The baton exchange during the 4×100 m relay: a mathematical analysis

Using mathematical analysis, we examined the three baton exchanges that occur during a 4×100 m relay. Identical representative 100 m running performances were assumed for each of four elite male athletes, and the calculations were made for optimal or near-optimal positions of the baton exchanges and starting positions of the athletes running the second, third and fourth legs as determined by Ward-Smith and Radford (2002). In this paper, we focus on the calculation of the checkmark position and demonstrate the complexity of the baton exchange process. The results of the mathematical analysis show that, for optimal performance, the checkmark should be located differently for each of the three exchanges in a single race, and is further affected by lane draw and free distance (the distance between the runners at the baton exchange). For a representative free distance of 1 m at each exchange, the checkmark distance ranges from a minimum of 11.04 m at the third exchange in Lane 1 to 12.20 m for the first exchange in Lane 8. Failure by teams and their coaches to consider adequately the complexities of the baton exchanges may help explain why 25.5% of teams in recent World Championships were disqualified or did not finish.