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Time is money: An economic analysis of the optimal pacing problem

Richard Watt and Philip Gunby

Mathematical Social Sciences, 2020, vol. 108, issue C, 50-61

Abstract: Athletes in many sports can potentially earn significant amounts of prize money from taking less time to complete a given distance than their competitors. Time is literally money in these cases. The objective of an athlete is to choose an optimal race strategy that minimizes race time without becoming prematurely exhausted. If the first part of a race is completed too quickly, the fatigue generated makes the second part of the race slow and painful. If completed too slowly, the second part will be fast but it cannot make up for the time lost earlier on. Either way, the total time taken to complete the entire distance will not be as fast as it could otherwise have been. This optimal decision problem has long been debated by athletes, coaches, and more recently by physicists and applied mathematicians. We show that this optimal choice problem can be solved with solutions that are both simple enough for them to be of practical use but flexible enough for them to be personalized for an athlete. We use the 800 m running race to demonstrate how our technique works since it is a well known ideal example of an event that combines both the elements of speed and endurance.

Keywords: Constrained optimization; Microeconomics; Optimal pacing; Athletics (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.mathsocsci.2020.08.003

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