Optimal Pacing of 400m and 800m Races: A Standard Microeconomics Approach

Abstract

The optimal way for an athlete to run 400m and 800m races has long been debated by athletes, coaches, and more recently by physicists and applied mathematicians. These two particular running events are different from both shorter and longer races, due to their emphasis upon an athlete’s lactate system. If the first part of the race is run either too quickly (in which case the fatigue that is generated makes the second half of the race both slow and painful) or too slowly (in which case even though the second half will be fast, it cannot make up for the time lost earlier on),2 the total time for the entire distance will not be as fast as it could otherwise have been. In this paper we discuss this choice problem in a standard microeconomic setting, and we solve for the optimal “split” times for the first and second half of the race.