# Special endurance coefficients enable the evaluation of running performance

## TL;DR

This paper introduces a new metric called the coefficient of special endurance to evaluate how pace declines with race distance in male runners.

## Contribution

The study introduces the coefficient of special endurance (KsA), a novel and statistically validated metric for quantifying pace loss across race distances.

## Key findings

- KsA values are nearly constant and show low variability across decades in national-level male runners.
- KsA predicts race times with less than one percent error and provides reference ranges for performance evaluation.
- The metric can help individualize training and identify optimal race distances for runners.

## Abstract

Running performance from sprint to long distance is largely determined by the interplay between basic speed and endurance. Existing power-law, physiological, and theoretical models describe and explain the characteristic decline in pace with increasing distance. However, normative and statistically validated measures that capture both the average and variability of pace decline across standard track distances remain incomplete. To address this gap, we analysed over 14,000 race times from competitive male runners and introduce the coefficient of special endurance (KsA), a novel metric that quantifies relative pace loss between adjacent race distances, from 100/200 to 5000/10,000 m. The KsA values obtained for seven distance pairs are nearly constant over decades in national runners, show low variability, and predict race times with less than one percent. The KsA-based reference ranges allow performance to be evaluated from the international to the regional level. This provides specific insight into runners’ strengths, weaknesses and progression for individualizing training, selecting the most promising race distance, and identifying and developing talent. Overall, we provide empirically derived KsA values that serve as statistical norms for pace loss from 100 m to 10,000 m to evaluate running performance of males. The current approach should also be applicable to women, juniors, and road runners.