Roger Federer recently observed this: “Even top-ranked tennis players win barely more than half of the points they play,” he told Dartmouth graduates in a June commencement speech. Can this possibly be true? Yes, it’s an actual fact. According to ATP statistics, Federer won just 54 percent of the points he played. Novak Djokovic and Rafael Nadal have the same efficiency rate. Yet their 54 percents are good for a combined 66 Grand Slam titles.

Three or four percentage points, sometimes less. That’s the difference between a great and a chaser. Young Alcaraz wins just 53 percent of his points — but one percentage point was all he needed against Tiafoe. The 21-year-old Spaniard took just 51 percent of their points in the third-round encounter, a 5-7, 6-2, 4-6, 7-6 (7-2), 6-2 victory. The advantage continually swung back and forth with the action on practically every other point, so fleet and soft-shoed across the grass. Check this out: By the time Alcaraz took a 2-1 lead in the fifth set, the two men had played 288 points — and the split was a dead-even 144-144.

But in the end, Alcaraz was living proof of what Federer told those Dartmouth grads. “The best in the world are not the best because they win every point,” Federer explained. “It’s because they know they’ll lose — again and again — and have learned how to deal with it.”

When Tiafoe recovers from his disappointment and gets around to analyzing how he relinquished his hold on a match in which he twice led by a set, he will want to examine the smallest percentages. Tiafoe has won 50 percent of the points he has played in his career. Three percentage points — that’s the difference between him and Alcaraz. Yet it represents the yawning difference between a multiple Grand Slam winner and a perennial quarterfinalist who is languishing at No. 29 in the world. And you can’t say that difference is due to talent. “He showed it once again that he deserves to be at the top,” Alcaraz said afterward. “He deserves to fight for big things.”

So much of the tension in their match Friday seemed to reside between the points, in the exposed stillness — that’s when you saw the tics, the plucking at their shirts, the compulsive bouncing of the ball before serving, the repetitive wiping of the forehead with a wristband. It’s also when that small percent of self-certainty could be detected. It came down to which player ultimately coped better with the continual undressing by his opponent. In this case it was Alcaraz. Tiafoe’s strangely frantic activity between the fourth and fifth sets partly told the story. Alcaraz drank from his neatly lined up bottles, then retook the court and waited calmly as Tiafoe decided he needed an entire change of gear, hastily ripping open new packages of sweatbands and a headband and tugging on a new shirt, which was still riding up his back when he finally came out. These were the rattled actions of someone who sought not just fresh clothes but missing conviction.

You suspect that in his heart Tiafoe knows he has yet to make the jump from promising to great, from interesting foil to overlord, in his daily habits. After his electrifying break into the top 10 last season, he has undeniably backslid in his form. He seems interested in chasing greatness only when the lights are bright as opposed to when no one is looking.

The good news for Tiafoe is that the last three percentage points are attainable — no one is born with them, not even Federer. Listen to him explain the great turning point in his own career. What’s hardly ever remarked on, in the gloss of Federer’s trophies, is that he played in 18 Grand Slam tournaments before he won his first major title. Eighteen times he finished a loser. The transformation, he said at Dartmouth, began when a rival publicly questioned his fortitude. “Roger will be the favorite for the first two hours, then I’ll be the favorite after that,” an opponent said of him.

An embarrassed Federer finally understood from that statement that what he lacked was “mental discipline.” He became a player who sought resilience more than outright winners, who strove for the same standard even in the less meaningful matches so that he wasn’t so easily destroyed in the biggest ones.

“When you lose every second point, on average, you learn not to dwell on every shot,” Federer told the students. “You teach yourself to think: ‘Okay, I double-faulted. It’s only a point. Okay, I came to the net and I got passed again. It’s only a point.’”

When Tiafoe studies this loss, he will see that Alcaraz ultimately won just eight more points than he did over the five sets (161-153). Only eight. He should do himself a favor and call up the stat sheet from the 1980 Wimbledon final between John McEnroe and Bjorn Borg. Borg, remember, won it by 1-6, 7-5, 6-3, 6-7 (16-18), 8-6. It too came down to just eight points despite five sets and 55 games. Though it left him bent double in grief, McEnroe chose not to make it a defining loss. He came back and beat Borg the following year.

Federer’s commencement speech ought to be required reading for all adults, not just Tiafoe. So often, the rest of us want a silver bullet, a grand solution, instead of the three percentage points. Such a small differential hardly seems important — until you see its real application and how those three percentage points compound over years for those willing to consistently seek them. “The truth is, whatever game you play in life, sometimes you’re going to lose,” Federer said. “… You want to become a master at overcoming hard moments. That is, to me, the sign of a champion.”