Olympic Competition
Why is our sense of things different for Olympic competition, where we widely believe that small changes in force effectiveness can make the difference between gold medalist and loser? The answer, in brief, is that, unlike force-on-force combat, Olympic competition takes place between players who are all many standard deviations out on the extreme favorable tail of a probability distribution defined by the general population.
As an idealized model, suppose that a country’s Olympians are drawn from the extreme tail of a Gaussian (normal) probability distribution with selectivity S. That is, only one out of S in the eligible population (say, country residents between the ages of 16 and 25) can “make the team”.
Plausible values of S might be in the range 104 to 105. The number of standard deviations t by which a typical Olympic team member exceeds the population mean in some performance variable (long jump distance, e.g.) is then related to the fraction of the population making the team 1/S by
Why is our sense of things different for Olympic competition, where we widely believe that small changes in force effectiveness can make the difference between gold medalist and loser? The answer, in brief, is that, unlike force-on-force combat, Olympic competition takes place between players who are all many standard deviations out on the extreme favorable tail of a probability distribution defined by the general population.
As an idealized model, suppose that a country’s Olympians are drawn from the extreme tail of a Gaussian (normal) probability distribution with selectivity S. That is, only one out of S in the eligible population (say, country residents between the ages of 16 and 25) can “make the team”.
Plausible values of S might be in the range 104 to 105. The number of standard deviations t by which a typical Olympic team member exceeds the population mean in some performance variable (long jump distance, e.g.) is then related to the fraction of the population making the team 1/S by
For large S and t >> 1, an approximate inverse to this relationship is
So t ≈ 3.5 for S = 104, while t ≈ 4.1 for S = 105.
Put differently, a performance increase of 4.1/3.5 − 1 = 17% (as measured in standard deviations of a performance variable from the population mean) is the equivalent of a full factor of 10 greater selectivity S, from 104 to 105. This, roughly, is how a small country like the German Democratic Republic (DDR) was able, by the use of performance enhancing drugs, to produce Olympic teams competitive with countries that were an order of magnitude or more larger in population. On the tail of a distribution, small changes in your performance lead to large changes in how many people you are better than.
