A Simple Random Walk Model for Predicting Track and Field World Records

This article proposes a simple model for the prediction of track and field world records. It is best characterized as a one-sided random walk model with a mixture distribution for the error term. The mixture distribution contains one discrete and one continuous component. The discrete piece pertains to the probability that a record is broken and can be modeled as a function of time. The continuous component corresponds to a positive-valued random variable that may also depend on time and essentially models the amount by which a record is broken. The proposed model and corresponding inference procedures are grounded in maximum likelihood principles. Monte Carlo techniques can be used to obtain prediction intervals for future records. Data for the men's 100 meter dash is used to illustrate the proposed methodology.