Evert, one of the people Hingis admires most, was the first of only seven players who have been named No 1 since computer rankings started to be used in women's tennis in November, 1975. The other five are Martina Navratilova, Tracy Austin, Steffi Graf, Monica Seles and Arantxa Sanchez Vicario.
The temptation to pigeon-hole sports personalities is irresistible. Although Martina Hingis was named after Martina Navratilova, her game has drawn comparisons with Maureen Connolly, Evonne Goolagong Cawley, and Evert.
"When Jennifer [Capriati] came up, and Monica and Steffi, everybody was always quick to compare," Evert says. "Because they're baseliners, the question was always will they be the next Chrissie. With the exception of maybe temperament, I don't feel like my game was that similar to any of those players.
"But I think when Martina came along, I saw a player who doesn't necessarily blow people off the court and doesn't have that one big weapon necessarily. She uses her head at a young age, is very composed, and anticipates well. She certainly has more shots than I ever did, especially at that age, so I'm not saying that I was that good. But she is the closest one, I feel, that plays the way I used to play. I wouldn't blow anybody off the court, but I would use accuracy and consistency and use my head out there."
Evert, from Fort Lauderdale, Florida, came to international prominence as a 15-year-old when she defeated the then Wimbledon champion, Margaret Court, 7-6, 7-6, in the semi-final of a tournament in Charlotte, North Carolina. Evert went on to win 18 Grand Slam singles titles, three of them at Wimbledon, in 1974, 1976 and 1981.
Now 42, she is excited at the prospect of analysing Hingis's matches for some time to come. "I can't say she's going to dominate tennis for the next 10 years, let's put it that way, but I'm not surprised that she has reached the No 1 position. I think a little bit of it is obviously Steffi's injuries. It's hurt her that she hasn't played. But I think Martina can only get get better.
"She's still growing, so physically she can still get stronger. Her body can get more athletic. I think she can work on the athleticism a little bit more. I don't think they've been concentrating as much on that while she was young and growing, because I think they feared too much, too soon. But she's got all the shots, that's for sure. She's an all-round player, and she seems to enjoy it, so I don't see a burn-out factor there. The atmosphere around her is very conducive to playing for a long period of time. So I think she's very special."
On a point of style, how does Evert rate the strengths and weaknesses of the two-handed backhand (which she favoured), the two-handed shots on both wings, a la Seles, and the traditional one-handed backhand as used by Graf and Navratilova?
"I don't think there's anything better than a good two-handed backhand," she says. "Unfortunately, not a lot of players hit it the right way. Martina Hingis does hit it the right way, because the players that hit great two- handed backhand down-the-line shots are the ones that know how to hit it. Martina has that shot. Two hands on both sides, I think, still limits your reach a little bit too much. But I really feel that if you have a good solid two-handed backhand, that's your best bet, because you can learn it at a young age and really develop it over a long period of time."
The 23-year-old Seles, we know, has found it difficult to sustain her momentum because of the injuries which have interrupted her comeback following the trauma of her stabbing four years ago. But Graf, 27, seems to fight a constant battle against injuries and ailments, while in the men's game, Andre Agassi, approaching 27, appears to be in free-fall. How would Evert counsel a player to know when it's time to quit?
"I think they're more like in mid-life crisis in their careers," she says. "I don't think they're at the end of their career. Agassi is still young. When I was 24 years old, I took a break. I took three or four months off and didn't pick up a racket, and I thought maybe my career was over. I'd just gotten married [to John Lloyd], and I wanted to do other things, and then I realised it took me time away to understand how much I appreciate the talent that I had. With these players, I don't see their injuries being retirement.
"Why don't they just get away for three or four months? Why don't they impose it upon themselves, not just be forced out of the game because of injuries? If they feel burned out, they should get out of it on their on accord, and then I think they'd realise how lucky they are and special they are and that they have another six to eight years of vintage tennis.
"Steffi Graf has been No 1 for ho many years? If she got off the tour for four months, or even six months, and did the things that she missed out on and just relaxed and was with her family, so what? She'd come back at No 15, or whatever, but it wouldn't take her long to get back up. You have to think of your own longevity and your own career.
"I retired at 34. It was entirely mental. Mental burn-out, period. Nothing more, because I felt great, and actually the two years after I retired I feel like I played my best tennis. I went on the exhibition tour, I felt I was more relaxed, and physically I hit the ball better than ever. But I needed more mental abilities than other players, because I didn't have the physical talent to fall back on like a Martina Navratilova or Evonne Goolagong or Steffi Graf. And I just got burned out, plain and simple."
Hingis has been coached by her mother, Melanie Molitor, since she was a tot. When does Evert intend to start training her children, Alexander James, five, Nicholas Joseph, two and half, and Colton Jack, nine months?
"When do I start training them? I'm not bringing up my kids necessarily the way that I as brought up. I was brought up exclusively to play tennis. My dad brought all the kids over to the courts at five years old, but he never had dreams of anybody being No 1, that's for sure. It was a way for the whole family to be together. Andy [Andy Mill, her second husband] and I expose our kids to every sport, from snow boarding to skiing, to softball to soccer. I think they'll figure out where their niche is, if it's sports. Maybe sports is just going to be recreational, and maybe they'll be an accountant or maybe they'll use their brains a little more. I don't know."