images & thoughts \ weekly \ Grabov Rat

exponential tennis

You’ve probably noticed how huge are differences in ranking points among the leading ATP players, typically four of them. Downstairs, the differences are still impressive to the rank 8, still significant to the rank 16, less so to 32, even less to 64, and so on. The graph above is, in essence, a straight line on the log-log plot indicating an exponential distribution of points which are the base for ATP rankings. There are two reasons for that: (1) the allocation and assignment of points at ATP tournaments is exponential in nature, see the graph on the right; (2) the mechanism of seeded players at ATP tournaments is to further insure the dominance of a small number of players. Why?

Professional tennis is a business. If you are in that busi- ness, you want more fans, more sold tickets, more com- mercial messages on players and courts. You know that most people are easily impressed by individual achieve- ments and they tend to identify with them. But, you don’t expect someone to change his/her hero every two weeks, so you establish structural control on the number and duration of heroes. A new, young lion is welcome from time to time, don’t get me wrong, but let’s polish the current ones, write about their megalithic rivalry, write about their girlfriends and visits to orphanages.

Seeded payers are the real smack to the sportsmanship in tennis; I’ve discussed that earlier [100207]. ATP obviously wants the heroes to play at the end of a tournament, at weekends and larger audience. But, how someone with a straight face can arrange that the seed number one, the leading hero, in the first round plays the weakest opponent? By the way, the deviations from the straight line on the above graph are due to the seedings.

To revive the sportsmanship in tennis, the seeding should be abandoned in favor of the pure chance draw and the assignment of ranking points in each match should be related to the ranking of players involved - the higher the rank of the player you have defeated, the more points you gain. This way it may happen that you gain more points in the first or second round than in the final! Some scaling factors could be introduced based on "historical value" or size of the tournament, although it may prove unnecessary because at large tournaments there are more rounds to gain the points. As simple as that.