“You have to learn to go forward to the net,” said Corey Gauff, her father and head coach. “The game is changing. If you want to have a long career, you can’t be out there playing 30 balls per point.”

Part of what makes Gauff so promising is that she can play the game in all manner of ways. She has the foot speed to grind from the baseline and extend rallies when necessary, but she also has the power with her serve — and second serve — to end points in a hurry.

The buzz surrounding Gauff is a brand of mania to which Williams can certainly relate, considering the buzz she herself generated as a teenager in the 1990s.

“She clearly wants it, works very hard, is extremely mature for her age,” Williams said of Gauff. “I think the sky’s the limit for her.”

Williams said the same about Gauff at Wimbledon, and it was quite a surprise that they got met again so soon in an opening round.

“When we saw the draw, we went, ‘There’s no way that’s random,’” Corey Gauff said with a chuckle.

The Gauff family has seen a lot of the Williams sisters of late. Serena Williams’s coach, Patrick Mouratoglou, has been one of Gauff’s longtime benefactors, and he organized a preseason training camp in December in Boca Raton, Fla., that included Gauff and Serena Williams, as well as Chris Eubanks and Marius Copil.