The pool of potential competitors

We now make a 'reasonable' assumption about the size of the population of 'elligible' people from which Olympic competitors was chosen in each year. We assume that there were 20,000 in the 'pool' who were wealthy enough to be chosen in 1896 and that the number increased quadratically to 2,000,000 for the 2000 Olympics.

Year Potential competitors
1896
1900
1904
1908
1912
1916
1920
1924
1928
20,000
36,000
57,000
83,000
114,000
--
189,000
234,000
284,000
Year Potential competitors
1932
1936
1940
1944
1948
1952
1956
1960
1964
339,000
398,000
--
--
605,000
684,000
767,000
855,000
948,000
Year Potential competitors
1968
1972
1976
1980
1984
1988
1992
1996
2000
1,046,000
1,148,000
1,256,000
1,368,000
1,484,000
1,606,000
1,733,000
1,864,000
2,000,000

Expected Winning Times

The red line on the diagram below shows how the expected winning speed would change as the 'sample size' increased from 20,000 to 2,000,000, assuming that the times to run 1500 metres in the overall population remained normally distributed with mean 458 seconds and standard deviation 50 seconds.

From the diagram above, it seems possible to explain the observed improvement in winning times in terms of a reasonable assumption about the distribution of abilities in the population without any other improvements in technique or training.

The mean and standard deviation of the underlying population

The decrease in expected winning times is highly dependent on the mean and standard deviation of the underlying distribution of abilities. Drag the red arrows on the left and right of the diagram to adjust the mean and standard deviation of the underlying distribution.

It seems as though you are dragging the line but you are (indirectly) changing the two parameters of the underlying distribution. The diagram is clever enough to work out the population mean and standard deviation that make the curve pass through any two points that you specify!