Combinatorial Models of Cross-Country Dual Meets: What is a Big Victory?

TL;DR

This paper introduces combinatorial and probabilistic models for analyzing cross-country dual meets, focusing on the likelihood of various outcomes and the significance of big victories.

Contribution

It presents two novel models for cross-country dual meets, incorporating assumptions about runner rankings and team compositions to better understand meet results.

Findings

Models provide probabilistic frameworks for meet outcomes

Analysis of the likelihood of big victories in dual meets

Foundation for further statistical analysis of cross-country competitions

Abstract

Combinatorial/probabilistic models for cross-country dual-meets are proposed. The first model assumes that all runners are equally likely to finish in any possible order. The second model assumes that each team is selected from a large identically distributed population of potential runners and with each potential runner's ranking determined by the initial draw from the combined population.