I wanted to find out what sort of trends, if any, appeared when taking the ratios between the top (i.e. fastest) men's and top women's ratio of times in two sports: swimming and running. I define a ratio as the following
Ratio = [Time for a woman to complete distance X]/[Time for a man to complete distance X]
For example, if considering the 10,000 m track event and a woman's time is 32 minutes while a man's is 29 flat, their time ratio is 32:00/29:00 = 1.10. Let's then take another fictitious ratio of 1500m times as 4:20(female)/3:59(male) = 1.08.
Why go to the trouble taking these ratios? To skip ahead, what I've found is that as distance X increases, this ratio goes up for running and down for swimming. Using the same two examples as above, the fictitious ratio goes up from 1.08 to 1.10 as I increase X from 1.5 km to 10km. Here my argument holds because I invented the numbers. All numbers from this point onward will be quite real. Below is an illustration of what I will soon show with actual data: