Florida is where the United States manufactures its élite tennis players. Other countries have their national-federation training centers, of course; America’s is in Orlando. The state has year-round tennis weather, and it has become the home of the big-name coaches, the camps and academies, and all the best young players for an aspiring phenom to compete against. The parents of these kids—who, often enough, are athletes of some sort themselves—frequently uproot their families to move here, homeschooling their would-be prodigies during the few hours a day that they are not on a tennis court. Ten- and twelve- and fourteen-year-olds get evaluated like yearlings on a Kentucky horse farm. They either turn into world-class players or, more often than not, they stall, get injured, or burn out. It’s an expensive process, and it’s neither as pretty nor as clean as the ground strokes that fans gather to ooh and ah at the big tournaments.

The talk of the latest big tournament, the Miami Open, as it got under way last week was a story in the Sun-Sentinel about Naomi Osaka’s South Florida years, when she was one of these tennis kids. It is the story of a mother, Tamaki Osaka, working an office job to house her family while her husband, Leonard François, tried to do for his daughters what Richard Williams did for Venus and Serena. It is also a story of coaches reportedly going unpaid: one of them filed a lawsuit last month over a contract he says François signed that allegedly granted the coach twenty per cent of the future tennis-competition earnings of both Naomi and her older sister Mari, in return for free coaching in Pompano Beach. Last Wednesday, reporters gathered around Osaka and asked about the lawsuit; she said that she couldn’t talk about it. On Saturday, she was upset by the tricky Taiwanese slice-master, Hsieh Su-wei. (Osaka has struggled some since her Australian Open victory, and she could slip from her world No. 1 ranking by the time the Miami Open is over.)

Meanwhile, Cori (Coco) Gauff played her first W.T.A. tour-level match. Gauff is fifteen years old. She is thought by tennis insiders to be the best next-next-generation prospect in Florida. She is coached by her father, Corey, who grew up in South Florida and played basketball for Georgia State. He and his wife, Candi, who ran track for Florida State, moved the family to Florida from Atlanta when Gauff was in second grade. By the age of eight, she was attracting tennis-world attention, winning the “Little Mo” Internationals, in Palm Beach Gardens. (The competition is named for Maureen (Little Mo) Connolly Brinker, who won nine Grand Slam singles titles, in the early fifties.) Two years ago, Gauff became the youngest player ever to reach the girls’ final at the U.S. Open. Last summer, she became one of the youngest players ever to win the French Open girls’ title. On Thursday, Gauff stepped onto tiny Court 7 at the Miami Open, with Corey and Candi there in the first row of bleachers to cheer her on. Patrick Mouratoglou, who coaches Serena Williams, sat with them. Gauff has trained with him, at his academy in the South of France, and there will come a time, if things unfold as they tend to do for young tennis phenoms, when Gauff’s father will bring on a seasoned coach of top pros to aid in his daughter’s development.

Like all of the side courts at the recently revamped Miami Open, Court 7 is situated on what used to be a parking lot for the Dolphins’ Hard Rock Stadium. Gauff, who is still ranked far from the top hundred, was playing in the tournament thanks to a wild-card bid, as was her opponent, another young American prospect, the seventeen-year-old Caty McNally, whom Gauff bested in last year’s French Open girls’ final—and who did not come up in Florida but in Cincinnati, where her mother, who played at Northwestern, is a coach. (McNally’s parents were on hand, too.) The couple hundred spectators who could cram into the bleachers got quite a show. Gauff is broad-shouldered, athletic, and a fierce competitor. She is disinclined to leave the baseline: from that position, she pounds balls with the kind of topspin that drives an opponent back, then back some more. She has talked of copying Serena’s service motion—though her toss is as yet far from Serena’s level of consistency—and she already produces reasonable facsimiles of Serena’s stare-down and, when she blasts a winner, her deeply growled “Come on!” McNally has a more all-court game. Her volleys are remarkable—I wouldn’t be surprised to see her on tour as a doubles player if she doesn’t make it in singles. (Small world, tennis: she and Gauff partnered to win the 2018 U.S. Open girls’ doubles championship.)

Both Gauff and McNally were tight as the match began. Both made errors they wouldn’t make in practice. Both went on to play stretches where they were seeing and feeling the ball, and confidently constructing fine points. Both hit patches where little seemed to go right. That’s what tennis is like when it’s being played by even the best high-school-age players. Gauff eventually outlasted McNally, 3–6, 6–3, 6–4. They hugged at the net, clearly worn out by the heat and each other, and made their way back to the locker room, largely unnoticed by the ticket holders crowding the grounds. (By week’s end, Gauff would be gone, losing to Russia’s Daria Kasatkina, the tournament’s No. 14 seed, in straight sets.)

Later, speaking with reporters, Gauff sounded like a seasoned pro, discussing how she works to stay positive and to control what she can control. She also sounded precisely fifteen: “I hit with Kyrgios this week. We didn’t play a practice match, obviously, because I would have lost. But I hit with him, and he told me that you’re going to go far in this tournament. I was, like, ‘All right, that’s basic.’ He’s, like, ‘No, you’re really going to go far.’ I was, like, ‘O.K.’ ”