FLUSHING MEADOWS, N.Y. — As she came back to the U.S. Open, where she made her first major final just 12 months ago, Jessica Pegula was still of the top American women in tennis. She still barely backed herself to do it all over again.

She lost in the fourth round of the French Open to Loïs Boisson, the wild card who made it all the way to the semifinals. Pegula won a Wimbledon tune-up in Bad Homburg, Germany, but then lost to a peaking version of Elisabetta Cocciaretto, who at the time was 113 places below her in the world rankings. Boisson was 358 places lower.

After losing to Aryna Sabalenka in her home Grand Slam, and getting past the quarterfinals at a major for the first time in the process, she was expectant of more Grand Slam success. The defeats to Boisson and Cocciaretto reset her expectations. It was time to start thinking about winning one, but she hadn’t come close.

“It was kind of back to the drawing board,” she said after the mostly dominant quarterfinal win over Barbora Krejčíková, a two-time Grand Slam champion from the Czech Republic, which set her up for a rematch of her 7-5, 7-5 defeat to Sabalenka on Arthur Ashe Stadium, this time in the semifinals.

The drawing board has worked in New York, but it didn’t right away. After Wimbledon, she went to the Citi Open in Washington D.C. and lost her first match. Then she went to the Canadian and Cincinnati Opens, where she won just one match in two tournaments and lost to more players far below her pedigree. When she thinks about and talks about that period, she gets this look on her face like she has just smelled something really bad.

“A lot of ups and downs, a lot of interesting practices, even leading up to the week before here,” she said.

And then it was back to the drawing board all over again. Or back to a different one. For Pegula, who is 31 and more than a decade into a pro career that didn’t begin to take off until the second half of her 20s, all the drawing boards kind of blend together.

That said, here’s what Mark Knowles, one of her coaches of the past two seasons alongside Mark Merklein, knows to be true about her: She is one of the cleanest hitters in the world.

“Her foundation is striking, moving the ball, being aggressive from the back of the court, but the real key to her summer last year was her movement,” Knowles said. “She was moving exceptionally well.”

Pegula doesn’t have the blazing speed of Coco Gauff or the gracefulness of Karolína Muchová. But movement in tennis is as much about anticipation as anything else. If a player sees where a ball is going, she can often get to it. And Pegula is really good at seeing where the ball is going.

When he began coaching her, Knowles had the same experience with Pegula as he had had with other elite players. Players hire coaches to make them a little bit better. But elite players can also be stubborn, which is part of what makes them great. They know what they do well and they like to do it.

Pegula didn’t give those signals in her initial conversations with Knowles. She was 30. She likely had played more of her career than was left. It was now or never.

“She could have easily been satisfied with a bunch of quarterfinals and top 4 in the world or whatever she was, and the world No. 1 in doubles,” Knowles said. “She’s having an incredible career but you know she took it upon herself that she wanted to see exactly where she could get to, her peak.

“I think that’s what makes these athletes a little different from others.”

Still, coaching an elite player becomes a dance. How much can they be pushed into a zone of discomfort, into trying new stuff, and how much will they dig their feet in and say they know themselves best? The trick for coaches is to figure out how to impart their beliefs, alongside those of the players.

In Pegula’s case, that meant combining the ball striking with moving forward, and then maybe working in some variety, like the drop shots that Sabalenka used to torture her during last year’s final. Then they tried to optimize her movement, too.

Pegula has been nursing a minor knee injury for most of the year, which hasn’t helped, but despite the Grand Slam disappointments, she has continued to post enough of the solid, reliable play that makes her both bankable and easy to overlook.

So what changed to allow her to win five matches at this U.S. Open? Pegula admitted that she has had a “favorable draw” up until facing the world No. 1, but that isn’t all it is.

“The goal was to simplify things and to get me back playing my game, and I feel like we’ve been able to do that,” Pegula said Tuesday. “So I’m really happy that the challenge was met, I guess.”

Not emphatically conclusive either. But Knowles has another idea: the mixed doubles. Pegula used to play a lot of doubles with Gauff. That ended after the Olympics, so they could both concentrate more on singles.

Then, Pegula signed up to play the revamped mixed doubles with Jack Draper at the U.S. Open. They made the semifinals, losing in a match tiebreak to Iga Swiatek and Casper Ruud.

Knowles said he hadn’t mentioned this theory to her. He thinks that the run reinstated Pegula’s confidence in her all-court game.

“I think it just kind of recalibrated her belief — ‘I am pretty good at the net. I have good hands. I have good instincts up there,’ even though it’s something that we’ve been preaching.”

He’s seen a carryover from there to the singles. Pegula is transitioning more to the front of the court, trusting herself in places where she wasn’t trusting herself before, while still moving well and clocking the ball.

And now she’s in the semifinals, with a chance to exact some revenge on the world No. 1, Sabalenka, in the big stadium that now feels kind of like home.

“I’ve really just tried to get back to competing, keeping the attitude great and positive and enjoying playing on Ashe in front of the fans. Taking that into account and getting back to more of the fun aspect of playing,” she said.

“That is fun. It’s not fun to go out there and stress yourself out and be worried about how you’re playing every second of the day.”

This article originally appeared in The Athletic.

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