Coco Gauff and Naomi Osaka meet at a tennis coaching crossroads in Beijing

The other-man theory about coaches is a sporting truth.

A team that loses more than it wins with a so-called player coach, someone who specializes in dealing with athletes and creating a relaxed atmosphere, will often replace them with a disciplinarian. Reserved coaches who don't find success are replaced by energetic, emotional types who are big on motivation. The studious type who focuses on the X's and Os will come back when that act becomes scarce.

Tennis players are no different, the latest cases being Coco Gauff and Naomi Osaka, who dueled in Beijing on Tuesday during the penultimate WTA 1000 tournament of the year.

Both players entered the year with high expectations, but did not live up to them. After early eliminations from the US Open, Gauff lost in the fourth round, Osaka in the second round and both announced coaching changes.

Gauff jettisoned Brad Gilbert, one of the sport's biggest personalities. He is an ESPN commentator and former coach of Andy Roddick and Andre Agassi, with a grand uniform theory of tennis known as Winning Ugly. Gauff then brought in Matt Daly, a little-known grip specialist, to work with Jean-Christophe Faurel, the low-profile French coach who has worked with Gauff on and off since she was 14.

Faurel rejoined Gauff's entourage for the last time last spring, to work with Gilbert. Gilbert and Gauff barely knew each other when she hired him in the summer of 2023. Weeks later she became US Open champion.

Osaka, meanwhile, turned to Wim Fissette, the quiet, cerebral Belgian who helped her win two Grand Slam titles in 2020 and 2021. Fissette would be fine if he never appeared on television. Osaka's new coach is Patrick Mouratoglou, the former coach of Serena Williams. He has a gift for motivation and self-promotion, with a brand empire that includes an academy in the south of France, plus the freewheeling Ultimate Tennis Showdown (UTS) tennis exhibitions and coaching camps in luxury resorts.

He was almost too recognizable for Osaka. Mouratoglou's history with Williams and his presence in the game made her want to avoid him.

His personality is so big, Osaka said at a news conference in Beijing. So great that she was skeptical of his coaching abilities: anyone who coached the greatest female player of the modern era might have enjoyed his part in Williams' success.

Then I met him, talked to him and worked with him in the fields, she said.

He is definitely a very good coach.

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John Kerry, former senator, US secretary of state and US climate czar, once reduced his philosophy of government, war and diplomacy to, essentially, getting things right as quickly as possible when you're wrong.

Sporting aphorists often quote the first law of holes: if you're in one, stop digging.

Both essentially sum up Osaka and Gauff's coaching pivots. Players usually make these moves as soon as the season is over, rather than with two months left. Gauff and Osaka are on the Asian swing, which is especially important for Osaka, the Japanese torchbearer at the Tokyo Olympics three years ago. Then come the WTA Finals in Riyadh, Saudi Arabia, for which Gauff may qualify, and the Billie Jean King Cup in Malaga, Spain, where Osaka plans to play.

But by mid-September they already had all the data they needed to conclude that they were either going in the wrong direction (Gauff) or stuck (Osaka).

Although Gauff's results were off target with a fourth round exit at Wimbledon to Emma Navarro before Donna Vekic beat her in the third round of the Paris Olympics, the bigger problem was technique. Gilbert's ability to cover up her weaknesses, one of his greatest strengths as a coach, had faded.

Quality opponents had figured out how to counter the forehand he introduced to cover up her shakiness on that side. They intervened and took the ball with them as it bounced up, before it bounced high enough to trap them at the back of the pitch.

Against Navarro at Wimbledon, she begged Gilbert to tell her something, realizing at that moment that she did not have the tools she needed to escape Navarro.

Then there is her service. At the US Open, her fourth-round defeat to Navarro included 19 double faults.

I don't want to lose these kinds of matches anymore, she told reporters afterwards.

Gilbert, who has forgotten more about tennis than most people know, would never project himself as a service specialist, or even the kind of coach that someone as mired in technical limitations as Gauff now needs. Even during Gilbert's tenure, Gauff had worked with Roddick on some minor service adjustments.

In an interview last week, Gilbert declined to get specific about his work with Gauff, but said it was a positive experience overall.

He believes the ultimate parameters of tennis have not changed. Players need to figure out what their strengths are, and then they need to figure out what their opponent does well. They then plan to impose their own strengths on the match while nullifying those of their opponent. But at 63, after more than four decades in the professional game, Gilbert knows the ropes. Once a player wins one of the Grand Slams, expectations rise, even though the competition remains fierce. Everyone wants to win and there are only four majors a year.

The women's game has a little more unpredictability, Gilbert said, but still there aren't many opportunities.

Every coaching experience is a unique experience and you move on, he added. That's a beautiful thing.

Still only 20 years old, Gauff longs for success, but she is looking at the long term. She is approaching the fall tournaments in Asia as an extended preseason, prioritizing improvement over wins and a top-eight finish for the season, which would qualify her for the season-ending tour finals.

Her team prefers that her coaches talk little about her; she notices that the subtle changes Daly has made are already starting to pay off.

Daly, 45, played at Notre Dame and briefly coached Denis Shapovalov. He is the founder of a company that sells a gadget called GripMD, which wraps around the handle of a racket to help players use a traditional continental grip.

Gauff hits her forehand with a heavy western grip, essentially holding the racket under the handle. Don't expect her to switch to a continental grip on her forehand anytime soon, it just won't cut it. Her immediate focus is on her service, but that's about it It may take some time for the dividends to appear on the statistics. She had six double faults and 27 unforced errors in the two sets on Tuesday, which she and Osaka shared before Osaka retired with a back injury.

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If Gauff looks longer term, Osaka wants results now. It wasn't always this way.

She has faced tough draws all season, especially when she came close to knocking Iga Swiatek out of the French Open. At the time, she was introspective and came up with her own aphorism: The results were not forthcoming, she told reporters. Fissette and Osaka focused on her comeback for this season and the next five years. Waiting for the summer and fall, when tennis moves to the hard courts on which Osaka built its reputation, has been the mantra.

That wait steadily eroded Osaka's confidence. After Karolina Muchova defeated her in New York, she told reporters that a part of her dies when she loses. That Osaka was not the wry, magnanimous Osaka of Paris. The French Open was a lifetime ago in her world, and she had believed she would have more success on her favorite surface. Muchova, who floated to the semifinals of the US Open and was probably one volley away from the final, is doing pretty much what Osaka wants to do.

Osaka and the rest of the locker room know she must return better, improve her second serve and regain the confidence that, in her best moments, made her an absolute banker in times of crisis. More than anything, that was her superpower, and it was largely missing this year.

That is why she switched to Mouratoglou in the 2024 season with two months to go. She is world number 73 and is desperate to get into the top 32 so she can be seeded at the Australian Open in January.

Fissette, her former coach, is known as a master strategist and tennis technician. Trust comes from results in his world. He shares with Mouratoglou a belief in playing aggressively and building that intensity when it yields results, but he is not the definition of a hype man. Mouratoglou could urge a postman to deliver the mail.

Osaka had considered hiring Mouratoglou before contacting Fissette again as she planned a comeback after her maternity leave. She then went with the Belgian because of their history of success. When it didn't return, she and Mouratoglou worked together in California after the US Open and then decided to take on the women's tour together.

I don't want to have any regrets, Osaka added in Beijing last week.

I really need to learn as much as possible at this stage of my career. Patrick seemed to be the man with the information.

They got off to a good start, with three straight wins, including Osaka's first comeback from a set down in more than two years, against Yulia Putintseva. But eEven the best coach can't have much success with an injured player.

After shaking Gauff's hand at one point before the American carried her bag off the field, Osaka said her back stiffened so much in practice that she locked up. She was able to start, but her condition deteriorated as the race progressed.

Totally worth it lol, she wrote on Threads.

Sounds like something Mouratoglou would say.

(Top photo: Yanshan Zhang / Getty Images)