Assessing course difficulty and the effect of weather in amateur cross country running races

Cross country running races are different to track and road races in that the courses are not typically accurately measured and the condition of the course can have a strong effect on the finish times of the participants. 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. We model the natural logarithm of the 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, fit distance as a covariate, and investigate the effect of time via the season of the race, in particular investigating any evidence of a pre- to post-Covid effect. We use random athlete effects to model the 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 strong differences between the difficulty of the courses, effects of rainfall in the month of the race and the previous month to increase finish times and an effect of increasing distance increasing finish times. We find no evidence that windspeed affects finish times.