A mathematical analysis of the 4 x 100 m relay

In this study, we examined aspects of the 4 x 100 m relay that are amenable to mathematical analysis. We looked at factors that affect the time required to complete the relay, focusing on the performance of elite male athletes. Factors over which the individual athletes, and the team coach, can exercise some control are: the starting positions of the runners on legs 2, 3 and 4, the positions at which baton exchanges occur, the free distances at the baton exchanges and the running order of the athletes. The lane draw is shown to have an important influence on the relay time, although it is outside the control of the team coach. Teams drawn in the outside lanes benefit from the inverse relation between bend radius of curvature and running speed. For teams composed of athletes with different times over 100 m, we show that the fastest relay times are achieved with the fastest athlete taking the first leg, with the slowest two runners allocated to the final two legs.