Mathematical Modelling and Optimization of 800m Pacing Strategies to Evaluate the Probability of Sub-2-Minute Performance

This exploration investigates the most efficient pacing strategy for an 800m race to determine the probability of achieving a sub-2-minute performance. The author utilizes primary data from eight trials, employing quadratic regression to model pacing and comparing results with elite athletes using logarithmic and quadratic functions.

The methodology integrates calculus—specifically differentiation for fatigue rate analysis and optimization to identify peak performance—and integration to quantify pacing distribution. Probability is assessed via normal distribution and z-scores. The study concludes that a sub-2-minute time is statistically improbable based on current performance. It is a strong exemplar for its comprehensive application of multiple mathematical domains and critical reflection on model limitations.