The science of 54%

Roger Federer and the slim margin of difference between winners and losers

Athletes aren’t always great at explaining their competitive mindset or giving speeches (Lou Gehrig aside), which is what made Roger Federer’s commencement address at Dartmouth College last month all the more remarkable.

Federer is no longer the owner of the most Grand Slam titles in men’s tennis, but he is still, to many observers, the greatest men’s player to have ever competed. Always classy and dignified, albeit a little aloof, I somewhat doubt even Dartmouth’s board expected Federer to wow them with words.

But he delivered an address for the ages.

After a few jokes about never attending college, his discomfort in a robe, and how much he likes green (i.e. Dartmouth’s colors/Wimbledon’s playing surface, ha ha), Federer got into what he really wanted to impart: How hard it is to be a champion.

“In the 1,526 singles matches I played in my career, I won almost 80 percent of those matches,” Federer said. “Now, I have a question for all of you. What percentage of the points do you think I won in those [1,526] matches?”

The answer: 54 percent.

Amazingly, this checks out. According to ATP statistics, Federer held a 1251-275 record in his lifetime, and yet he won just 54 percent of the total points that he played.

Scan the stat sheets and you’ll find similar results.

Rafael Nadal: Has won 83 percent of his career matches, but only 54.5 percent of total points.

Novak Djokovic: 83.8 percent of matches, 54.5 percent of total points.

Jimmy Connors: 81.7 percent of matches, 49.7 percent of total points.

Pete Sampras: 77.4 percent of matches, 53.5 percent of total points.

“In other words,” Federer says, “even top-ranked tennis players win barely more than half of the points they play.”

Some readers might point out here that Stephen Curry is a career 47.3 percent field-goal shooter, or that Wayne Gretzky had a career 17.6 percent shooting percentage, or that Ted Williams only hit safely in 34 percent of his career at-bats. Failure is a part of sports, and athletes have to learn to thrive within (or because of) persistent rejection. Yet I think Federer’s example is particularly striking. Tennis is an individual sport, and these individuals are persistent and dominant winners. But their margin of error is shockingly slim. If golfers only made 54 percent of their putts, from any distance, it would be far more difficult for any single competitor to emerge with any regularity.

How does a top-ranked tennis player handle this constant, bludgeoning struggle? “You learn not to dwell on every shot,” Federer said. “You teach yourself to think, ‘OK, I double-faulted. It’s only a point. … Even a great shot, an overhead smash that ends up on Sportscenter’s Top 10 playlist, that, too, is just a point.”

Just a point. You won’t hear that from a Nike ad.

It’s a terrific graduation speech pearl of wisdom, though, and one that carries a lot of implications for achieving greatness in practically any line of work where perfection isn’t necessarily expected or required (ie., a 54% success rate for a bomb disposal specialist wouldn’t get you very far). But even in areas where some performances can appear extraordinary (be it stock picking, or car sales, or cooking, or tennis), the end result can belie a lot of fickleness in the steps leading up to it.

For tennis stars, Federer suggests, the key to overcoming a 46-percent fail rate on every shot has to begin with an even-keeled temperament. As fans, we hate this. We expect our athletes to live and die with each possession, refuse to accept failure, and outwardly project our own “win or else” ultimatum. Federer says this same inclination is there, internally. But his competitive nature can’t and shouldn’t be winning the power struggle against a chiller mindset.

“When you’re playing a point, it has to be the most important thing in the world,” he says. “But when it’s behind you, it’s behind you.”

Here’s the full speech:

54 percent

Federer’s 54 percent number has another historical antecedent in recent sports.

It’s exactly the figure that Seattle Mariners general manager Jerry DiPoto cited last October as being the measure of a “successful” franchise in baseball.

“If you go back and you look in a decade, those teams that win 54 percent of the time always wind up in the postseason,” Dipoto told reporters. “And they, more often than not, wind up in the World Series. So there’s your bigger-picture issue. Nobody wants to hear the goal this year is, ‘We’re going to win 54 percent of the time.’”

DiPoto got a lot of heat for his comments, which came after the Mariners had just been eliminated from postseason contender despite having won (you guessed it) 54.3 percent of their games last season. That’s still a great record, DiPoto suggests, and if extrapolated over a decade, it’s actually an achievement.

Fans mocked DiPoto’s answer and put “54 percent” on T-shirts, but he, too, is right:

Over the last 10 years (of full, 162-game seasons), only five have won more than 54 percent of their games:

Dodgers

Yankees

Cardinals

Astros

Guardians

Only the Atlanta Braves (53.2 winning percentage), Boston Red Sox (53.8), Chicago Cub (51.7), and Tampa Bay Rays (53.5) have played in more postseason games than any of those teams mentioned.

Despite what fans think, 54 percent seems like a relevant delineation point for successful teams, just as 54 percent separates fine tennis players from all-time greats.

Sports bettors often cite a related figure as being “the most important number” in their line of work: 52.4 percent.

That’s the percentage that long-term bettors have to win to overcome the “vig” (sportsbook commission) in order to break even. Get to 52.5 percent, and you’re a profitable sports gambler. It seems like a reasonably attainable figure, but it requires about 5 percent more accuracy than the sportsbooks in picking games to make money. That’s a tough test of handicapping skill, and probably why most bettors can’t hack it in the long run. Next time you see someone claiming to be the “Federer of Sports Gambling,” know that they’re likely only right about 53 percent of the time.

The 54

What Federer doesn’t mention in his speech is that there is a secret to his success hidden beneath the 46 percent of points that he lost. Some points are more important than others.

A 2019 study in the German Journal of Exercise and Sport Research looked at 128 singles matches played by both men and women during the 2012 London Olympics. They found that, for male players, the strongest discriminators between winning and losing were the percentage of break points won, the percentage of first-serve points won, and the percentage of return points won on the first serve. Winning players won roughly 48.9 percent of their breaks, 79.5 percent of their first serve points, and 32 percent of their return points on the first serve. Losers (20.9% on breaks, 67% on first serve, 20.7% on returns) trailed considerably in those three winning variables.

[Female player success was much more heavily influenced by break points won, with winning players owning 57 percent of their break points, and losers just 32.3.]

Look at Roger Federer’s career statistics and you’ll notice some commonalities. Fed won 50.1 percent of the break points he faced, 77 percent of his first serve points, and 32 percent of his return points on the first serve.

A different study from 2023, looking at 4,669 points played during the 2021 French Open, Wimbledon, and U.S. Open, found that a successful first serve increased the chances of winning the point by roughly 17.5 percent. Statistically, the optimal route to winning a point was by delivering a strong first serve, maintaining a rally of less than five shots, and ending with the ball dropped into service zone, which usually produced an error by the opponent. Tennis fans would have to chime in here, but I’d venture a guess that Federer did that a lot.

Ten thousand hours

Moving on from cold, hard statistics, I think there is another “soft” lesson from Federer’s speech, about grit and determination.

The most universally accepted theory about the foundation of expertise is K. Anders Ericsson’s so-called Ten Thousand Hours rule, positing that a minimum of 10 years of deliberate, effortful practice is the true hallmark of expert performance. My takeaway from this research is less about the number. I’ve always been floored by the years.

Years. Years of obsessive, intensive, deliberate, effortful, practice. Practice. We’re talking about practice. Years. I played saxophone growing up; couldn’t last more than two years. Didn’t have the patience, the time, the obsessiveness to keep it going, all three of which is absolutely required to even begin a march on the path toward 10,000 Hours. Few do. That’s where the experts truly separate from the rest of us. They’re maniacs.

Federer’s example makes me marvel at the grit and bonkers tenacity of a performer whose skill only manifests a successful point at a rate just above chance.

I have to imagine that requires some psychological extremes to belong and remain in the upper echelon, including, as Federer mentions, an extraordinary ability to move on, forget the last play, and fight for the next. For years. Few have it. They’re maniacs.

But the rest of us can learn a thing or two.

Links

Faster, stronger, smarter? New research shows the importance of brain training for junior athletes … India’s newest addition to its Olympic team: a sleep expert … The secretive art and science of picking USA’s Olympic gymnasts … Engineering a fast swimming pool … Humans are built to go faster in the 50-meter freestyle and 100-meter dash than current records show … The science of Simone Biles … How to take the perfect soccer penalty kick … The number theorist teaching Olympic swimmers to swim more efficiently … Golf putter works so well “it feels like cheating” … The spray-on sneaker is gunning for gold in Paris

References

Fernández-García, Ángel Iván, et al. Differences in competition statistics between winners and losers in male and female tennis players in Olympic Games. No. ART-2019-114269. 2019.

Prieto-Lage, Iván, et al. "Match analysis and probability of winning a point in elite men’s singles tennis." Plos one 18.9 (2023): e0286076.

Culver, J. “Why 52.4% is the most important percentage in sports gambling.” Medium, 2020: https://medium.com/the-intelligent-sports-wagerer/why-52-4-is-the-most-important-percentage-in-sports-gambling-16ade8003c04