As Roger Federer and Rafael Nadal fight for the top ranking in men’s tennis, the best women in the world are having their own power struggle — or at least, their own struggles. They struggle to stay healthy. They struggle to play a full slate of tournaments. They struggle to matter in a sport in which the attention increasingly goes to the men, or more specifically, to two men who have produced one of the most exciting seasons in years.

In Montreal this week, the best of the women’s tour — minus the Williams sisters, who are nursing injuries — have gathered for their first and last tournament together before the Olympic Games in Beijing, which begin August 8. The no. 1 ranking, and perhaps the top seed at the U.S. Open, hangs in the balance. There’s no Federer-Nadal battle here, however, no duel between two players who consistently test each other’s limits, and push the limits of tennis, in pursuit of excellence. No, in the women’s game at the moment, the top spot has more to do with who plays less badly, who can underachieve the least. If all goes wrong in Montreal this week, as it did at Wimbledon for everyone not named Williams, the no. 1 ranking might very well end up in the hands of a woman who doesn’t deserve it in the least.

That woman? Jelena Jankovic. The Serb is a fine player and has a wonderful personality. She’s great for tennis: Few players captivate a crowd like she can, and few hustle and play with as much verve. Few hit a two-handed backhand as well as she does. But no. 1 in the world? It would be a sad moment for the tour. Jankovic has never reached a major final, much less won a major tournament. She can’t serve. She often loses matches because she can’t keep her composure. Alhough the tour has had past top players who had not won a Grand Slam title (Amelie Mauresmo and Kim Clijsters were no. 1 before they eventually won majors), no one has been so little-qualified for the position as Jankovic. She would be, without doubt, the worst no. 1 in the history of the game.

The task of keeping the top ranking out of Jankovic’s hands falls to Ana Ivanovic, the current, and mostly deserving, no. 1. When Justine Henin retired and left the top ranking vacant, Ivanovic quickly stepped in by winning her first major title at the French Open. Yet it still takes a vivid imagination to see Ivanovic rattling off three or four successive majors, or even two majors a season, for a string of years. If Ivanovic, who looked rusty in her second-round match in Montreal yesterday, a 6-3, 4-6, 6-3 victory against no. 64 Petra Kvitova, finishes the year at the top, she probably won’t do it by much. A number of other women, including Maria Sharapova, Serena Williams, and Svetlana Kuznetsova, are within striking distance.

The more I watch of any of these women (the Williams sisters aside, as they have dominated the game in the past and now limit their appearances) the more I’m convinced that there is no true leader among them. After Nadal defeated Federer in the Wimbledon final earlier this month, Novak Djokovic, the no. 3 player in the world, reportedly sent the following text message to his public relations manager: “I still have a lot to learn.” Djokovic’s counterparts on the women’s tour — Ivanovic, Jankovic, Kuznetsova, and Sharapova — have a lot to learn, too, but no one to teach them, no one to put them in their respective places and push them to improve. They are all good enough, compared to their peers and to each other, to earn the requisite points for the no. 1 ranking. Yet by definition, then, not one of them is good enough to be called the best, at least not in the way previous top players such as Steffi Graf, Martina Hingis, Martina Navratilova, and Chris Evert were the best. Top players of that kind stay on top for long stretches and impose their skills on the rest of the field. With Henin gone, none of the young women who remain are mature enough to take her place.

In tennis, true no. 1 players are a necessity — the sport suffers dearly without them. What good is a sport that rewards individual achievement without a standard bearer? All through the Open Era, the very best man and woman has urged his or her colleagues forward and given up-and-comers a level to surpass, a goal to achieve. It’s no coincidence that only 17 women (including Ivanovic) have held the top ranking since the invention of the ranking system in 1975 and only 23 men (soon to be 24) for the men since 1973. A position as important as that one deserves to be kept in the best of hands.

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In his four years at no. 1, Federer has rarely needed luck. Earlier this week, he did, and Robby Ginepri, the talented but combustible American, was happy to oblige. Ginepri was a mere two points from sending Federer to his third consecutive loss, a defeat that would almost certainly would have ended his reign at the top by week’s end and would have caused all of us to wonder if the formerly great man had lost a lot more than his Wimbledon title at the All England Club earlier this month. After his narrow escape, though, Federer may well loosen up and swing freely the rest of the week in Cincinnati, where he is the defending champion. Though his no. 1 ranking won’t last much longer without a collapse from Rafael Nadal, his confidence might receive a much-needed boost if he wins this title.

Mr. Perrotta is a senior editor at Tennis magazine. He can be reached at tperrotta@ tennismagazine.com.