ArticlePloS one2026
World-record envelopes: The speed-distance trade-off in racing events.
Article in PloS one, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Abstract
The concept of a mathematical envelope, which is widely used in economics, can be applied to the relationship between world-record racing speeds and event distances. This paper derives and estimates world-record envelopes for running, freestyle swimming, and speed skating and shows how these envelopes are related to the underlying family of individual performance curves. It also compares world-record envelopes for men and women and shows that the world-record envelope in men's running has shifted upward over time but has not changed shape in 120 years. Finally, this paper shows that the speed-distance envelope reflects not only the trade-off between speed and distance for individual athletes but also the change in this trade-off as one moves from one athlete to another. The failure of existing studies to recognize the second effect leads to a misinterpretation of the observed link between world-record performances and human physiology. The paper also shows how this problem can be avoided by estimating individual performance curves using the personal best times of elite athletes.
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