The last two women to win the French Open before Serena Williams share an agent, a common foe in the American and a huge desire to get their title back.
Maria Sharapova, winner in 2012, and Li Na, the champion in 2011, have both come off second-best against Williams more often than not, bludgeoned by the sheer power - of the mind and body - of the world No 1.
It is 10 years since Sharapova last beat Williams but the Russian still believes there is more joy around the corner. "I want to achieve more, I want to win more Grand Slams and I want to get back to No 1," said Sharapova, who won the title in Stuttgart last month.
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"I think when you have that feeling of being there before and holding those trophies, they are so memorable. You spend so many hours training to feel that excitement, to feel that energy, that adrenaline for those moments of match-point victories. That's why I [still] play, because that's what I've known for my whole life. And my body still allows me to do that. I have done it since I was a very young girl. I love the thrill of it. I don't think there is anything else that would give me that much satisfaction in what I do."
Ten years after she won Wimbledon, it is arguable that the woman who off the court has become a brand in her own right, has transformed herself on clay, too, to the point where it could almost be considered her best surface.
"I don't know about that," she said. "I don't like to say any is my favourite. I feel like I've evolved on it. Clay was very different because I was always physically challenged on it, I never thought I could stand those long matches and have the strength to come back the next day.
"It's a learning process because you have so much more time to see point construction, to see the game and to understand it. I really enjoy that. I've always liked to have hitting partners to challenge me to hit an extra ball, and that's helped me a lot in recent years I think."
Li, like Sharapova, never believed clay was a surface she could win on and yet her first Grand Slam title came in Paris. Feted by the millions of people watching back home in China, it took her some time to cope with the adulation of a nation and her results were inconsistent for much of the following year.
But since teaming up with Carlos Rodriguez, the former coach of Justine Henin, Li has gone up another level and victory in the Australian Open at the start of the year gave her a second Grand Slam title.
"I never thought I could win on clay," Li laughed. "Hard courts yes, but not clay. But then I did. When I won in Paris, I don't think people could believe it. But when I won in Australia, they knew that I could, so that was better."
Since winning in Melbourne, Li has been playing consistently good tennis and at the age of 32, she remains one of the best athletes on Tour.
"I think my chances here are good," Li said, with a smile. "I am playing well. I am always trying to be consistent and it's good."
There will be British interest in the women's singles after Heather Watson's crushing victory over Anett Kontaveit in the final round of qualify- ing yesterday. The British No 2 needed just 48 minutes to defeat 18-year-old Estonian Kontaveit 6-1, 6-1, making . it eight victories in a row.
While things have been going well on the court, it has been a poignant week off it for all associated with British tennis after Monday's funeral of Elena Baltacha. Watson was a Fed Cup team-mate of the former British No 1, who died from liver cancer this month. The 22-year-old said: "It's so sad. I'm just using it as motivation that life is short, you don't know when it's going to be your last so just make the most of every day. She was so feisty on the court. I can picture her now saying, 'Come on'. I just can't believe she's not here any more."
Watson has a winnable first-round match against Czech world No 63 Barbora Zahlavova Strycova, although fourth seed Simona Halep is likely to lie in wait for the winner.