She will surely never get there altogether. Navratilova won 167 career singles titles, which ranks her first in the Open era. Evert, 58, won 154, which ranks second. Williams, even after all her trophy hoisting in 2013, still has won only 56.

But she has closed the Grand Slam gap voraciously, winning the French Open and U.S. Open this year to bring her career total of major singles titles to 17. That is just one short of Navratilova and Evert, who are tied for fourth on the all-time list with 18, behind Margaret Court with 24, Steffi Graf with 22 and the pre-World War II star Helen Wills Moody with 19.

“We’re already kind of teasing each other about Australia,” Evert said of Williams and next year’s Australian Open. “Because she’s going to tie us in Australia if she wins it and then next year she could pass Martina and I, and then there’s Steffi, and that’s very doable. And if she passes by Margaret Court, that’s like Hercules, a Herculean effort to me. That would be almost not human to win what, eight more?”

Much could derail the Williams train: injury, age, ennui, complacency, the continued improvement of Victoria Azarenka or the rapid rise of a generation-next star like Sloane Stephens, Eugenie Bouchard or Madison Keys.

But for now, it is Williams’s tour, and everyone else is just playing on it.

Navratilova and Evert, who spoke at length about Williams and her season in interviews last week, are deeply impressed.

“Again, it’s weird that she’s going through this now at 32, but it’s like she’s kind of discovered herself in this last year in that she’s really improved her game, improved that median game,” Navratilova said. “She’s adding more spin to the ball so she can rally with anybody for as long as it takes and then of course she has that bazooka that most players don’t have. And she likes it; she likes the security and not wondering . She’s got a Plan B. She can go for broke or she can just dial it back. In the past, usually she couldn’t dial it back.”

Williams’s equipment switch last season from natural gut string to a blend of gut and synthetic appears to have played a significant role.