Patrick Mouratoglou remembers clearly the day when Serena Williams walked into his Paris academy following her shocking loss to Virginie Razzano, the world No 111, at this year's French Open – her first defeat in the opening round in 47 appearances at Grand Slam tournaments.
"It was two or three days later," Mouratoglou recalled here on Sunday night after Williams (below) had won her 15th Grand Slam title at the US Open, beating Victoria Azarenka 6-2, 2-6, 7-5 in a dramatic final. "She just wanted to practise. She came and she said: 'I want to win Wimbledon. I want to start now'."
Williams' fourth US Open title completed an extraordinary summer. Since her defeat to Razzano, the 30-year-old American has won 26 out of 27 singles matches – her only defeat was against Angelique Kerber in Cincinnati – and won, among others, the Wimbledon, US Open and Olympic titles, not to mention the doubles crowns at Wimbledon and the Olympics in partnership with her sister, Venus.
She remains at No 4 in the world rankings – largely because she played in only three tournaments in the seven months following last year's US Open – but nobody doubts her status as the best player in the women's game.
The win over Azarenka, the world No 1, was Williams' 14th in a row against top-five players, although she went desperately close to defeat. Azarenka served for the match in the third set and was only two points from victory at one stage. In the second set, in particular, Williams tightened up under the pressure of wanting to succeed at her home Grand Slam tournament for the first time since 2008.
Mouratoglou, however, never doubted her. "I knew that if there was even the smallest chance that she would take it," he said. "And I knew she would have the chance."
The Frenchman believes that Williams' dip in the second set was down to exhaustion. "We have to understand how tired she is because of the summer she had," he said. "Physically and mentally she was completely exhausted. So in a final against a better player than any other she had played in the tournament, she could not keep her focus – and when she lost her focus she lost her footwork and then she started to miss. But the most impressive thing is that when she really needed it, her tennis suddenly came back."
He added: "It was just one more confirmation that she is the biggest champion of all the current players and one of the best in history, if not the best."
Mouratoglou said that Williams was "a machine – you just have to show her how to use the key of the machine and if she uses it I think she's the best player in the world." He does not believe she will lose her motivation in the future and said she was a perfectionist in practice.
"She keeps on working," he said. "The things she wants she gets. Sometimes we go for 30 minutes and it lasts two hours because she's not satisfied. She still wants to make progress. When you see other players who haven't won a Grand Slam and think they know everything, it's really impressive."
When Williams was asked to compare herself now with the teenager who won her first US Open title here in 1999, she said: "Gosh, we both have so much to look forward to. Even though I'm 30, I feel so young and I've never felt as fit and more excited and more hungry. Even with this win I'm sitting here so excited still to play the next Grand Slam and see what I can do. Just to do more, I love that feeling. I feel like it's overdue. I'm excited."
Williams said that Mouratoglou, who has worked with many players including Marcos Baghdatis and Laura Robson, had been a "really positive" influence. "I love how calm he is," she said. "I'm a little crazy. Whenever I look up he always looks so confident. I love that. So we have a good strategy going on. We have a good chemistry.
"It's been fun to get a change of scenery at 30 years old. It's like doing the same thing day after day, year after year, and then I have a change. It's kind of cool. I think it's just made me more excited to play."
Williams, who has an apartment in Paris, added with a laugh: "I don't live there, for the record. Can't pay those taxes. I live in the United States of America. I am American."