Crowding at the Front of the Marathon Packs

TL;DR

This paper analyzes the distribution of finish time gaps in major marathons, revealing a saturation and a sociologically influenced maximum near the top finishers, challenging naive expectations of increasing gaps.

Contribution

It provides a probabilistic explanation for the observed saturation and maximum in finish time gaps among top marathon runners.

Findings

Gaps increase from middle to around 20th place

Gaps saturate among top 10-20 finishers

A sociological factor influences the maximum gap near the top

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 suggests that the gaps have a weak maximum around the 10th place, a feature that seems to have a sociological origin.