The second-round clash between No.6 seed Coco Gauff and former World No.1 Naomi Osaka at the Mubadala Silicon Valley Classic on Thursday will be the fourth chapter in an intriguing rivalry.

Their careers have been intertwined ever since Osaka comforted Gauff after defeating her at the 2019 US Open. Following her first-round win against Zheng Qinwen this week, Osaka compared her matches with Gauff to the family events where she would watch Venus and Serena Williams on television.

"Seeing that, seeing people who looked like me, was definitely inspiring," Osaka said.

Gauff hopes her growing rivalry will inspire young black girls the way the Williamses inspired her. "If I was a young girl, I wouldn't care who even won the match."

"Arthur Ashe and Althea Gibson were the real firsts, but as a kid, Serena was the first to lead that change for me," Gauff said. "I hope another girl in that moment can say the same about me and Naomi and hopefully I'm still playing and I get to play her. That's my goal, to play someone who played because of me."

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The head-to-head to date

The pair have met once in each of the past three years, with the results reflecting the twists and turns of their careers. At the 2019 US Open, Osaka was the defending champion and top seed. She swept past the wild card Gauff, who was playing the fourth tour-level main draw of her career, in the third round 6-3, 6-0. At the same stage of the 2020 Australian Open, Osaka was again the defending champion -- but Gauff took a 6-3, 6-4 revenge for her first Top 5 win.

Last year, Osaka endured a rough summer stretch in which she won two out of four matches during the North American hard-court swing. This week, she has said that she felt anxious for the whole period. But one of those victories still saw her edge Gauff 4-6, 6-3, 6-4 in the second round of Cincinnati.

Osaka levels up to beat Gauff in three sets: Cincinnati Highlights

2021 Cincinnati

"On the court we're going to fight really hard against each other but off the court we have nothing but respect for each other for what we do on and off the court," Gauff said. "So that type of energy. I don't want to say we're on the level of Federer and Nadal, but that type of energy you get from them when you see them on the court and you're like, they dislike each other in that moment and as soon as the match is over it's nothing but friendship."

What's at stake

Who needs the win more? Both Osaka and Gauff have made strides this year, but still find themselves with something to prove. Osaka's run to the Miami final was an eye-catching comeback statement that lifted her ranking back into the Top 50, but her aspirations on clay and grass were undone by an Achilles injury. Back on her favoured hard courts, Osaka needs to pick her Miami momentum back up again.

Gauff is newly minted as a Grand Slam finalist. In June, she finished as the runner-up to Iga Swiatek at Roland Garros. But a third-round loss against Amanda Anisimova at Wimbledon marked the first time she failed to make the second week at SW19. Gauff will want to show that was a mere blip after a rigorous clay-court swing -- and to level the head-to-head with Osaka again.

Keys to the match

Osaka came through one of the toughest openers in the draw, defeating fast-rising 19-year-old Zheng Qinwen 6-4, 3-6, 6-1. The four-time major champion's serve was crucial. She fired 11 aces and saved seven of the eight break points she faced.

By contrast, Gauff stormed past Anhelina Kalinina 6-1, 6-0 in just 55 minutes. Kalinina was playing her first match since retiring due to a right wrist injury in Budapest three weeks ago, but Gauff also demonstrated supremacy on serve. The 18-year-old only faced one break point throughout.

Asked about Gauff's greatest strength, Osaka's response was not to highlight a particular shot, but to underline her opponent's mentality.

"When I was her age, I would find myself getting frustrated and I would show it," Osaka said. "I just think it's really cool how she's able to stay mature all the time."

Intentionally or not, that praise was a reverse echo of how Osaka admitted to getting "overwhelmed" by the hype around their match in Australia two years ago, and "tense" in Cincinnati last summer. Mentality will be key for her once again this time round, but she struck a note of confidence looking ahead.

"When I go on the court, I know who I am," Osaka said, "so I just want to see what she's going to bring."