The race to year-end #1 between Roger Federer and Rafael Nadal is heating up after Nadal took the week off to take care of his knees. Meanwhile, Federer defeated Juan Martin del Potro in three sets to take home his eighth career title in Basel. This victory has cut Nadal’s lead at World #1 to 1,460 points–no small number, but also not an insurmountable lead.

There are two points-awarding tournaments remaining on the calendar. There is the final Masters 1000 event of the season (in Paris-Bercy) this coming week. After that, players get a week of rest, followed by the World Tour Finals, where the top eight players from the season will compete. The Masters event in Paris offers 1,000 points to the winner. The World Tour Finals–in the O2 Arena in London–offers a maximum of 1,500 points.

This chart shows how ranking points are given out for the Masters 1000 event in Paris:



Points at the World Tour Finals are more simple. A player earns 200 points for each round robin victory (each player plays three round robin matches), 400 points for a semifinal victory, and 500 points for winning the title. Thus, if a player goes 3-0 in round robin play, he will win 1,500 points if he takes home the title.

Federer needs to gain 1,460 points on Nadal. Titles in Paris and London–and the Swiss will almost certainly be the favorite in both–are worth up to 2,500 points. However, Nadal can cement his World #1 ranking just by reaching both finals. Even if Nadal makes the final of the Tour Finals after going 1-2 in group play, the 1,200 total points from both runner-up showings would be too much for Federer to overcome.

Federer, for his part, has a path to World #1 even if he doesn’t win both titles. (Actually, if Nadal loses early in Paris and earns no points in London, Federer could technically end the year as World #1 with a runner-up showing in each of the final two tournaments.) However, the Swiss would then need some serious help from Nadal not playing well. It’s possible–the Spaniard often struggles on fast indoor surfaces, and he did just have to rest his knees–but it’s certainly not something to rely on.

The math

So what are the paths to 1,460 points for Federer? First of all, he has to, at the very least, equal Nadal in Paris. If Nadal earns 45 points more than him (which is guaranteed if Nadal outlasts him, as both have a first-round bye), then it will be impossible for Federer to catch the Spaniard, no matter what happens in London.

If Nadal reaches the final of Paris, then Federer would have to win the title, then outdo the Spaniard by 1,060 points at the World Tour Finals. That means that Nadal would have to win a maximum of two round robin matches (and lose in the semifinal) if Federer gets 1,500 points en route to the London title–if Federer only gets 1,300 points, Nadal would need to win a maximum of one round robin match.

If Nadal loses in the semifinals of Paris, Federer has more possibilities. If the Swiss loses in the Paris final, then he would need to out-earn Nadal by 1,220 points at the World Tour Finals–which either means a 1,500 point title with Nadal earning 200 points, or a 1,300 point title with Nadal earning zero points. If Federer wins the Paris final, though, then he only needs to make up 820 points in London. That can happen in many ways, but I’ll just name one: If Federer wins the title in London, then he is guaranteed the top spot as long as Nadal doesn’t reach the final.

If Nadal loses in the quarterfinals or earlier, the scenarios for Federer to take the top spot become too numerous to mention. Just remember, 1,460 is the operative number. Federer needs to outgain Nadal by 1,460 points the rest of the year.

Also, there are still a few scenarios possible where Federer and Nadal would tie for the top spot. In that case, the World #1 title would go to the Swiss based on the tiebreakers in the ATP rulebook.

There is still a lot of tennis to be played in 2017, but what once seemed like a pipe dream of Roger Federer getting back to World #1 now is a real possibility.

If it doesn’t happen now, though, it’s unlikely to see it happen for a long while. After all, Federer has 4,000 points to defend in the first three months of 2018, as he won the Australian Open and the “Sunshine Double” (the Indian Wells and Miami Masters) to start this season.

Update: Federer has withdrawn from Paris. His only path to #1 now is if Nadal loses his first match in Paris and every match in London–and if Federer wins the title in London without dropping a match.

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