Roger Federer needs to win the title at the BNP Paris Masters this week to become world No. 1 by week’s end, but he can only do so if Novak Djokovic fails to reach the final.

Here’s how it shapes up:

• With points from last year’s World Tour Finals and Paris Masters dropping off this week, Djokovic will see 2500 points fall off against only 760 for Federer.
• Currently Djokovic holds a 11,510 to 9,280 edge over Federer in the rankings, but that edge will be cut to 9,010 to 8,520, or 490 points (prior to the addition of this week’s Paris points).
• Federer and Djokovic have each earned 180 points for their quarterfinal appearances in Paris, so the gap is still 490.

If Djokovic loses to Andy Murray on Friday:

Federer would close the gap to 310 points by reaching the semifinals on Friday.

Federer would close the gap to 70 points by reaching the final, and he would take the lead by 330 points if he won the title.

If Djokovic and Federer both end up losing in the same round (quarters or semis):

The gap will remain 490 heading into London.

If Djokovic reaches the semis and Federer reaches the final:

Federer would pick up 240 points on the Serb, closing the gap to 250.

If Djokovic reaches the semis and Federer wins the title:

Federer would move to No. 1 with an edge of 150 points.

If Federer defeats Djokovic in the final:

Djokovic would maintain a slim edge of 90 points.

Things get dicey for Federer if he fails to outperform Djokovic.

If Federer loses tomorrow and Djokovic goes on to win the title:

Djokovic would extend his lead to 1,310 points, which is an almost insurmountable lead heading into London.

If Federer reaches the semis and Djokovic wins the title:

The lead for Djokovic would be 1130, and if Djokovic defeated Federer in the final the lead would be 890.

If Federer loses tomorrow and Djokovic loses in the semis:

Djokovic’s lead would be 670.

If Federer loses tomorrow and Djokovic loses in the final:

Djokovic's lead would be 910.

Finally, if Federer loses in the semis and Djokovic reaches the final:

Djokovic’s lead would stretch to 730.