What I Should’ve Known About Playing Styles and Upsets

In the podcast Carl Bialik and I recorded yesterday, I mentioned a pet theory I’ve had for awhile, that upsets are more likely in matches between players with contrasting styles. The logic is fairly simple. If you have two counterpunchers going at it, the better counterpuncher will probably win. If two big servers face off, the better big server should have no problem. But if a big server plays a counterpuncher … then, all bets are off.

We’ve seen Rafael Nadal struggle against the likes of John Isner and Dustin Brown, and and we’ve seen big servers neutralized by their opposites, as in Marin Cilic’s 1-6 record against Gilles Simon. There are upsets when similar styles clash, as well, but as untested theories go, this one is appealing and not obviously flawed.

Then, to kick off the 2019 Australian Open, Reilly Opelka knocked out Isner. Playing styles don’t come much more evenly matched, and the veteran was the heavy favorite. It was a perfect example of the kind of match I would expect to follow the script, yet the underdog came out on top. They played four tiebreaks and there were only two breaks of serve, but Opelka didn’t even need the Australian Open’s new fifth-set 10-point tiebreak. While it’s just one match, of course, it suggested that I ought to look more closely at my assumptions.

After a couple of hours playing with data this afternoon, my theory is no longer untested … and it turned out to be flawed. Fortunately, it isn’t just another negative result. Playing style is related to upset likelihood, but not in the way I predicted.

Measuring predictability

Let me explain how I tested the idea, and we’ll work our way to the results. First, I used used Match Charting Project data to calculate aggression score for every ATP player with at least 10 charted matches since 2010. Aggression score is, essentially, the percentage of shots that end the point (by winner, unforced error, or inducing a forced error), as will serve as our proxy for playing style. That gives us a group of 106 players, from the conservative Simon and Yoshihito Nishioka with aggression scores around 13%, to the freewheeling Brown and Ivo Karlovic, with scores nearing 30%. I divided those 106 players into quartiles (by number of matches, not number of players, so each quartile contains between 21 and 31 players) so we could see how each general playing style fares against the others. Here are the groups:

(Aggression score conflates two things: big serving/big hitting and tactical aggression. Isner is sometimes not particularly aggressive, but because of his size and serve skill, he is able to end points so frequently that, statistically, he appears to be extremely aggressive. Accordingly, I’ll refer to “big servers” and “aggressive players” interchangeably, even though in reality, there are plenty of differences between the two groups.)

Limiting our view to these 106 men, I found just over 11,000 matches to evaluate and divided them into groups based on which quartiles the two players fell into. Each of the ten possible subsets of matches, like Q1 vs Q2, or Q4 vs Q4, contains at least 400 examples.

For every match, I used surface-adjusted Elo ratings to determine the likelihood that the favorite would win. That gives us pre-match odds that aren’t quite as accurate as what sportsbooks might offer, though they’re close.

Those pre-match odds are key to determining whether certain groups are more predictable than others. If there are 100 matches in which the favorite is given a 60% chance of winning, and the favorites win 70 of them, we’d say that the results were more predictable than expected. If the favorites win only 50, the results were less predictable.

Goodbye, pet theory

For the matches in each of the ten quartile-vs-quartile subsets, I calculated the average favorite’s chance of winning (“Fave Odds”), then compared that to the frequency with which the favorites went on to win (“Fave Win%”). The table below shows the results, along with the relationship between those two numbers (“Ratio”). A ratio of 1.0 means that matches within the subset are exactly as predictable as expected; higher ratios mean that the favorites were even better bets than the odds gave them credit for, and lower ratios indicate more upsets than expected.

[table id=1 /]

There’s a striking finding here: The largest ratio, marking the most predictable bucket of matches, is for the most conservative pairs of players, while the smallest ratio, pointing to the most frequent upsets, is for the most aggressive players.

Before analyzing the relationship, let’s check one more thing. The very best players aren’t evenly divided throughout the quartiles, since Q1 has two of the big four. Elo-based match predictions–one of the building blocks of these results–are tougher to get right for the best players and the most uneven matchups, so we need to be careful whenever the elites might be influencing our findings. Therefore, let’s look at the same numbers, but this time for only those matches in which the favorite has a 50% to 70% chance of winning. This way, we exclude many of the best players’ matchups and all of their more lopsided contests:

[table id=2 /]

We discard about 40% of our sample, but the predictability trend remains the generally the same. In both the overall sample and the narrower 50%- to 70%-favorite subset, the strongest relationship I could find was between the predictability ratio and the quartile of the less aggressive player. In other words, a counterpuncher is likely to have more predictable results–regardless of whether he faces a big server, a fellow counterpuncher, or anyone in between–than a more aggressive player.

Back to basics

My initial theory is clearly wrong. I expected to find that Q1 vs Q1 matches were more predictable than average, and I was right. But by my logic, I also guessed that Q4 vs Q4 matches went according to script, and that other pairings, like Q1 vs Q4, would be more upset-prone. I would have done better had I let the neighbor’s cat make my predictions for me.

Instead, we find that that matches with more aggressive players are more likely to result in surprises. That doesn’t sound so groundbreaking, and it’s something I should’ve seen coming. Big servers tend to hold serve more often and break serve less frequently, meaning that their matches end with narrower margins, opening the door for luck to play a larger role, especially when sets and matches are determined by tiebreaks.

After all this, you might be thinking that I’ve squandered my afternoon, plus another few minutes of your attention, arriving at something obvious and unremarkable. I agree that it’s not that exciting to proclaim that big servers are more influenced by luck. But there’s still a useful–even surprising–discovery buried here.

Exponential upset potential

We know that the most one-dimensional players are more subject than others to the ups and downs of luck, thanks to the narrow margins of tiebreaks. For a man who rarely breaks serve, no match is a guaranteed win; for a man who rarely gets broken, no opponent is impossible to beat. However, I would have expected that the unpredictability of big servers was already incorporated into our match predictions, via the Elo ratings of the big servers. If a player has unusually random results, we’d expect his rating to drift toward tour average. That’s one reason that it’s very difficult for poor returners to reach the very top of the rankings.

But apparently, that isn’t quite right. The randomness-driven Elo ratings of our big servers do a nearly perfect job of predicting match outcomes against counterpunchers, and they’re only a little bit too confident against the more middle-of-the-road players in Q2 and Q3. Against each other, though, upsets run rampant. That extremely volatile fraction of results–the tiebreak-packed outcomes when the biggest servers face off–only accounts for part of these players’ ratings.

We’re accustomed to getting unpredictable results from the most aggressive players, with their big serves, inconsistent returns, and short rallies. Today’s findings give us a better idea of when these do and do not occur. Against counterpunchers, things aren’t so unpredictable after all. But when big servers play each other, we expect the unexpected–and the results are even more unpredictable than that.

Podcast Episode 44: Murray’s Retirement and an Australian Open Preview

Episode 44 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, starts with some reflection on the outstanding career and premature retirement of Andy Murray. We spend some time talking about the surprising ATP aging curves I wrote about a few days ago, then delve into the 2019 Australian Open.

We assess the dangers awaiting the coachless Simona Halep, including a potential fourth-round meeting with Serena Williams, as well as the long list of women with a plausible chance to lift the trophy two weeks from now. We agree on the predictable pick to win the men’s title, but note that Novak Djokovic’s last few months carry a few warning signs.

Thanks for listening!

(Note: this week’s episode is about 67 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.

Match Charting Project Update and New Template

The Match Charting Project is a crowd-sourced, volunteer effort to gather exhaustive shot-by-shot data on professional tennis matches. We’re closing in on the 5,000-match mark, and are building a wide range of meaningful datasets for subsets of players and matches. We have shot-by-shot records of nearly all grand slam finals, most Masters finals, many major semi-finals and Premier finals, all head-to-head matches between members of the Big Four, and nearly every match ever played by Simona Halep.

Here’s the complete list of charted matches, and here’s an example of the data assembled for a single player.

I hope you’re inspired by what we’ve already achieved to contribute to the project. We have several dedicated charters and over 100 people have charted matches over the lifetime of the project, but the more data we have, the more valuable the entire effort becomes. Click here to find out more about getting started.

The immediate impetus for today’s post is the updated Excel template I’m releasing today, version 0.3.0. Revising the template was a necessity ahead of the 2019 Australian Open, because of the unique new rules under which AO matches will be played. The template now handles several rules variations, including 2019 AO rules (a super-tiebreak at 6-6 in the deciding set), 2019 Wimbledon rules (a standard tiebreak at 12-12 in the deciding set), and ATP NextGen Finals rules (no-ad, first to four games, standard tiebreak at 3-3). We’ve already posted the first charted match from the NextGen Finals, last year’s title match between Tsitsipas and De Minaur.

If you’re already familiar with charting and the MCP Excel template, all you need to know is that you can enter “A” in cell B14 to indicate that the match is played under 2019 AO rules. (For 2019 Wimbledon, use “T”, and for NextGen Finals, use “N”.)

I’ve also made an addition to the shot-by-shot syntax to handle situations in which a player stops a rally to challenge (or have a mark checked) but is proven wrong. If you’re charting, check the Instructions tab in the new Excel template for more details.

Finally, the MatchStats tab now includes a running tally of total shots and average rally length.

For those of you who are already contributors to the MCP: Thank you very much for your efforts. For everyone else, I hope 2019 is the tennis season when you decide to give it a try.

Click here to download the new template.

Economist: Announcing his retirement, Andy Murray begins to get his due at last

For The Economist’s Game Theory blog, I wrote about Andy Murray’s legacy, as he approaches retirement:

[B]ecause of the quality of his competition, it is easy to underrate the career on which Mr Murray is calling time. Several of his tallies at the grand slams rank among the top ten in the modern era, including his 11 finals, 21 semi-finals, 30 quarter-finals, and 189 match wins. Only nine other men have spent more time in the top five of the world rankings. His three major titles sit much further down the all-time list, but the rest of the big four blocked him from at least six more. Comparing tennis players across eras is devilishly difficult, thanks to changes in technology, tactics, training regimens, and geographical breadth, but these raw totals probably underrate his standing among the all-time greats. He doesn’t belong in the top three, but few men other than his present-day rivals can unambiguously claim to have been stronger players.

Read the whole thing.

The Big Four and Grand Slam Title Blocks

Italian translation at settesei.it

This is a guest post by Edoardo Salvati

In the last fifteen years, Roger Federer, Rafael Nadal, Novak Djokovic, Andy Murray—the Big Four—have dominated the ATP tour like no one before them. It’s hard to find a better example of oligarchy outside of geopolitics.

Since Wimbledon 2003, Federer’s first Grand Slam title, they have amassed 54 of 62 majors (or 87%) and been involved in another four finals. Similarly, since Federer’s first Masters win at Hamburg in 2002, they have won 106 of 159 titles at that level (or 66%) and contested 12 more finals. Since 2003 they have won 12 of 16 ATP Finals (or 75%) and contested one of the other four finals. 2017 and 2018 was the first time that outsiders won back-to-back season-ending titles in fifteen years.

It is an unprecedented level of domination that has left little glory for other players. But who are these others and how much would have they won had they been able to overcome the Big Four? At the Match Charting Project, we like to collect data (and you’re always welcome to contribute). Recently, we started working on a subset of matches that comprises all the Slam semi-finals back to 1980. Plenty of those featured recurring names from this second tier, so I was intrigued to see which players would have benefitted most in a world where the Big Four were not as good.

Deep inside of a parallel universe

Starting from Wimbledon 2003, I considered a hard-to-imagine scenario: What if the Big Four never won a major semi-final or final? For instance, when Grigor Dimitrov reached the final four at the 2017 Australian Open, he would have beaten Nadal (instead of losing in five sets), and then defeated Federer to win the title. When Juan Martin del Potro played Nadal in the 2018 French Open semi-final (he lost in straight sets), we rewrite history to make Delpo the winner, going on to face Dominic Thiem in the final. At the same event, in our parallel universe, Thiem wins the final against Nadal (he really lost in straight sets) and becomes the French Open champion for a second theoretical time.

The resulting slam tallies aren’t a precise redistribution of some of the Slams won by the Big Four, because there can be two different parallel-universe winners for the same tournament. Nevertheless, the title and final counts provide a general idea of who would’ve thrived in a Big Four-less sport. The following table lists the additional titles and finals (to a player’s actual wins, not shown) belonging to a parallel universe of tennis.

Player                 Extra Slams              Extra Finals      
Stan Wawrinka          6 (2 AO - 2 FO - 2 US)   0                 
David Ferrer           6 (2 AO - 2 FO - 2 US)   0                 
Andy Roddick           5 (1 AO - 3 WIM - 1 US)  2 (1AO - 1 WIM)   
Jo Wilfried Tsonga     4 (2 AO - 2 WIM)         0                 
Tomas Berdych          3 (1 AO - 1 FO - 1 US)   2 (WIM)           
Richard Gasquet        3 (2 WIM - 2 US)         0                 
Milos Raonic           3 (1 AO - 2 WIM)         0                 
Juan Martin del Potro  2 (1 WIM - 1 US)         3 (2 FO - 1 US)   
Marin Cilic            2 (1 AO - 1 WIM)         2 (1 AO - 1 US)   
Nicolay Davydenko      2 (1 FO - 1 US)          1 (US)            
Dominic Thiem          2 (FO)                   1 (FO)            
Marat Safin            2 (1 AO - 1 WIM)         0                 
Marcos Baghdatis       2 (1 AO - 1 WIM)         0                 
Robin Soderling        2 (FO)                   0                 
Kevin Anderson         2 (1 WIM - 1 US)         0                 
Grigor Dimitrov        2 (1 AO - 1 WIM)         0                 
Lleyton Hewitt         1 (US)                   2 (1 WIM - 1 US)  
Gael Monfils           1 (FO)                   1 (US)                       
Mark Philippoussis     1 (WIM)                  0                 
Andre Agassi           1 (US)                   0                 
Fernando Gonzalez      1 (AO)                   0                 
Jonas Bjorkman         1 (WIM)                  0                 
Mariano Puerta         1 (FO)                   0                 
Ivan Ljubicic          1 (FO)                   0                 
Rainer Schuettler      1 (WIM)                  0                 
Fernando Verdasco      1 (AO)                   0                 
Mikhail Youznhy        1 (US)                   0                 
Ernests Gulbis         1 (FO)                   0                 
Jerzy Janowicz         1 (WIM)                  0  
Kei Nishikori          0                        1 (US)                
Juan Carlos Ferrero    0                        1 (AO)            
Sebastian Grosjean     0                        1 (WIM)           
Tim Henman             0                        1 (US)            
Nicolas Kiefer         0                        1 (AO)            
David Nalbandian       0                        1 (FO)            
Tommy Haas             0                        1 (WIM)           
Hyeon Chung            0                        1 (AO)            
Jurgen Melzer          0                        1 (FO)            
Total                  62                       23

It’s no surprise to see Stan Wawrinka, a three-time winner and nine-time major semi-finalist, at the top. He would triple his overall count for each Slam he won, though Wimbledon would remain elusive. Had he beaten Federer in the quarter-final in 2014, he would have gotten as far as the semi-final against Milos Raonic.

There’s a group of players whose careers would look even more outstanding. David Ferrer, Jo Wilfried Tsonga, Tomas Berdych, Richard Gasquet and Raonic could all claim to be Slam winners. Ferrer lost all his semi-finals and a final to the Big Four, and winning a Slam would have been a fitting reward for his many years of elite-level performance.

And, of course, there’s Andy Roddick, who must have wished that the only illustrious citizen from Basel was Jacob Bernoulli. After winning the US Open in 2003, Roddick lost all the finals he played to Federer, including three Wimbledon Championships. 

One player who may deserve to be even higher on the list is del Potro, who had to face a member of the Big Four in every semi-final he played and never went beyond the quarter-finals at the Australian Open, twice knocked out by Federer. You would expect del Potro to have won more than two of these hypothetical majors.

The gatekeeper

A few years ago, in an article for FiveThirtyEight, Carl Bialik investigated the assumption that Nadal led all the Open-era greats as the biggest obstacle to Grand Slam titles. Inventing a stat called the “title block,” he quantified every loss to Nadal with a fraction of the title depending on the round: half a title block for a loss to Nadal in the finals, a quarter for the semi-finals, and so on. 

Let’s use that stat and extend the analysis to see how many titles, since Wimbledon 2003, the Big Four cost the other players, as shown in the following table. Walkovers and retirements were included.

Blocked                  AO    RG   WIM   USO  Titles Cost  
Roger Federer          2.00  2.50  1.50  1.00         7.00  
Andy Murray            2.94  1.25  1.38  0.88         6.44  
Novak Djokovic         0.06  2.13  1.00  2.50         5.69  
Rafael Nadal           1.13  0.13  1.75  0.75         3.75  
Andy Roddick           0.50  0.00  1.78  0.88         3.16  
Tomas Berdych          1.03  0.19  1.31  0.25         2.78  
David Ferrer           0.88  1.13  0.13  0.51         2.63  
Stanislas Wawrinka     0.72  1.00  0.19  0.63         2.53  
Juan Martin Del Potro  0.25  0.70  0.45  1.03         2.43  
Marin Cilic            0.81  0.09  0.94  0.44         2.28  
Jo Wilfried Tsonga     0.94  0.19  0.81  0.34         2.28  
Lleyton Hewitt         0.25  0.19  0.56  0.78         1.78  
Milos Raonic           0.56  0.13  0.88  0.06         1.63  
Robin Soderling        0.00  1.13  0.23  0.25         1.62  
Richard Gasquet        0.03  0.38  0.63  0.41         1.46  
Gael Monfils           0.11  0.75  0.00  0.57         1.43  
Kevin Anderson         0.07  0.00  0.64  0.50         1.21  
Dominic Thiem          0.00  1.02  0.00  0.13         1.14  
Marcos Baghdatis       0.64  0.03  0.44  0.02         1.13  
Nikolay Davydenko      0.27  0.25  0.01  0.53         1.05  
Fernando Gonzalez      0.56  0.17  0.13  0.16         1.02  
Fernando Verdasco      0.30  0.25  0.13  0.28         0.96  
Kei Nishikori          0.38  0.20  0.13  0.25         0.96  
Mikhail Youzhny        0.05  0.06  0.41  0.42         0.95  
Grigor Dimitrov        0.47  0.03  0.31  0.06         0.88  
Marat Safin            0.53  0.00  0.28  0.00         0.81  
Andre Agassi           0.13  0.00  0.03  0.63         0.78  
Tommy Haas             0.11  0.22  0.41  0.00         0.73  
Tommy Robredo          0.19  0.13  0.11  0.25         0.67  
Feliciano Lopez        0.11  0.01  0.19  0.34         0.65  
Gilles Simon           0.30  0.06  0.19  0.03         0.58  
Juan Carlos Ferrero    0.25  0.00  0.32  0.00         0.57  
David Nalbandian       0.13  0.25  0.03  0.16         0.56  
Jurgen Melzer          0.10  0.25  0.06  0.09         0.51  
Mark Philippoussis     0.00  0.00  0.50  0.01         0.51  
Mariano Puerta         0.00  0.50  0.00  0.00         0.50  
Nicolas Almagro        0.06  0.41  0.00  0.03         0.50

As expected, the Big Four have blocked each other more than they have any other player, costing themselves a whopping 22.88 majors, with Federer and Murray paying the highest price, 7.00 and 6.44 respectively. Other familiar names are just below the top four. There are 17 players who were blocked from at least one major title.

Nadal retains his status as the Slam gatekeeper: you have to pass through him to win a major. Not only did the rest of the Big Four fails to block him as much as he did them–he has the lowest major titles cost among the Big Four at 3.75–but he also has blocked the rest of the quartet more than any other player.    

Blocker         Blocked         Titles cost  
Rafael Nadal    Roger Federer          3.75  
Rafael Nadal    Novak Djokovic         3.13  
Rafael Nadal    Andy Murray            1.44  
Total                                  8.32  
                                             
Novak Djokovic  Andy Murray            3.13  
Novak Djokovic  Roger Federer          3.00  
Novak Djokovic  Rafael Nadal           1.88  
Total                                  8.01  
                                             
Roger Federer   Andy Murray            1.88  
Roger Federer   Novak Djokovic         1.56  
Roger Federer   Rafael Nadal           1.50  
Total                                  4.94  
                                             
Andy Murray     Novak Djokovic         1.00  
Andy Murray     Rafael Nadal           0.38  
Andy Murray     Roger Federer          0.25  
Total                                  1.63

Nadal boasts a net credit of 2.25 major titles versus Federer, of 1.25 against Djokovic and of 1.06 compared to Murray. Just as the rest of the men’s tour would prefer that the Big Four had pursued a different sport, three-quarters of the Big Four have had plenty of reasons to wish that Rafa had shifted his focus to golf.

At this month’s Australian Open, Nadal continues to loom large. With the No. 2 seed, he is a potential semi-final opponent for Federer or Murray and, of course, a possible foe in the final for top seed Djokovic. There’s no guarantee that Nadal will stand in anyone’s way, but with these men accounting for the top three seeds at yet another major, the era of Big Four title blocks is far from over.

Edoardo Salvati is on a mission to raise the level of the Italian sports conversation. He founded settesei.it and has written about tennis and other sports for publications such as Contrasti, Undici, Il Tennis Italiano. He is a prolific and proud contributor to the Match Charting Project.

Ivo Karlovic’s Survival and the Key to Aging in Men’s Tennis

Italian translation at settesei.it

Let’s just get this out of the way first: Ivo Karlovic is amazing. The Croatian didn’t play his first tour-level match until he was 22 years old, and he didn’t crack the top 100 for two years after that. Yet he eventually reached No. 14 in the world, won over 350 career matches, and claimed nine tour-level titles. Now, a few weeks shy of his 40th birthday, he’s coming off an ATP final in Pune, where he came within two points of ousting top-ten stalwart Kevin Anderson and ensured that he’ll remain in the top 100 through his milestone birthday next month.

The fact that Karlovic is one of the tallest men ever to play the game and that he holds a wide array of ace records is beside the point. (Though it’s certainly worthy of discussion, and I hope to dive into aging patterns and playing styles in a future post.) Yes, his first-strike brand of tennis, avoiding the bruising rallies that have worn down the likes of David Ferrer, may make it easier to compete at an advanced age. On the other hand, he remains of the few men on tour to regularly serve-and-volley, a tactic that scores of younger, quicker men can’t execute effectively. He is, quite simply, one of a kind.

Despite his uniqueness, Karlovic represents an important aspect of men’s tennis in the 2010s. The ATP has gotten older since he broke in almost two decades ago, and ten men aged at least 33 are ranked higher than the Croatian. One of them, 37-year-old Roger Federer, remains one of the best players in the game. The average age of elite men’s tennis may be creeping back down, but it is still the golden age of 30-somethings.

Men like Karlovic and Federer have seemed to defy the usual logic of aging. Most sports have a reliable “peak age” at which players can be expected to to perform their best. Up to that point, competitors are developing both physically and mentally; after the peak age, physical deterioration sets in and performance declines. There’s always plenty of variation around the average, but the overall trajectory–break in, rise, peak, fall, retire–is predictable enough.

In part, Karlovic has followed that path, just with a late start and a surprise second peak in his 30s. To compare year-to-year performances, I calculated each player’s dominance ratio (DR), a useful measure of overall performance calculated as the ratio of return points won to opponents’ return points won, and adjusted it for quality of competition. (The adjustment algorithm gets complicated; I first outlined how it controls for each player’s mix of opponents here.) 1.0 is average, and the typical range runs from about 0.8 (soon to head back to challengers) to 1.2 (big four territory). The following graph shows Ivo’s DR at each age, along with a smoother three-year moving average:

Karlovic hit his primary peak around age 31, a bit late but not entirely atypical for the era. Even if we ignore the surprise spike at age 36, he remained an average player (roughly speaking, a card-carrying member of the top 50) until age 35. In 2017 and 2018, we finally witnessed a downward trend, but if Ivo’s feat in Pune is any indication, he might be turning things around once again.

Nearly every professional tennis player retires before they reach Karlovic’s current age, so we’ll never know what bonus peaks we missed. Of course, many of those retirement decisions are due to injury, so at least some of the Croatian’s late-career success must be credited to his ability to stay healthy enough to soldier on. Let’s look at an even more baffling aging pattern, one that belongs to a player who will almost definitely retire before seeing the kind of late-career decline that Karlovic experienced in 2017 and 2018. Here’s Federer:

By the measure of competition-adjusted DR, Federer’s best season came at age 34. Even if you don’t buy that, the overall trend is clear. He continues to play at or near his peak, past the age at which his peers become Davis Cup captains and have Tour Finals round-robin groups named after them.

Federer has been able to stay off the injured list for almost all of his 20 years on tour, and health–the simple fact of showing up for most tournaments–may be the most underrated skill in men’s tennis. The vast majority of players who don’t survive to post elite seasons in their mid- and late-30s aren’t slowly drifting down the ranking list, like a baseball player who plays every game in his 20s, then moves into more and more limited part time roles as he ages. Instead, they drop out, perhaps because of a single career-ending injury, the general accumulation of nagging problems, or lack of desire to wholeheartedly pursue the sport at the expense of everything else.

The following graph shows the two ways in which players fail to maintain their previous level from one year to the next: Playing worse tennis (measured by competition-adjusted DR), or leaving the tour. The latter is defined by contesting fewer than 20 tour-level matches, something that any reasonably healthy player with a ranking in the top 100 should be able to manage. At every age, players drop out at a surprising clip, and that rate begins to overtake the percentage of players who stay on tour but perform at a weaker level around the late 20s:

The “Leave tour” rates slightly overstate the number of disappearing players, since about one-quarter of them eventually return to the tour, like Andy Murray is trying to do in 2019. But even accounting for the number of comebacks, a hefty share of the players we expect to steadily decline are either forced off tour by injury or choose not to continue.

Selection bias

All of these disappearing players make it extremely difficult to construct an aging curve for men’s tennis. One common approach to measuring such a trajectory is to identify all the players who competed in consecutive seasons (say, their age-25 and age-26 campaigns), figure out how much better or worse they performed in the latter year, and average the differences. When we do that for ATP players born since 1970, the results are downright bizarre. The worst year-to-year change is from age 21 to age 22, when DR decreases by about 2.3%, even though we would expect youngsters to be developing their game for the better. The strongest year-to-year change is from age 30 to age 31, with an improvement of 4.0%, when we would expect a plateau or even a slight decline.

Because these ratios don’t include the players who drop out, most of the year-to-year ratios reflect an improvement:

Age       Year-to-year DR ratio  
19 to 20                  -1.7%  
20 to 21                  +0.9%  
21 to 22                  -2.2%  
22 to 23                  -0.3%  
23 to 24                  +1.5%  
24 to 25                  +1.1%  
25 to 26                  +0.7%  
26 to 27                  +1.5%  
27 to 28                  +1.2%  
28 to 29                  +3.5%  
29 to 30                  -0.8%  
30 to 31                  +4.0%  
31 to 32                  +2.6%  
32 to 33                  +0.7%  
33 to 34                  -0.5%  
34 to 35                  +3.0%  
35 to 36                  -0.4%

If we assembled these ratios into an aging curve, we’d see a line staggering upwards, as if we could expect players to continue improving for as long as they cared to compete.

However, things start to make sense when we acknowledge the selection bias and reframe our findings accordingly. It isn’t true to say that the average player steadily improves forever. But it is more believable to say this: The average player who remains healthy enough to play a full season and has the desire to compete full-time can expect to improve well into his 30s. The older a player gets, the less likely that the second claim applies to him.

As they say, half of success is just showing up. By age 39, most pro tennis players have long since started showing up somewhere else. By dint of sheer perserverance, a bit of luck, and one of the most dominant serves the world has ever seen, Karlovic has shown that tennis’s aging curve is even more flexible that we thought.

Identifying Underrated Players With Minor League Elo

I’ve just revised my published Elo ratings (men, women) to better reflect the performance of players who mostly compete at the (men’s) ATP Challenger and (women’s) ITF levels. Previously, my Elo ratings used only tour-level main-draw matches. For top players, it makes very little difference–not only do Novak Djokovic and Simona Halep play no matches at the lower levels, they rarely encounter opponents who spend much time there. But for the second tier of players, the effect can be substantial.

The Elo system rates players according to the quality of their opponents. Beat a good player with a high rating, and your own rating will jump by a healthy margin. Beat a weakling, and your rating will inch up a tiny bit. Essentially, Elo looks at each result and asks, “Based on this new result, how much do we need to adjust our earlier rating?” When Bianca Andreescu upset Caroline Wozniacki in Auckland last week, the system responded by upping Andreescu’s rating by quite a bit, and by penalizing Wozniacki more than for the typical loss. After a more predictable result, like Djokovic’s defeat of Damir Dzumhur, ratings barely move.

It’s important to understand the basic mechanics of the system, but the main takeaway for most fans is that Elo just works. The algorithm generates more accurate player ratings (and resulting match forecasts) than the official ATP and WTA rankings, among other attempts to rank players. Now, you can see Elo rankings for a much wider range of players.

Of of my main uses of Elo ratings is identifying players whose official rankings haven’t caught up to reality. For instance, a few months ago I noted when Daniil Medvedev moved into the Elo top ten, even though he has yet to crack that threshold on the official list. Most players who reach the top ten on the Elo table eventually do the same in the ATP or WTA rankings. Another two current examples are Aryna Sabalenka and Ashleigh Barty, considered by Elo to be two of the top three women on tour right now, even though neither is in the top ten of the WTA rankings. That may be too aggressive, and the margins at the top of the women’s list are tiny right now, but it is a clear signal that these women’s results bear watching. (We talked about this on the most recent Tennis Abstract podcast.)

Now that we have unified Elo lists that cover more players, let’s dig deeper. For each tour, let’s find the players current outside the official top 100s who are rated the highest by the more sophisticated formula. First, the ATP:

Player                  ATP Rank  Elo Rank  
David Ferrer                 124        36  
Thanasi Kokkinakis           145        62  
Miomir Kecmanovic            126        66  
Jack Sock                    105        77  
Reilly Opelka                102        84  
Ricardas Berankis            107        86  
Marcos Baghdatis             122        87  
Gilles Muller                137        88  
Daniel Evans                 190        89  
Viktor Troicki               201        90  
Horacio Zeballos             182        92  
Jared Donaldson              115        94  
Mikael Ymer                  196        95  
Egor Gerasimov               157       100  
Lloyd Harris                 119       102  
Tommy Paul                   195       104  
Guillermo Garcia Lopez       101       106  
Felix Auger Aliassime        106       108  
Alexei Popyrin               149       109  
Dudi Sela                    240       114

One thing that pops out from the list is the number of veterans. Elo ratings are “stickier” than ATP rankings, since the official system works with only 52 weeks worth of results. Elo ratings make constant adjustments, but quality performances–even when they are more than 52 weeks old–continue to affect current ratings for some time. David Ferrer has had a hard time staying healthy enough to compete at his former level, but according to Elo, he remains fairly dangerous when he is able to take the court.

Fortunately the list isn’t all veterans. Elo suggests that younger players such as Thanasi Kokkinakis, Miomir Kecmanovic, Mikael Ymer, and Tommy Paul are better than their current rankings indicate.

The WTA list is even more laden with veterans, players who are still competing at a high level, if not as frequently as they used to:

Player                WTA Rank  Elo Rank  
Lucie Safarova             105        39  
Coco Vandeweghe            100        40  
Shuai Peng                 129        43  
Svetlana Kuznetsova        106        50  
Sara Errani                114        52  
Varvara Lepchenko          134        80  
Laura Siegemund            110        84  
Kristyna Pliskova          101        96  
Anna Kalinskaya            167        97  
Viktorija Golubic          104        98  
Ivana Jorovic              117        99  
Marie Bouzkova             120       103  
Kateryna Bondarenko        140       104  
Sachia Vickery             123       105  
Veronika Kudermetova       111       107  
Sabine Lisicki             198       109  
Vitalia Diatchenko         131       112  
Yanina Wickmayer           126       113  
Nao Hibino                 115       114  
Danielle Lao               169       115

Part of the reason why so few prospects appear on this list is because of my decision to exclude ITF $25Ks. For example, up-and-coming 18-year-old Kaja Juvan, who knocked out Yanina Wickmayer in Australian Open qualifying today, hasn’t played nearly enough matches at higher levels to appear on my Elo list. But last year, she was 29-7 at ITF $25Ks, and won her last ten matches at that level.

Another issue is that the most promising women tend to climb into the top 100 more quickly. Another 18-year-old, Dayana Yastremska, rocketed up the rankings with a tour-level title in Hong Kong last fall. She sits at No. 59 on the WTA table, but after 13 top-100 wins in 2018, Elo is even more optimistic, placing her at No. 27, just ahead of Maria Sharapova and Venus Williams.

I’ll continue to update these expanded Elo ratings weekly and use them to generate forecasts for every tour-level and Challenger event. Enjoy!

Podcast Episode 43: Berdych’s Comeback, Andreescu’s Breakthrough, and Karlovic’s Longevity

Episode 43 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, plows through the wealth of results from the 2019 season’s first week. We start with Bianca Andreescu’s breakthrough in Auckland and a high-quality first-rounder in Brisbane, then move on Aryna Sabalenka’s title in Shenzhen, along with her aggression and possibly-related predilection for three-set matches.

On the men’s side, we talk about Ivo Karlovic’s surprise run to the Pune final at age 39, the ups and downs of Kei Nishikori’s career, especially in title matches, and a strong showing from Tomas Berdych in his first tournament since June.

We wrap things up by touching on the extremely strong women’s field in Sydney, and the vast difference between the competitiveness there and at the smaller event in Hobart.

Thanks for listening!

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

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

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.