The stats from the Wimbledon final told a clear story. Over five sets, Roger Federer did most things slightly better than did his opponent, Novak Djokovic. Djokovic claimed a narrow victory because he won more of the most important points, something that doesn’t show up as clearly on the statsheet.
We can add to the traditional stats and quantify that sort of clutch play. A method that goes beyond simply counting break points or thinking back to obviously key moments is to use the leverage metric to assign a value to each point, according to its importance. After every point of the match, we can calculate an updated probability that each player will emerge victorious. A point such as 5-all in a tiebreak has the potential to shift the probability a great deal; 40-15 in the first game of the match does not.
Leverage quantifies that potential. The average point in a best-of-five match has a leverage of about 4%, and the most important points are several times that. Another way of saying that a player is “clutch” is that he is winning a disproportionate number of high-leverage points, even if he underwhelms at low-leverage moments.
In my match recap at The Economist, I took that one step further. While Djokovic won fewer points than Federer did, his successes mattered more. The average leverage of Djokovic’s points won was 7.9%, compared to Federer’s 7.2%. We can represent that difference in the form of a leverage ratio (LR), by dividing 7.9% by 7.2%, for a result of 1.1. A ratio of that magnitude is not unusual. In the 700-plus men’s grand slam matches in the Match Charting Project, the average LR of the more clutch player is 1.11. Djokovic’s excellence in key moments was not particularly rare, but in a close match such as the final, it was enough to make the difference.
Recording a leverage ratio above 1.0 is no guarantee of victory. In about 30% of these 700 best-of-five matches, a player came out on top despite winning–on average–less-important points than his opponent did. Some of the instances of low-LR winners border on the comical, such as the 2008 French Open final, in which Rafael Nadal drubbed Federer despite a LR of only 0.77. In blowouts, there just isn’t that much leverage to go around, so the number of points won matters a lot more than their timing. But un-clutch performances often translate to victory even in closer matches. Andy Murray won the 2008 US Open semi-final over Nadal in four sets despite a LR of 0.80, and in a very tight Wimbledon semi-final last year, Kevin Anderson snuck past John Isner with a LR of 0.88.
You don’t need a spreadsheet to recognize that tennis matches are decided by a mix of overall and clutch performance. The numbers I’ve shown you so far don’t advance our understanding much, at least not in a rigorous way. That’s the next step.
DR, meet BLR
Regular users of Tennis Abstract player pages are familiar with Dominance Ratio (DR), a stat invented by Carl Bialik that re-casts total points won. DR is calculated by dividing a player’s rate of return points won by his rate of service points lost (his opponent’s rate of return points won), so the DR for a player who is equal on serve and return is exactly 1.0.
Winners are usually above 1.0 and losers below 1.0. In the Wimbledon final, Djokovic’s DR was 0.87, which is extremely low for a winner, though not unheard of. DR balances the effect of serve performance and return performance (unlike total points won, which can skew in one direction if there are many more serve points than return points, or vice versa) and gives us a single-number summary of overall performance.
But it doesn’t say anything about clutch, except that when a player wins with a low DR, we can infer that he outperformed in the big moments.
To get a similarly balanced view of high-leverage performance, we can adapt leverage ratio to equally weight clutch play on serve and return points. I’ll call that balanced leverage ratio (BLR), which is simply the average of LR on serve points and LR on return points. BLR usually doesn’t differ much from LR, just as we often get the same information from DR that we get from total points won. Djokovic’s Wimbledon final BLR was 1.11, compared to a LR of 1.10. But in cases where a disproportionate number of points occur on one player’s racket, BLR provides a necessary correction.
We can capture leverage-adjusted performance by simply multiplying these two numbers. For example, let’s take Stan Wawrinka’s defeat of Djokovic in the 2016 US Open final. Wawrinka’s DR was 0.90, better than Djokovic at Wimbledon this year but rarely good enough to win. But win he did, thanks to a BLR of 1.33, one of the highest recorded in a major final. The product of Wawrinka’s DR and his BLR–let’s call the result DR+–is 1.20. That number can be interpreted on the same scale as “regular” DR, where 1.2 is often a close victory if not a truly nail-biting one. DR+ combines a measure of how many points a player won with a measure of how well-timed those points were.
Out of 167 men’s slam finals in the Match Charting Project dataset, 14 of the winners emerged triumphant despite a “regular” DR below 1.0. In every case, the winner’s BLR was higher than 1.1. And in 13 of the 14 instances, the strength of the winner’s BLR was enough to “cancel out” the weakness of his DR, in the sense that his DR+ was above 1.0. Here are those matches, sorted by DR+:
Year Major Winner DR BLR DR+ 2019 Wimbledon Novak Djokovic 0.87 1.11 0.97 1982 Wimbledon Jimmy Connors 0.88 1.20 1.06 2001 Wimbledon Goran Ivanisevic 0.95 1.16 1.10 2008 Wimbledon Rafael Nadal 0.98 1.13 1.10 2009 Australian Open Rafael Nadal 0.99 1.13 1.12 1981 Wimbledon John McEnroe 0.99 1.16 1.15 1992 Wimbledon Andre Agassi 0.97 1.19 1.16 1989 US Open Boris Becker 0.96 1.22 1.18 1988 US Open Mats Wilander 0.98 1.21 1.18 2015 US Open Novak Djokovic 0.98 1.21 1.18 2016 US Open Stan Wawrinka 0.90 1.33 1.20 1999 Roland Garros Andre Agassi 0.98 1.25 1.23 1990 Roland Garros Andres Gomez 0.94 1.34 1.26 1991 Australian Open Boris Becker 0.99 1.30 1.29
167 slam finals, and Djokovic-Federer XLVIII was the first one in which the player with the lower DR+ ended up the winner. (Some of the unlisted champions had subpar leverage ratios and thus DR+ figures lower than their DRs, but none ended up below the 1.0 mark.) While Federer was weaker in the clutch–notably in tiebreaks and when he held match points–his overall performance in high-leverage situations wasn’t as awful as those few memorable moments would suggest. More often than not, a player who combined Federer’s DR of 1.14 with his BLR of 0.90 would conclude the Wimbledon fortnight dancing with the Ladies’ champion.
Surprisingly, 1-out-of-167 might understate the rarity of a winner with a DR+ below 1.0. Only one other best-of-five match in the Match Charting Project database (out of more than 700 in total) fits the bill. That’s the controversial 2019 Australian Open fourth-rounder between Kei Nishikori and Pablo Carreno Busta. Nishikori won with a 1.06 DR, but his BLR was a relatively weak 0.91, resulting in a DR+ of 0.97. Like the Wimbledon final, that Melbourne clash could have gone either way. Carreno Busta may have been unlucky with more than just the chair umpire’s judgments.
What does it all mean?
We knew that the Wimbledon final was close–now we have more numbers to show us how close it was. We knew that Djokovic played better when it mattered, and now we have more context that indicates how much better he was, which is not a unusually wide margin. Federer has won five of his slams despite title-match BLRs below 1.0, and two others with DRs below 1.14. He’s never won a slam with a DR+ of 1.03 or lower, but then again, there had never before been a major final that DR+ judged to be that close. Roger is no one’s idea of a clutch master, but he isn’t that bad. He just should’ve saved a couple of doses of second-set dominance for more important junctures later on.
If you’re anything like me, you’ll read this far and be left with many more questions. I’ve started looking at several, and hope to write more in this vein soon. Is Federer usually less clutch than average? (Yes.) Is Djokovic that much better? (Yes.) How about Nadal? (Also better.) Is Nadal really better, or do his leverage numbers just look good because important points are more likely to happen in the ad court? (No, he really is better.) Does Djokovic have Federer’s number? (Not really, unless you mean his mobile number. Then yes.) Did everything change after Djokovic hit that return? (No.)
There are many interesting related topics beyond the big three, as well. I started writing about leverage for subsets of matches a few years ago, prompted by another match–the 2016 Wimbledon Federer-Raonic semi-final–in which Roger got outplayed when it mattered. Just as we can look at average leverage for points won and lost, we can also estimate the importance of points in which a player struck an ace, hit a backhand unforced error, or chose to approach the net.
Matches are decided by a combination of overall performance and high-leverage play. Commonly-available stats do a pretty good job at the former, and fail to shine much light on the latter. The clutch part of the equation is often left to the speculation of pundits. As we build out a more complete dataset and have access to more and more point-by-point data (and thus leverage numbers for each point and match), we can close the gap, enabling us to better quantify the degree to which situational performance affects every player’s bottom line.