And yes, a power law is recognizable on the log-log plot (upper right; the horizontal axis carries a binary scale which is more meaningful for the rankings), particularly for the main field from 8th to 128th player. The existing deviations could be easily related to the current world of professional tennis. First of all, the apparent Roger Federer dominance is not so much his own brilliance (he is just slightly above the power law prediction for the 1st position) as it is the under-achievement (from the power law point of view) of the players from 3rd to 8th position. One may predict that these positions are currently above average ‘vulnerable’ and of rather short lifetime. The situation is even more pronounced in WTA ranking where top six payers are underachievers and the top three substantially so; a lot of changes is due there.

Notice the change of slope for the 129 to 256 rankings. This is probably the consequence of the rules for tournament draws: if you are not among the top 128 players, your access to a higher points tournament is rather limited.