World-record speed–distance trade-offs reflect more than athlete physiology

Mathematical envelopes applied to world-record performances reveal a speed–distance trade-off in running, freestyle swimming and speed skating. The analysis also finds that these records cannot be interpreted solely through individual athletes’ physical limits, because the records combine performance differences within each sport with differences among athletes.

The researchers derive and estimate world-record envelopes for the three racing events and relate them to the broader family of individual performance curves. In this framework, an envelope captures how the fastest recorded performances change as event distance increases. Comparisons between men and women show that the envelope has shifted upward over time in men’s running, while retaining the same shape across 120 years.

A central complication is that a world-record envelope reflects two distinct effects: the trade-off between speed and distance for an individual athlete, and the way that trade-off changes from one athlete to another. Existing studies that account only for the first effect can therefore misinterpret the relationship between world-record performances and human physiology, according to the paper.

The authors show that the interpretive problem can be avoided by estimating individual performance curves from elite athletes’ personal-best times. This approach separates the characteristics of individual performance from the variation created by comparing athletes with different capabilities. The findings provide a more rigorous way to interpret record-breaking speed–distance patterns without assuming that every point on a world-record envelope represents the same underlying physiological trade-off.

Subject of Research: Analysis of world-record speed–distance envelopes in running, freestyle swimming and speed skating

Article Title: World-record envelopes: The speed-distance trade-off in racing events

Article References: Yinger, J. (2026). World-record envelopes: The speed-distance trade-off in racing events. PLOS One, 21(10), e0359859. https://doi.org/10.1371/journal.pone.0359859

Image Credits: AI Generated

DOI: 10.1371/journal.pone.0359859

Keywords: world records, running, freestyle swimming, speed skating, performance curves, sports science, human physiology, elite athletes, World-record, envelopes, speed-distance, trade-off