Over time, though, the academy hardens them mentally as well as physically. I asked Dylan how he felt about his coach’s being fired. He shrugged. “The football world is a hard world,” he replied. “He has made the decision to send boys away. Now he knows how it feels.”

LATE ONE AFTERNOON in the cafe at De Toekomst, I was talking with a coach, Patrick Landru, who works with the academy’s youngest age groups, when he asked if he could take my writing pad for a moment. I handed it over, and he put down five names, then drew a bracket to their right. Outside the bracket, he wrote, “80 million euros.” The names represented five active “Ajax educated” players, as he called them, all of whom entered the academy as children, made it through without being sent away and emerged as world-class players. Eighty million euros (or even more) is what Ajax got in return for selling the rights to the players to other professional clubs. Once a team pays this one-time transfer fee, it then negotiates a new, often very large, contract with the player.

Wesley Sneijder, the first name on the list and probably the most accomplished young Dutch player at the moment, started at the academy when he was 7. At 23, Real Madrid acquired him for 27 million euros. (He now stars for Inter Milan, the current Italian champion and the winner of this year’s Champion’s League tournament, Europe’s highest club competition.) The other four players named on my pad were, like Sneijder, highly paid pros for clubs outside the Netherlands and prominent members of the Dutch national team that will compete in the World Cup beginning this week in South Africa.

An emerging national-team star, Gregory van der Wiel, was not among the names on the list, because he still plays for Ajax, but it is widely assumed that he will be the next big sale. A heavily tattooed rap aficionado who likes to spend his downtime in Miami’s South Beach, van der Wiel, now 22, was sent away from Ajax at 14 because of a poor attitude — “I was an angry little boy who had not yet learned to listen,” he told me — then was invited back after spending three years in the academy of another Dutch pro club, now defunct, which he recalls as having had inferior facilities, coaching and even uniforms. I asked Martin Jol, the coach of Ajax’s first team, if it was difficult for him to nurture young players knowing he would lose them just as their talent blossomed. “I think that is the purpose of Ajax, to develop players and bring them up to the first team as young as possible,” he answered. “And then we sell them, not for peanuts but for a lot of money.”

In the U.S., we think of money as corrupting sport, especially youth sport. At Ajax, it is clarifying. With the stakes so high — so much invested and the potential for so much in return — De Toekomst is a laboratory for turning young boys into high-impact performers in the world’s most popular game.

The Ajax youth academy is not a boarding school. The players all live within a 35-mile radius of Amsterdam (some of them have moved into the area to attend the academy). Ajax operates a fleet of 20 buses to pick up the boys halfway through their school day and employs 15 teachers to tutor them when they arrive. Parents pay nothing except a nominal insurance fee of 12 euros a year, and the club covers the rest — salaries for 24 coaches, travel to tournaments, uniforms and gear for the players and all other costs associated with running a vast facility. Promising young players outside the Ajax catchment area usually attend academies run by other Dutch professional clubs, where the training is also free, as it is in much of the rest of the soccer-playing world for youths with pro potential. (The U.S., where the dominant model is “pay to play” — the better an athlete, the more money a parent shells out — is the outlier.)

Ajax makes mistakes, plenty of them. It sends the wrong boys away, and some of them become stars elsewhere with no compensation returning to the club. As a production line, it is grossly inefficient; only a small percentage of its youngsters become elite players. But the club does not throw money after pure fantasy, encouraging visions of pro careers that never have a chance of materializing for children who do not have the foundational talent to reach such goals. The club decides which boys have potential — “Please note,” its Web site advises, “Ajax’s youth academy cannot accept individual external applications” — and then exposes them to scientific training and constant pressure.