How the Ranking System Works
In order to answer that question properly, a brief explanation of the ATP ranking system is necessary. Players' rankings on tour are based on how well they can match their performances in the same tournaments the year before. At the beginning of each tournament, the points a player gained from that particular tournament the year before are dropped, and the Monday following the tournament, new rankings are released and a player receives points based on his performance in the tournament that just ended. In other words, a player must try to reach the same round he reached the previous year in the same tournament, to keep the same number of points he has, and naturally, if a player improves on his performance from the year before, he will gain more points and the opposite happens if he loses earlier in the tournament, hence the term, defending a title.
An example will help explain this better. Federer won Wimbledon last year and received 1000 points for that feat. This year, at the start of Wimbledon, those 1000 points were dropped. When he lost to Rafael Nadal in the final, it meant that Federer did not defend his points and he only received 700 points instead of the 1000 that were dropped at the beginning of the Wimbledon fortnight. Which meant that Federer lost 300 points after his Wimbledon defeat. Ultimately, a player guarantees that he will gain points from a tournament if he did not participate in it the year before (since any points he gets will be fresh points), and a player who fails to attend a tournament that he played the year before, will lose all the points he had from that tournament.
The Massive Return
After conceding his number one spot to Nadal, and failing to win a consolation medal for himself in the singles competition at the Beijing Olympics, many considered Federer's season to be over but the Swiss talisman quietened the skeptics by defending his title at the US Open, which marked his 13th Grand Slam triumph. After this huge confidence boost, Federer is now looking to defend his Masters Cup title in Shanghai and try to recapture his number one spot in the rankings. In order for that to be possible, the world number two must close on the 1070-point difference that currently separates him from Nadal.
What Federer Needs to Do
Next up for Federer after his Davis Cup duty is Stockholm, where he will be playing for the first time. Obviously the Swiss is trying to gain some extra ranking points because defending his points from last year will not suffice for him to close on Nadal. If Federer wins Stockholm he can narrow the gap between him and Nadal to 845 points ahead of the Madrid Masters.
Nadal's next tournament will be with Federer in Madrid. Federer reached the final in Madrid last year while Nadal lost in the quarterfinals, both players falling to David Nalbandian. Federer has the chance of adding 150 points to his tally if he improves on his final showing last year and wins the tournament and the lead can be further reduced if Nadal fails to make it to the quarters.
The Swiss then needs to defend his title in his home tournament, Basel, then move on to fight it out with Nadal again at the Paris Masters. Last year, Federer lost in Paris in the third round, while Nadal lost in the final, again both players stunned by Nalbandian. The competition between the top two players of the world will probably be fiercest in Paris as Federer will have the chance to add 425 points to his account and Nadal will have 350 valuable points to defend.
The verdict will officially come out after the Masters Cup in Shanghai where Federer will be looking to defend his title and Nadal has a semifinal showing to equal.
The Best Case Scenario for Federer
The best case scenario for Federer would be assuming him making maximum points while Nadal losing maximum points. Here's the point breakdown for that hypothetical scenario:
Current situation: Nadal 7000 points , Federer 5930
After Stockholm: Nadal 7000 points, Federer 5930 + 225 = 6155
After Madrid: Nadal 7000 - 120 = 6880 points, Federer 6155 + 150 = 6305
After Basel: Nadal 6880 points, Federer 6305 points (no change)
After Paris: Nadal 6880 - 345 = 6535 points, Federer 6305 + 425 = 6730 points
In the best case scenario, the earliest Federer can overtake Nadal will be after Paris but he will have to defend his 650 points from the Masters Cup or at least reach the final and Nadal must not win the title (Nadal can gain 450 points if he wins meaning he can surpass Federer again).
