rethinking the Mental Game

Italian translation at settesei.it

Everyone seems to agree that a huge part of tennis is mental. It’s less clear exactly what that means. Pundits and fans often say that certain players are mentally strong or mentally weak, attributes that help explain the gap when there’s a mismatch between talent and results.

Here are three more adjectives you’ll hear in ‘mental game’ discussions: clutch, streaky, consistent. I’ve frequently railed against commentators’ overuse of these terms. For instance, hitting an ace facing break point is ‘clutch,’ in the sense that the player executed well in a key moment. But that doesn’t mean the player himself can be described as clutch. Just because he sometimes performs well under pressure doesn’t mean he does so any more than the average player. Same goes for ‘streaky’–humans tend to overgeneralize from small samples, so if you see a player hit three down-the-line backhand winners in a row, you’ll probably think it’s a hot streak, even though such a sequence will occasionally arise by luck alone.

Some players probably are more or less clutch, more or less streaky, or more or less consistent than their peers, even beyond what can be explained by chance. At the same time, no tour pro is so much more or less clutch that their high-leverage performance explains a substantial part of their success or failure on tour. Most players win about as many tiebreaks as you’d expect based on their non-tiebreak records and convert about as many break points as you’d predict based on their overall return stats. Nothing magical happens in these most-commonly cited pressure situations, and no player becomes either superhuman or completely hopeless.

If you’re reading my blog, you’ve probably heard most of this before, either from me or from innumerable other sports analysts. I’m not taking the extreme position that there is no clutch (or streakiness or consistency), but I am pointing out that these effects are small–so small that we are unlikely to notice them just by watching matches, and sometimes so tiny that even analysts find it difficult to differentiate them from pure randomness.

Still, we’re left with the unanimous–and appealing!–belief that tennis is a mental game. In trying to explain various simplified models, I’ll often say something like, “this is what it would look like if players were robots.” Even though some of those models are rather accurate, I think we can all agree that players aren’t robots, Milos Raonic notwithstanding.

Completely mental

An extreme version of the ‘mental game’ position is one I’ve heard attributed to James Blake, that the difference between #1 and #100 is all mental. (I’m guessing that’s an oversimplification of what Blake thinks, but I’ve heard similar opinions often enough that the general idea is worth considering.) That’s a bit hard to stomach–does anybody think that Radu Albot (the current No. 99) is as talented as Rafael Nadal? But once we backtrack a little bit from the most extreme position, we can see its appeal. At the moment, both Bernard Tomic and Ernests Gulbis are ranked between 80 and 100. Can you say with confidence that those guys aren’t as talented as top-tenners Kevin Anderson or Marin Cilic? Yet Tomic often excels in pressure situations, and Cilic is the one known to crumble.

The problem with Tomic, Gulbis, and so many of the innumerable underachievers in the history of sport, isn’t that they fall apart when the stakes are high. We can all remember matches–or sets, or other long stretches of play–in which a player seems uninterested, unmotivated, or just low-energy for no apparent reason. Even accounting for selection bias, I think the underachievers are more likely to provide these inexplicably mediocre performances. (Can you imagine Nadal appearing unmotivated? Or Maria Sharapova?) In a very broad sense, I could be talking about streakiness or consistency here, but I don’t think it’s what people usually mean by those two terms. It operates at a larger scale–an entire set of mediocrity instead of say, three double faults in a single game–and it offers us a new way of thinking about the mental aspect of tennis.

Focus

Let’s call this new variable focus. There are millions of potential distractions, internal and external, that stand in the way of peak performance. The more a player is able to ignore, disregard, or somehow overcome those distractions, the more focused she is.

Imagine that every player has her own maximum sustainable ability level, and on a scale of 1 to 10, that’s a 10. (I’m saying ‘sustainable’ to make it clear that we’re not talking about ninja Radwanska behind-the-back drop-volley stuff, but the best level that a player can keep up. Nadal’s 10 is different from Albot’s 10.) A rating of 1, at the bottom of the scale, is something we rarely see from the pros–imagine Guillermo Coria or Elena Dementieva getting serve yips. The more focused the player, the more often she’s performing at a 10 and, while she may not be able to sustain that, the more focused player remains closer to a 10 more of the time.

This idea of ‘focus’ sounds a lot like the old notion of ‘consistency’, and maybe it’s what people really mean when they call a player consistent. But there are several reasons why I think it’s important to move away from ‘consistency.’ The first one is pedantic: ‘consistent’ isn’t necessarily good. If you tell a player to be consistent and she hits nothing but unforced errors on her forehand, she has followed your directions by being consistently bad. More seriously, ‘consistency’ is often conflated with ‘low-risk’, which is a strategy, not a positive or negative trait. A player like Petra Kvitova will never be consistent–her signature level of aggression will always result in plenty of errors, sometimes ugly ones, and occasionally in ill-timed bunches. Even an optimized strategy for a highly-focused Kvitova will appear to be inconsistent.

If you’re the type of person who thinks a lot about tennis, you probably see the limitations in my definition of consistency. I agree: The concept I’ve knocked down is a bit of a strawman. If I could do a better job of consisely defining what tennis people talk about when they talk about consistency, I would–again, part of the problem is that the term is overloaded. Even if you mean ‘focus’ when you’re saying ‘consistency,’ I think it’s valuable to use a separate term with less baggage.

Chess

Is ‘focus’ any better than the other mental-game concepts I’ve knocked down? We can objectively measure clutch effects, but it’s a lot harder to look at the data from a match or an entire season and quantify a player’s level of focus.

Nonetheless, I strongly suspect that at the elite level, focus varies more than, say, micro-level streakiness. Put another way: The difference in focus among top players has the potential to explain much of their difference in performance.

I started to think about the importance of focus–again, the ability to sustain a peak or near-peak level for long periods of time–while following last month’s World Chess Championship between Magnus Carlsen and Fabiano Caruana. (I wrote about the chess match here.) Chess is very different from tennis, of course. But because it doesn’t rely on physical strength, speed, or agility at all, it has a much stronger claim to the ‘mental game’ moniker than tennis does. While flashes of brilliance have their place in chess, classical games require sustained concentration at a level that few of us can even fathom. One blunder against an elite player, and you might as well give up and get some extra rest before the next game.

A common stereotype of a chess grandmaster is an old man, whose decades of knowledge and savvy help him brush aside younger upstarts. Yet Carlsen and Caruana, the two best chess players in the world, are in their mid-20s. The current top 30 includes only four men born before 1980. 12 of the top 30 were born in the 1990s, two of them since 1998. The age distribution in elite chess is awfully similar to that of elite tennis.

The aging curve in tennis lends itself to easy explanations: Players can start reaching the top when they hit physical maturity in their late teens, they continue to improve throughout their 20s as they gain experience and enjoy the benefits of physical youth, and then physical deterioration creeps in, beginning to have an effect in the late 20s or early 30s and increasing in severity over time. There’s obviously some truth in that. No matter how important the mental aspect of tennis, it’s hard to compete once you’ve lost a step, and even harder with chronic back or knee pain.

Yet the chess analogy persists: If tennis were mental, with much of the variation between elites explained by focus, the aging curve would look about the same. As modern science has improved training, nutrition, and injury recovery–thus reducing the effect of physical deterioration–tennis’s aging curve has developed a flatter plateau in the late 20s and 30s. In other words, as physical risks are mitigated, the elite career trajectory of tennis looks even more like that of chess.

Thinking ahead

For now, this is just a theory. Maybe you agree with me that it’s a very appealing one, but it remains untested, and it’s possibly very difficult to test at all.

If sustained focus is such a key factor in elite tennis performance, how would we even identify it? The most direct way would be to avoid the tennis court altogether and devise experiments so that we could measure the concentration of top players. I doubt we could convince the ATP top 100 to join us in the lab for a fun day of testing. There is some long-term potential, though, as national federations could do just that with their rising stars. Some might be doing so already; some professional baseball and American football teams administer cognitive tests to potential signees as well.

Unfortunately, we can’t make the best tennis players in the world our guinea pigs. If we looked instead at match-level results, we could try to measure focus using a similar approach to what I’ve done before in the name of quantifying consistency (oops!). My earlier algorithm attempted to measure the predictability of a player’s results–that is, is the 11th best player usually losing to the top ten and beating everyone else, or are his results less predictable? That’s not what we’re interested in here, because by that definition, ‘consistency’ isn’t necessarily good.

We could work along similar lines, though. Given a year or more or results, we could estimate a player’s peak level, perhaps by taking the average of his five best results. (His absolute best result might be the result of an injured opponent, an untimely rain delay, or something else unusual.) That would indicate the level that marks a ’10’ on his personal scale of 1 to 10. Then, compare his other results to that peak. If most of his results are close to that level–like the ‘consistent’ player who loses to the top ten and beats everyone else–he appears to be focused, at least from one match to the next. If he has a lot of bad losses by comparison, he is failing to sustain a level we know he’s capable of.

That sort of approach isn’t entirely satisfying, as is often the case when working with match-level stats. Perhaps with shot-level or camera-based data, we could do even better. Using a similar approach to the above–define a peak, compare other performances to that peak–we could look at serve speed or effectiveness, putting returns in play, converting opportunities at net, and so on. It would be complicated, in part because opponent quality and surface speed always have the potential to impact those numbers, but I think it’s worth pursuing.

If I’m right about this–that tennis isn’t just a mental game, it’s a game heavily influenced by sustained concentration–the long term impact is on player development. Academies and coaches already spend plenty of time off court, talking tactics and utilizing insights from psychology. This would be a further step in that direction.

The mental side of tennis–and sports in general–remains a huge mess of unknowns. As the next generation of elite players tries to develop small technical and tactical improvements in order to find an edge, perhaps the mental side is the next frontier, one that would finally enable a new generation to sweep away the old.

Podcast Episode 41: A Breakthrough for Zverev, a Season In the Books, and a New Team Event

Episode 41 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, focuses on the man of the hour, Alexander Zverev, who defeated Roger Federer and Novak Djokovic to win the season-ending event and record his career-best result. We discuss how he did it, and what it says about his chances to take a step forward at majors in 2019.

We also talk about the opportunity for longer-format matches at the Tour Finals, especially in doubles, and the questionable aggregate stats that TennisTV introduced during the week in London. Finally, we cover the plans for the first ATP Cup in January 2020, as well as a quick preview of this weekend’s Davis Cup final between France and Croatia.

Thanks for listening!

(Note: this week’s episode is about 61 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.

Podcast Episode 40: Fed Cup, the ATP Tour Finals, and a Sandbox Full of Rule Changes

Episode 40 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, starts with the Czech Republic’s victory in the Fed Cup final, and quickly diverts to a discussion of how we can evaluate players, and whether stylistic varietey is all it’s cracked up to be.

We preview the ATP Tour Finals, with a look at Djokovic, Federer, and a half-dozen dark horses, then discuss the plethora of experiments in progress at the NextGen Finals in Milan, including a fast-four-like scoring system, which neither of us are all that excited about, even if it’s supposed to make things more, well, exciting.

Thanks for listening!

(Note: this week’s episode is about 57 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.

Podcast Episode 39: Khachanov’s Paris Title, and WTA Finals in Review

Episode 39 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, covers the breakthrough Masters title of Karen Khachanov, along with the memorable semi-final between Novak Djokovic and Roger Federer. We also give an update on Jack Sock’s career choices and the career accomplishments of doubles whiz Rajeev Ram.

The second half of the episode is our recap of the WTA Finals in Singapore and the Elite Trophy in Zhuhai. We get distracted from our discussion of Svitolina, Sabalenka, and Barty by delving into the weeds of tournament formats, considering the pros and cons of the various round-robin and wild-card approaches that events use this time of year.

Thanks for listening!

(Note: this week’s episode is 61 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.

Podcast Episode 38: A Look at the WTA Finals Field

Episode 38 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, is our preview of the WTA tour championships. We look at Sloane’s weak position on the Elo table, Wozniacki’s comments about the strength of the field, and the strongest tacticians of the elite eight. We also consider the shifting career forecast of the resurgent Luxembourg finalist, Belinda Bencic.

We also have quick takes on Ivo Karlovic, who is setting records both in age and tiebreak frequency, and the new fifth-set tiebreak rule at Wimbledon. Thanks for listening!

(Note: this week’s episode is about 65 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.

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.

Daniil Medvedev’s Leading Elo Indicator

Italian translation at settesei.it

It is shaping up to be a breakthrough season for 22-year-old Russian Daniil Medvedev. His Tokyo title two weeks ago was his first at the ATP 500 level and his third on the season, after earlier triumphs in Sydney and Winston-Salem. The run in Japan was a particularly notable step, since he knocked out three top-20 players along the way. He had only four top-20 victories in the entire season leading up to Tokyo, and two of those were against the slumping Jack Sock.

His ATP ranking is rising alongside his results. The Winston-Salem title moved him into the top 40, and the Tokyo trophy resulted in a leap to No. 22. After a first-round win in Shanghai last week, Medvedev crept to his current career-high of No. 21. With a couple of wins in Moscow this week, he could overtake Milos Raonic and reach the top 20.

The improvement on the ATP ranking table is nothing next to the Russian’s race to the top of the Elo list. Last Monday, with the Japanese title in the books, Medevdev rose to No. 8 on my men’s Elo ranking. Since then, he has dropped two places but remains in the top ten, ahead of Marin Cilic, Kevin Anderson, and a host of others who outrank him on the official ATP list.

Given the discrepancy, what do we believe? Is Medvedev inside the top 10 or outside the top 20? Is Elo a leading indicator–that is to say, an early-warning signal for future ATP ranking milestones–or a misleading one? Elo is designed to be forward-looking, tuned to forecast upcoming match outcomes and weighting wins and losses based on the quality of the opponent. The official rankings explicitly consider a year’s worth of results, with no adjustments for quality of competition. In theory, Elo should be the better of the two measures for predicting longer-term results, but that assumes the algorithm works well, and that it doesn’t overreact to short-term successes. Let’s take a look at past differences between the two systems and see what the future might hold for the 22-year-old.

Precedents

Since 1988, 102 men have debuted in the ATP top ten. A slightly larger number, 113, have shown up in the top ten of my Elo ratings. There’s a very substantial overlap between the two, with 94 names appearing in both categories. Thus, 8 players have reached the ATP top ten without clearing the Elo threshold, while 19 have rated a spot in the Elo top ten without convincing the ATP computer to agree.

Here are the eight ATP top-tenners whose Elos have never merited the same status:

Player               ATP Top Ten Debut  ATP Top Ten Weeks  
Jonas Svensson                19910325                  5  
Nicolas Massu                 20040913                  2  
Radek Stepanek                20060710                 12  
Jurgen Melzer                 20110131                 14  
Juan Monaco                   20120723                  8  
Kevin Anderson                20151012                 31  
Pablo Carreno Busta           20170911                 17  
Lucas Pouille                 20180319                  1

A few of these players could still make progress on the Elo list, especially Kevin Anderson, who is currently 11th, a miniscule five points behind Medvedev.

Here is the longer list of Elo top-ten players without any weeks in the official top ten:

Player                 Elo Top Ten Debut  Elo Top Ten Weeks  
Carl Uwe Steeb                1989/05/22                  3  
Andrei Cherkasov              1990/12/11                  1  
Goran Prpic                   1991/05/20                  1  
David Wheaton                 1991/07/08                  9  
Jerome Golmard                1999/05/03                  2  
Dominik Hrbaty                2001/01/15                  2  
Jan Michael Gambill           2001/04/06                  6  
Nicolas Escude                2002/02/25                  4  
Younes El Aynaoui             2002/05/20                  2  
Paul Henri Mathieu            2002/10/14                  8  

Player                 Elo Top Ten Debut  Elo Top Ten Weeks
Agustin Calleri               2003/05/19                  2  
Taylor Dent                   2003/10/06                 10  
Andrei Pavel                  2004/05/10                  2  
Robby Ginepri                 2005/10/24                  1  
Ivo Karlovic                  2007/11/12                  3  
Roberto Bautista Agut         2016/02/22                  1  
Nick Kyrgios                  2016/03/04                 62  
Stefanos Tsitsipas            2018/08/13                  3  
Daniil Medvedev               2018/10/08                  2

* I define ‘weeks’ a little differently for Elo ratings, as ratings are generated only for those weeks with an ATP-level tournament or Davis Cup tie.

Most of these guys came very close to cracking the ATP top ten. For example, David Wheaton’s peak ranking was No. 12. With the exception of Nick Kyrgios, no one spent more than ten weeks in the Elo top ten without eventually reaching the same standard according to the ATP formula. This list shows that it’s possible to have a brief peak that cracks the Elo top ten but doesn’t last long enough to reflect the kind of success that the official ranking system was designed to reward. About one in six players with a top-ten Elo rating never reached the ATP top ten, though as we can see, the odds of remaining an Elo-only star fall quickly with each additional week in the top ten.

Kyrgios is a perfect example of the differences between the two approaches to player ranking. The Australian has recorded a number of high-profile upsets, which are the fastest way to climb the Elo list. But knocking out the second-ranked player in the world, as Kyrgios did to Novak Djokovic at Indian Wells last year, doesn’t have much impact on the ATP ranking when it happens in the fourth round. Usually, a player who can oust the elites will start piling up wins in a form that the official computer will appreciate. But Kyrgios, unlike just about every player in history with his talent, hasn’t done that.

In short, Elo will always elevate a few players to top-ten status even if they’ll never deserve the same treatment from the ATP formula. It’s too early to say whether Medvedev fits that mold. But where Elo really excels is identifying top players before the ATP computer does. Of the 94 cases since 1988 in which a man debuted in both top tens, Elo was first to anoint the player a top-tenner in 76 of them–better than 80%. The official rankings were first 10 times, and the two systems tied in the other eight instances. On average, players reached the Elo top ten about 32 weeks before the ATP top ten.

Here are the 11 most extreme gaps in which Elo got there first, along with the top-ten debuts of the Big Four:

Player               ATP Debut   Elo Debut  Week Diff  
Mariano Puerta      2005/07/25  2000/06/12        267  
Marc Rosset         1995/07/10  1990/11/05        244  
Fernando Gonzalez   2006/04/24  2002/10/07        185  
Guillermo Canas     2005/05/09  2002/08/05        144  
Mikhail Youzhny     2007/08/13  2004/11/15        143  
Gaston Gaudio       2004/06/07  2002/04/29        110  
Richard Gasquet     2007/07/09  2005/06/20        107  
Tomas Berdych       2006/10/23  2004/10/11        106  
Robin Soderling     2009/10/19  2007/10/08        106  
Mark Philippoussis  1999/03/29  1997/03/24        105  
Jack Sock           2017/11/06  2016/01/18         94  
                                                       
Player               ATP Debut   Elo Debut  Week Diff  
Roger Federer       2002/05/20  2001/02/19         65  
Andy Murray         2007/04/16  2006/08/21         34  
Novak Djokovic      2007/03/19  2006/07/31         33  
Rafael Nadal        2005/04/25  2005/02/21          9

And in case you’re curious, the ten cases in which the ATP computer beat Elo to the punch:

Player              ATP Debut   Elo Debut  Week Diff  
Stan Wawrinka      2008/05/12  2010/10/25        128  
David Ferrer       2006/01/30  2007/05/28         69  
Janko Tipsarevic   2011/11/14  2012/05/13         26  
Rainer Schuettler  2003/06/09  2003/08/25         11  
Tommy Robredo      2006/05/08  2006/07/24         11  
Fernando Verdasco  2009/02/02  2009/04/06          9  
Albert Costa       1997/04/21  1997/05/26          5  
Nicolas Almagro    2011/04/25  2011/05/22          4  
John Isner         2012/03/19  2012/04/15          4  
Jiri Novak         2002/10/14  2002/10/21          1

The 32-week average difference is suggestive. As I’ve noted, Elo ratings are optimized to forecast the near future, so at least in theory, they reflect each player’s level right now. The ATP algorithm tallies each man’s performance over 52 weeks, with equal weight given to the first and last weeks in that timeframe. Setting aside improvement and decline due to age, that means the ATP computer is telling us how each player was performing, on average, 26 weeks ago. If Medvedev continues to oust top-20 players on a regular basis and claims another 500-level title or two, he could well be 26 or 32 weeks away from a top-ten debut.

Elo isn’t designed to make long-term forecasts–the tools needed to do so, for the most part, have yet to be invented. And the system occasionally gives high ratings to players who don’t sustain them for very long. But in general, a superlative Elo rating is a sign that a similar mark on the ATP ranking list isn’t far behind. So far, Kyrgios has managed to defy the odds, but the smart money still points to an eventual ATP top-ten debut for Medvedev.