That sounded like heat-of-the-moment optimism in a sport that remains deeply and perhaps permanently fragmented, with too many management companies and governing bodies guarding their piece of the action and gumming up the work of change.

Tennis Australia and the United States Tennis Association, the governing bodies for the sports in two nations that host Grand Slam events, were on board here as investors and partners. But the ATP Tour and the International Tennis Federation, which runs Davis Cup, were not.

“This is just a journey for us, the building of a new brand and building something for the sport,” said Craig Tiley, the chief executive of Tennis Australia. “We know it’s had its critics because there are other events this week, and we understand that. But I’ve always had the view tennis needs to do things that attract more audience, and are cool and a bit different.”

The Laver Cup certainly had more global reach this week than low-level ATP Events. Still, we will only know whether this competition really has legs when it tries to to thrive without Federer and Nadal near the peaks of their power; it remains to be seen whether the will and paychecks remain big enough through the years to draw the best players of future generations.

But the quality of the spectacle and the depth of the emotions were real in Prague.

“The only way it was ever going to be successful is if the players cared, and they did,” Federer said. “I think you see it. I think you see the happiness.”

The dejection, too. Kyrgios dropped to one knee shortly after his final forehand slammed into the net against Federer, and he was soon in tears, surrounded by supportive Team World compadres.