Julyan Arbel plots world record running times vs. distance (on the log-log scale):
The line has a slope of 1.1. I think it would be clearer to plot speed vs. distance—then you’d get a slope of -0.1, and the numbers would be more directly interpretable.
Indeed, this paper by Sandra Savaglio and Vincenzo Carbone (referred to in the comments on Julyan’s blog) plots speed vs. time. Graphing by speed gives more resolution:
The upper-left graph in the grid corresponds to the human running records plotted by Arbel. It’s funny that Arbel sees only one line whereas Savaglio and Carbone see two—but if you remove the 100m record at one end and the 100km at the other end, you can see two lines in Arbel’s graph as well. The bottom two graphs show swimming records. Knut would probably have something to say about all this.
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