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Methods and explanation: Evidence It is well known that many human traits follow a Normal or Gaussian distribution. For example, the following figure:  It occurred to me that athletic performance might follow such a distribution. In general a Gaussian distribution is likely to hold when:
Consider a specific example. The best 100 m by a US high school runner last year was 10.14 s. This result has a speed of distance/time=100/10.14=9.86 m/s. The probability for such a mark would be 1/(8 million), since there were 8 million HS boys in the US in 2000. It is important, however, to be clear as to the sample. A distibution of Sumu wrestlers would not have the same atheltic performance distribution as a team of gymnasts, for example. I therefore restricted the analysis to high school students in California and the US. The analyis requires a series of points of the best performance in a group of known size. The size, or populations, for the marks used are shown in the following table. For "HS varsity", I have taken 333, assuming three runners from a school of 1000. "League", is 8 schools of 1000 students each, so 8th in league is one in 1000, etc. Estimated size of populations for each mark.
Although records might seem a useful source of data, the sample sizes associated with a given record is hard to assess. Rather, I have used ranking lists, which give the best perfomances in a given year. In particular, I have used the year 2000 ranking lists for California[1] and US [2] high schools. These are suitable because the populations are readily obtainable from census data.[3] To these "hard" numbers, I have added data based on my own observations of high school performance in San Jose, for schools that compete in the Blossom Valley League, and the Central Coast Section of California Interscholastic Federation. The Table gives the actual populations used. Good fits are obtained for all events using this approach. An example, for the high hurdles, is shown in the figure below.
 References:
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