At the college, high-school, and grade-school levels of basketball, there is always a tall guy sitting like a potted plant at the end of the bench, basketball’s version of the special-cases lounge. Such a person is called “a project.” A slight aura of pity and forbearance surrounds these players, beneficiaries of affirmative action for tall people. This extends all the way to the professional level. “Big men get paid,” is a basketball truism, and the N.B.A. has long been haunted by the spectre of marginal talents being paid huge sums mostly because of their size. There have been disappointing guards drafted out of college, but the legendary busts, from Sam Bowie to Greg Oden, tend to be big men. “You can’t teach height,” another basketball truism, is also a double entendre: you can’t teach someone to be tall; the tall are hard to teach.

But why is it that some big men develop and others do not? What is it that must be learned? I was fascinated to read, in Jonathan Abrams’s book “Boys Among Men: How the Prep-to-Pro Generation Redefined the NBA and Sparked a Basketball Revolution,” that when Kevin Garnett was a tall, slender thirteen-year-old, he would spend all his free time at his local basketball court in Greenville, South Carolina. The police would have to chase him out at night, and he would arrive with a ball before dawn. But, if the playground was a refuge, it was also a theatre of cruelty where a six-foot-four, three-hundred-pound player nicknamed Bear would dominate him verbally and physically. “I’ve got your mind in my pocket,” he would yell at Garnett after scoring on him. “I own you.” Even after Garnett outgrew his tormentor in height, even when he showed clear signs of becoming a star, the dynamic persisted. “Garnett did not verbally retaliate,” Abrams writes. “He maintained a straight face and returned daily.” Was this masochism or fortitude?

Garnett is now retired, and he was once one of the most ferociously competitive, trash-talking players that the league had ever seen. He is a direct antecedent of what are now called unicorns—big men who can dribble, pass, protect the rim, and shoot the three—but his most lasting legacy on the court may be his habit of knocking away the jump shots that opponents shoot after a whistle. One sees this all the time in today’s N.B.A.—a player shoots after the whistle just to get a stroke in, to see the ball go in the hoop, and an opponent expends considerable energy to rise up and swat it away before the ball can go in. It’s a bit of ritualized psychological warfare, as if to deprive the opponent of every possible satisfaction. “I’ve got your mind in my pocket. I own you.”

In my town of New Orleans, I’ve been closely watching the Pelicans star Anthony Davis, who, though he never rode the bench in the special-cases lounge, is nevertheless a kind of project. In spite of the fact that he was a blue-chip recruit out of high school, played basketball at Kentucky, where he won a national championship and was named most outstanding player of the N.C.A.A. tournament; was the No. 1 pick of the 2012 draft; and then played on the 2012 Olympic team (which won gold, and where he was the youngest player)—in spite of all this, for most of his career, Davis has been discussed in terms of potential. Even when he began to post impressive numbers, and made the All-Star team for the first time, in 2014 (as the replacement for an injured Kobe Bryant), the talk of the present was always accompanied by speculation about what was to come. As recently as this past December, ESPN’s Adrian Wojnarowski wrote, “Davis is still an ascending, transcendent talent, a size and skill set from the future plopped into the present.”

Some of this sense of anticipation regarding Davis is owing to the fact that the idea of growth is fundamental to his story. As Vinay Mullick, the former athletic director of Perspectives, the small charter school that Davis attended in Chicago, put it to me, “Sophomore year he was six feet one, very thin, very long. He wasn’t thrown onto the national stage until he was practically a twelfth grader. There were times when he didn’t think he would get looks. He would tell me, ‘I don’t know if basketball is going to work out for me.’ He had an uncharacteristically long period of innocence. He was six-ten by the time he graduated. You’re not going to see that again. The story of growth.”

Even though Davis has a height and wingspan unlike almost any other human—Wojnarowski referred to his “condor arms,” but why not go all the way and call them pelican wings?—he is somebody who young people can hope to be. He was once just like us, a six-foot-one sophomore whose fantastical dreams of basketball glory were dying. And look what happened!

The era of speculating on Davis’s upside has recently been replaced by a sense of astonishment at the present. Among the bevy of statistics generated by the Pelicans’ Game 4 sweep of the Portland Trail Blazers: Davis has now scored a total of two hundred and fifty-eight points in his first eight playoff games. “Only Michael Jordan (283) and LeBron James (266) have scored more points in their first eight playoff games over the last 40 years,” according to NBA.com. Also, Davis’s Game 4 totals of forty-seven points, ten rebounds, and three blocks are the most in a playoff game since Hakeem Olajuwon, who scored forty-nine points in 1987, in a game that went to double overtime.

Davis’s impact is just as substantial on defense. He was the most outstanding player when Kentucky won the N.C.A.A. championship, based almost entirely on his defense and rebounding. His length and his ability to move his feet were essential to the Pelicans’ strategy of containing Portland’s explosive guards. On offense, he exerts a gravitational pull wherever he is, inside or outside, and perhaps most of all when rolling to the basket off a pick-and-roll. There is something almost dreamy about the way he plays—things that should be out of reach are suddenly within his grasp.

I once sat with Davis along the baseline of the Smoothie King Center, the Pelicans’ arena, after practice. It was a few days after his twenty-first birthday, in March, 2014. He gazed out onto the court, where a few of his teammates were still taking shots, while I peppered him with banal questions to which he gave equally pro-forma answers. I was sufficiently focussed on him that I had no idea a ball was careening toward my face. I only learned of it when, with frog-tongue speed, his hand reached out across the empty seat between us and caught the basketball an inch or so from my cheek. He held it for a split second, then tossed the ball back onto the court. His hand retracted back onto his lap. By the time I turned to thank him, he was again looking away.

Back in 2014, his coaches were working on his moves in what they called “the Malone Zone.”