World No. 1 ranking on the line

It's no longer complicated. If Vijay places better than Tiger at this week's NEC, Vijay takes over No. 1. Of, if both tie in any position outside the top 10, then Vijay overtakes No. 1.

For Ernie Els to overtake No. 1, it's more complicated. He needs to finish at least 3rd, and then Tiger and Vijay finish in certain positions. See here for scenarios.