A stochastic analysis of the 4 × 100 m relay

Abstract

The baton exchanges are undoubtedly the most critical parts of the 4 × 100 m relay race. Timing of the outgoing runner is critical. In this paper we analyze the race as a minimization problem under uncertainty. We formulate a stochastic model in which the outgoing runner at the baton exchange cannot perfectly assess the incoming runner's exact location relatively a checkmark position, and therefore potentially misjudges the right moment to start running. Also, the team members’ daily shape is subject to uncertainty. To understand the effect of these two random variables—incoming runners’ distance to checkmark and the daily shape of the running team—we conduct a simulation study to investigate the trade-off between the team's expected race time and their probability of being disqualified due to overrunning the takeover zone. Conditioning on a low disqualification probability, the difference in expected race time is shown to be substantial between teams with different variation in distance assessment and forecasting running performance, respectively.