Serena, though, despite the waltz, sharpened herself for tougher tests ahead, at one point shouting to herself, “Come on!” after an unforced error. She bent and shook a fist at the ground after key points won.

This is not the woman so many once saw as not being passionate about tennis. Not caring enough.

During the match, between points, a young female voice was heard to call, “You’re my hero!” Serena heard. It moved her.

“It was so inspirational. I felt amazing,” she said. “I had a moment when I had to stop and think to myself that this is the ultimate compliment someone could give. I just never, when I was growing up, I never dreamt of someone saying that to me.”

Serena and older sister Venus Williams grew up in Palm Beach Gardens. This is their home tournament. I still recall the excitement of what might be when we saw her here for the first time at age 16 in 1998.

The next year, she wound up winning her first Grand Slam title.

And then, 13 years later, she won her 14th and 15th last season. You know the year LeBron had last year? Serena was right there, winning Wimbledon, the U.S. Open and an Olympic gold medal.

Her 15 majors place her sixth all time among women. Just ahead with a catchable 18 are Chris Evert and Martina Navratilova. The American record is 19 by 1920s and ’30s star Helen Wills Moody. The overall record, 24 by Margaret Court, seems out of reach — “seems” being the key word.

Legacy and place in history drive Williams now in a way she used to not admit.

“I don’t know if I could ever top Margaret Court, but, you know, I don’t know,” she said. “It would be exciting to try to reach some of my fellow countrywomen that are ahead of me.”

Serena’s personality is not entirely charming. She can be a bit combative in interviews, something of a diva. She has infamously attacked linemen with withering words. Years ago when his daughters were teens, father Richard Williams correctly predicted Serena would be even better than Venus. How did he know? “Because Serena’s meaner,” he said.

Give her this in the broadest appraisal, though: Serena Williams has designed and paced her tennis career for the long haul, and with rather spectacular results.

The latest reminder came here Thursday when the woman who needs no introduction heard the only one that matters:

“Ladies and gentleman, the No. 1 player in the world …”