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The Numbers Game

Deciphering the ATP’s world tennis rankings

Author Adam K. Raymond Illustration Meen Choi


When the 2013 Association of Tennis Professionals (ATP) World Tour ended last month, Rafael Nadal stood alone atop the world rankings. In tennis, that’s called being “year-end No. 1” and is akin to winning the Super Bowl, if the Super Bowl were a mathematical system complicated enough to make your head spin faster than a ground stroke from Roger Federer.

Take Nadal’s recent return to the top of the rankings, which he accomplished in early October at the China Open. He knocked Novak Djokovic off the ATP throne—which the Serb had occupied for the previous 48 weeks—without even playing him. And a day later, when Djokovic beat Nadal in the tournament’s final round, the Spaniard remained No. 1. It was an astounding achievement, made even more so by the indecipherable math behind the rankings that so many follow and so few understand.

With the 2014 pro tour getting under way at the end of this month, we thought now would be a good time to try to decode the ATP World Rankings system, before any new developments confused us even further.

“The first thing to know is that it’s a 52-week rolling ranking,” says ATP chief player officer and unimpeachable rankings guru Andre Silva. That’s how Nadal overtook Djokovic in the same tournament that saw Djokovic emerge as victor. Even with the loss, Nadal’s results from the previous 52 weeks were better than Djokovic’s. Don’t feel bad for the the Serb, though. Back in July he lost the Wimbledon final to Andy Murray and remained atop the world rankings, again, because his previous 52 weeks were the best.

Anyone who follows the rankings systems in major college sports should see why this is significant. NCAA basketball and football teams are re-ranked every week based on their most recent games, creating instability and emphasizing recent results over long-term performance. Consider this: If tennis were ranked like college sports, Roger Federer would never have achieved his astonishing streak of 237 consecutive weeks atop the world rankings. After all, he lost more than 20 times while wearing the crown.

“Next, you should know that the ranking is formed by 18 annual tournaments,” says Silva. Sixteen of those are mandatory, including all four Grand Slams, eight of nine Masters 1000 events and four of 11 500 series events (one of which can be replaced by the Davis Cup). The final two tournaments included in a player’s ranking come from the remaining 500 series events, a handful of 250 series events and, every four years, the Olympics.

Each tournament is worth points, which are the basis of a player’s ranking. Winning a Slam nets a player 2,000 points, a Masters 1000 event carries a 1,000-point prize, and so on. Those who finish second, third and down the line get points too, just not as many. Given the rolling nature of the rankings, each time a tournament is played, a player’s points earned the previous year are replaced by the most recent result. That’s why tennis commentators use the phrase “defending points,” which refers to the challenge of matching or exceeding one’s finish from the previous year.

Sometimes failures to defend points can lead to rankings anomalies. Andy Roddick was the beneficiary of one such fluke in early 2013, when he moved up two spots despite having retired five months prior. At the time, Roddick still had 970 points, which held steady one February week because he didn’t have points to defend from the previous year. When two middling players who did have 2012 points to defend failed to do so, their lower scores replaced the previous year’s and they dropped below Roddick, who moved from 42nd to 40th best in the world. Not bad for sitting on the couch.

If all of this sounds confusing, that’s because it is. To understand how the ATP rankings evolved, one must go back to a time before they existed. The year was 1973, and the ATP had just formed to advocate for male professional tennis players. The main issue of the day was player freedom and the power national federations wielded over a country’s tennis players.

The tipping point was Wimbledon, 1973, when onetime U.S. Open doubles champion Niki Piliç was suspended by the Yugoslav Tennis Federation for playing a professional match instead of representing his country in the Davis Cup. When the International Tennis Federation (ITF) announced it would recognize Piliç’s suspension at Wimbledon, the ATP took a stand. Eighty-one top players, including defending champion Stan Smith, refused to play at the All England Club, and tennis’ most storied tournament was forced to field amateurs and players with the name recognition of ball boys.

That was enough to scare the ITF into striking a deal with the ATP, granting players freedom to control their schedules by tying tournament entry to world rankings. Though the method for determining those rankings has evolved over the years—from requiring no tournaments, to counting them all, to today’s complicated model—the right the ATP fought for in 1973 remains unchanged. Players still gain entry into tournaments based on where they stand in the rankings and not on capricious bureaucratic whims.

“Their ranking is their tour card,” Silva says of professional players. “You get paid only by playing and you only play based on your ranking. It doesn’t matter what you did in the past. You have to continue to perform, or you’re history.”

That cutthroat nature encourages players never to take a day off. Loafing in the lower ranks could be the difference between playing in the U.S. Open and selling hot dogs at it. It also keeps the level of competition as high as possible.

In fact, it’s not uncommon to hear top pros lay out ranking scenarios. In April 2012, three months before recapturing what he called “My No. 1 ranking,” Federer showed how locked into the rankings he was when he said, “The number one spot is possible this year, but I have to play really well. Djokovic could win his fourth Slam in a row in Paris, and if he does it will be difficult for me to become No. 1.”

The ultimate achievement comes not in reaching the top spot, though, but in staying there. A few men on the illustrious list of No. 1s have lasted no longer than a tournament. Only 16 have been good enough long enough to end the season atop the rankings. And only five have spent a whole season at No. 1 for every single week. Federer managed to do it for three consecutive years, holding on to the top spot for the entirety of 2005, 2006 and 2007. The on-court dominance needed to achieve that kind of streak may never be seen again. But if it is, the man who does it will have to start at the same place Federer did in the utterly meritocratic ATP world rankings—all the way at the bottom.

Oakland, Calif.–based ADAM K. RAYMOND has greatly improved his math skills as a result of reporting this article. Tennis is another story.

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