Crowding at the front of marathon packs

Abstract

We study the crowding of near-extreme events in the time gaps between successive finishers in major international marathons. Naively, one might expect these gaps to become progressively larger for better-placing finishers. While such an increase does indeed occur from the middle of the finishing pack down to approximately 20th place, the gaps saturate for the first 10-20 finishers. We give a probabilistic account of this feature. However, the data suggest that the gaps have a weak maximum around the 10th place, a feature that seems to have a sociological origin.