Rory McIlroy, the incumbent, would realistically need to hold off challenges from Adam Scott and Sergio Garcia to retain his place at the top.
If Adam Scott was to win this week then there is nothing McIlroy can do to stop the Australian going back to the top of the rankings.
If Scott was to finish inside the top twenty, McIlroy was to miss the cut and neither of Stenson, Garcia or Rose was to win then Scott could still regain his place at the top.
If Sergio Garcia was to win however he has a chance to become number one for the very first occasion if McIlroy finished outside the top 5 this week and Scott outside the top 4.
Less likely, Henrik Stenson could also gain the game's top mantle if he was to win, McIlroy finished outside the top 14 and Scott outside the Top 9.
Justin Rose needs to win with McIlroy outside the Top 56 and Scott outside the Top 17.
Confused? Well they provide an interesting set of permutations but yet another reason to watch what promises to be a great PGA Championship.