Assessing course difficulty and variables affecting finish times in amateur cross country running races

Abstract Cross country running races differ from track and road races in that the courses are not typically measured accurately, and course conditions can have a strong effect on participants’ finish times. In this paper we investigate these effects by modelling the finish times of all participants in 28 cross country running races over 5 seasons in the North East of England, to answer the question “which course is the hardest?” We model the log finish times using linear mixed-effects models for both the senior men’s and senior women’s races. We investigate the effects of weather and underfoot conditions using windspeed and rainfall as covariates, include distance as an additional covariate and investigate temporal effects of race season, in particular investigating any evidence of a pre- to post-Covid effect. We include the effect of participant age group, use random athlete effects to model additional participant to participant variability and identify the most difficult courses using random course effects. The statistical inference is Bayesian. We assess model adequacy by comparing samples from the posterior predictive distribution of finish times to the observed distribution of finish times in each race. We find substantial differences in course difficulty and evidence that greater recent rainfall and longer race distances are associated with longer finish times. We find no evidence that windspeed affects finish times.