MELBOURNE, Australia — As the reigning Australian Open champion Naomi Osaka opened her season earlier this month, she checked herself as she expressed her goals for the rest of the year.

“I think just to try as hard as I can every match,” Osaka said. “Because for me, when I feel like I do that, I somehow end up winning the match, no matter what.” As she heard herself, her eyes widened. “Oh, that sounds really arrogant,” she said, clearly embarrassed.

Osaka had spoken into a microphone what she has already made clear with her racket over the past two years: Underneath her quiet demeanor, she has an assured confidence that has helped carry her to two Grand Slam titles. She may be soft-spoken in public, but she is also steely and determined.

Osaka, 22, showed that mettle most unmistakably during the 2018 United States Open final against Serena Williams, closing out a title even as Williams got into heated arguments with the umpire over penalties and the crowd booed what they felt was unfair treatment for the 23-time Grand Slam champion.