World-record envelopes: The speed-distance trade-off in racing events
- 1Professor Emeritus of Economics and Public Administration, Syracuse University, Syracuse, New York, United States of America
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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BibTeX
@article{yinger2026worldrecord,
title = {{World-record envelopes: The speed-distance trade-off in racing events}},
author = {John Yinger},
journal = {PLOS One},
year = {2026},
month = oct,
doi = {10.1371/journal.pone.0359859},
url = {https://doi.org/10.1371/journal.pone.0359859},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - World-record envelopes: The speed-distance trade-off in racing events
AU - John Yinger
PY - 2026
DA - 2026/10/07
JO - PLOS One
DO - 10.1371/journal.pone.0359859
UR - https://doi.org/10.1371/journal.pone.0359859
AB - 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.
SN - 1932-6203
ER -