Running the numbers

I got my final results back from the BAA and at first I was really pleased: My number was 9899 and yet I came in 6792. It should be remembered that your bib number is directly in proportion to your qualifying time.

At first I was pleased because I assumed that finish order was a zero-sum game: If one person finishes ahead of his number, then someone else must finish behind theirs. So for instance if # 1 finishes 20,001 and everybody else finishes in order, then they each gain one place position and that one runner looses 20,000 place positions. It all equals-out.

Just to confirm this hypothesis, I looked at 20 runners in order 9880-9899 and summed-up whether they gained or lost position. Here is what I found: There were three runners with no finish. Not everybody who signs-up ends up running and not all runners finish. In fact: there were around 28,000 entrants and about 23,000 finishers, so we are missing about 5,000 people. This will have no impact on #1, but # 28,000 should gain 5,000 finish positions just by completing the race. I had a # that put me around the 35th percentile part of the pack, so I should gain 1750 positions just by finishing at the top 35 percent point.

The average gain for the 17 runners I looked at was 1320 place positions. This is not far from my above estimate of 1750. When I sum up the three that did not finish and subtract from the aggregate gains, the average gain drops to 361.

I am still happy about picking up around 3,000 place positions, but around half of that was me and the other half simply a function of showing up and finishing.