Measuring a Season’s Worth of Luck

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In Toronto last week, Stefanos Tsitsipas was either very clutch, very lucky, or both. Against Alexander Zverev in Friday’s quarter-final, he won fewer than half of all points, claiming only 56.7% of his service points, compared to Zverev’s 61.2%. The next day, beating Kevin Anderson in the semi-final in a third-set tiebreak, he again failed to win half of total points, holding 69.9% of his service points against Anderson’s 75.5%.

Whether the Greek prospect played his best on the big points or benefited from a hefty dose of fortune, this isn’t sustainable. Running those serve- and return-points-won (SPW and RPW) numbers through my win probability model, we find that–if you take luck and clutch performance out of the mix–Tsitsipas had a 27.8% chance of beating Zverev and a 26.5% chance of beating Anderson. These two contests–perhaps the two days that have defined the youngster’s career up to this point–are the very definition of “lottery matches.” They could’ve gone either way, and over a long enough period of time, they’ll probably even out.

Or will they? Are some players more likely to come out on top in these tight matches? Are they consistently–dare I say it–clutch? Using this relatively simple approach of converting single-match SPW and RPW rates into win probabilities, we can determine which players are winning more or less often than they “should,” and whether it’s a skill that some players consistently display.

Odds in the lottery

Let’s start with some examples. When one player wins more than 55% of points, he is virtually guaranteed to win the match. Even at 53%, his chances are extremely good. Still, a lot of matches–particularly best-of-threes on fast surfaces–end up in the range between 50% and 53%, and that’s what most interesting from this perspective.

Here are Tsitsipas’s last 16 matches, along with his SPW and RPW rates and the implied win probability for each:

Tournament  Round  Result  Opponent     SPW    RPW  WinProb  
Toronto     F      L       Nadal      62.9%  21.1%       3%  
Toronto     SF     W       Anderson   69.9%  24.5%      27%  
Toronto     QF     W       A Zverev   56.7%  38.8%      28%  
Toronto     R16    W       Djokovic   77.2%  32.0%      85%  
Toronto     R32    W       Thiem      83.3%  30.2%      93%  
Toronto     R64    W       Dzumhur    82.8%  35.0%      98%  
Washington  SF     L       A Zverev   54.7%  25.5%       1%  
Washington  QF     W       Goffin     71.2%  32.7%      67%  
Washington  R16    W       Duckworth  80.0%  37.5%      98%  
Washington  R32    W       Donaldson  59.5%  45.5%      74%  
Wimbledon   R16    L       Isner      72.5%  18.0%      10%  
Wimbledon   R32    W       Fabbiano   64.0%  55.9%     100%  
Wimbledon   R64    W       Donaldson  70.1%  40.9%      95%  
Wimbledon   R128   W       Barrere    71.5%  39.0%      94%  
Halle       R16    L       Kudla      59.7%  28.8%       8%  
Halle       R32    W       Pouille    78.3%  42.9%      99%

More than half of the matches are at least 90% or no more than 10%. But that leaves plenty of room for luck in the remaining matches. Thanks in large part to his last two victories, the win probability numbers add up to only 9.8 wins, compared to his actual record of 12-4. All four losses were rather one-sided, but in addition to the Toronto matches against Zverev and Anderson, his wins against David Goffin in Washington and, to a lesser extent, Novak Djokovic in Toronto, were far from sure things.

In the last two months, Stefanos has indeed been quite clutch, or quite lucky.

Season-wide views

When we expand our perspective to the entire 2018 season, however, the story changes a bit. In 48 tour-level matches through last week’s play (excluding retirements), Tsitsipas has gone 29-19. The same win probability algorithm indicates that he “should” have won 27.4 matches–a difference of 1.6 matches, or about five percent, which is less than the gap we saw in his last 16. In other words, for the first two-thirds of the season, his results were either unlucky or un-clutch, if only slightly. At the very least, the aggregate season numbers are less dramatic than his recent four-event run.

For two-thirds of a season, a five percent gap between actual wins and win-probability “expected” wins isn’t that big. For players with at least 30 completed tour-level matches this season, the magnitude of the clutch/luck effect extends from a 20% bonus (for Pierre Hugues Herbert) to a 20% penalty (for Sam Querrey, which he reduced a bit by beating John Isner in Cincinnati on Monday despite winning less than 49% of total points). Here are the ten extremes at each end, of the 59 ATPers who have reached the threshold so far in 2018:

Player                 Matches  Wins  Exp Wins  Ratio  
Pierre Hugues Herbert       30    16      13.2   1.22  
Nikoloz Basilashvili        34    17      14.0   1.21  
Frances Tiafoe              39    24      20.0   1.20  
Evgeny Donskoy              30    13      10.9   1.19  
Grigor Dimitrov             34    20      17.1   1.17  
Lucas Pouille               31    16      13.7   1.17  
Gael Monfils                34    21      18.3   1.15  
Daniil Medvedev             34    18      15.8   1.14  
Marco Cecchinato            33    19      16.7   1.14  
Maximilian Marterer         32    17      15.2   1.12  
Leonardo Mayer              37    19      20.1   0.95  
Guido Pella                 37    20      21.2   0.95  
Marin Cilic                 38    27      28.8   0.94  
Novak Djokovic              37    27      29.3   0.92  
Marton Fucsovics            30    16      17.5   0.92  
Joao Sousa                  36    18      19.8   0.91  
Dusan Lajovic               34    17      18.7   0.91  
Fernando Verdasco           43    22      24.5   0.90  
Mischa Zverev               39    18      20.7   0.87  
Sam Querrey                 30    15      18.8   0.80

A difference of three or four wins, as many of these players display between their actual and expected win totals, is more than enough to affect their standing in the rankings. The degree to which it matters depends enormously on which matches they win or lose, as Tsitsipas’s semi-final defeat of Anderson has a much greater impact on his point total than, say, Querrey’s narrow victory over Isner does for his. But in general, the guys at the top of this list are ones who have seen unexpected ranking boosts this season, while some of the guys at the bottom have gone the other way.

The last full season

Let’s take a look at an entire season’s worth of results. Last year, a few players–minimum 40 completed tour-level matches–managed at least a 20% luck/clutch bonus, but with the surprising exception of Daniil Medvedev, none of them have repeated the feat so far in 2018:

Player                 Matches  Wins  Exp Wins  Ratio  
Donald Young                43    21      16.2   1.30  
Fabio Fognini               58    35      28.5   1.23  
Jack Sock                   55    36      29.8   1.21  
Jiri Vesely                 45    22      19.3   1.14  
Daniil Medvedev             43    22      19.7   1.11  
John Isner                  57    36      32.3   1.11  
Damir Dzumhur               56    33      29.7   1.11  
Gilles Muller               48    30      27.1   1.11  
Alexander Zverev            74    53      48.1   1.10  
Juan Martin del Potro       53    37      33.6   1.10

A few of these players have had solid seasons, but posting a good luck/clutch number in 2017 is hardly a guaranteed, as the likes of Donald Young, Jack Sock, and Jiri Vesely can attest. Here is the same list, with 2018 luck/clutch ratios shown alongside last year’s figures:

Player                 2017 Ratio  2018 Ratio     
Donald Young                 1.30        0.89  *  
Fabio Fognini                1.23         1.1     
Jack Sock                    1.21        0.68  *  
Jiri Vesely                  1.14        1.08  *  
Daniil Medvedev              1.11        1.14     
John Isner                   1.11        0.96     
Damir Dzumhur                1.11        1.01     
Gilles Muller                1.11        0.84  *  
Alexander Zverev             1.10        1.06     
Juan Martin del Potro        1.10        1.07

* fewer than 30 completed tour-level matches

The average luck/clutch ratio of these ten players has fallen to a bit below 1.0.

Unsustainable luck

You can probably see where this is going. I generated full-season numbers for each year from 2008 to 2017, and identified those players who appeared in the lists for adjacent pairs of seasons. If luck/clutch ratio is a skill–that is, if it’s more clutch than luck–guys who post good numbers will tend to do so the following year, and those who post lower numbers will be more likely to remain low.

Across 325 pairs of player-seasons, that’s not what happened. There is almost no relationship between one year of luck/clutch ratio and the next. The r^2 value–a measure of correlation–is 0.07, meaning that the year-to-year numbers are close to random.

Across sports, analysts have found plenty of similar results, and they are often quick to pronounce that “clutch doesn’t exist,” which leads to predictable rejoinders from the laity that “of course it does,” and so on. It’s boring, and I’m not particularly interested in that debate. What this specific finding shows is:

This type of luck, defined as winning more matches than implied by a player’s SPW and RPW in each match, is not sustainable.

What Tsitsipas accomplished last weekend in Toronto was “clutch” by almost any definition. What this finding demonstrates is that a few such performances–or even a season’s worth of them–doesn’t make it any more likely that he’ll do the same next year. Or, another possibility is that the players who stick at the top level of professional tennis are all clutch in this sense, so while Tsitsipas might be quite mentally strong in key moments, he’ll often run up against players who have similar mental skills, and he won’t be able to consistently win these close matches.

If Stefanos is able to maintain a ranking in the top 20, which seems plausible, he’ll probably need to win more serve and return points than he has so far. Fortunately for him, he’s still almost eight years younger than his typical peer, so he has plenty of time to improve. The occasional lottery matches that tilt his way will need to be mere bonuses, not the linchpin of his strategy to reach the top.