The deal got done, and results came quickly. Mr. Federer signed long-term deals with Rolex, Mercedes, Lindt chocolate and Credit Suisse over the next few years.

Mr. Godsick left IMG in 2012. In December of the next year, he announced that he was starting his own agency, taking with him Mr. Federer as both client and business partner. (The other two founding partners in Team8 are Ian McKinnon and Dirk Ziff. The name is a play on the word “teammate,” and a nod to the importance of the number 8 in China, where Mr. Federer is a huge star.)

Its initial clients, besides Mr. Federer, were the tennis players Juan Martín del Potro and Grigor Dimitrov. Mr. del Potro remains a client; Mr. Dimitrov, who at one point seemed on the verge of breaking into the top tier of players but who has since faded, left in 2017. The firm has since added Henrik Lundqvist, the hockey star, and Cori Gauff, a rising junior tennis player.

Mr. Godsick said that he had been thinking about leaving IMG for some time, and that he told Mr. Forstmann in 2010: “Ted, you know I am never going to own this company. I want to do my own thing.” (Mr. Forstmann died in 2011, but Mr. Godsick stuck to his commitment to wait two years before going out on his own.)

Did his new partner, Mr. Federer, not have any qualms about leaving one of the biggest sports agencies in the world for an untested boutique firm where he would also be part of management?

“I didn’t worry about leaving IMG, to be honest, because I had done it once before,” Mr. Federer said. “That taught me a lot about the business. It made me want to care about that side of my career. To build something with Tony, along with our other partners, who were also good friends of mine, felt very exciting.”

Moreover, he felt the time was right. “By then I was an experienced player, an experienced person,” he said. “At that point in my career I was able to sit in a room and discuss business, or entrepreneurial opportunities, and then walk out of that room, onto center court, and play a match. ”