{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Professor Emeritus of Economics and Public Administration, Syracuse University, Syracuse, New York, United States of America"
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "John Yinger"
    }
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  "bibtex": "https://research.draconitic.com/paper/0abrk8nmshee0.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0359859",
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  "id": "0abrk8nmshee0",
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    "1932-6203"
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  "landing_url": "https://doi.org/10.1371/journal.pone.0359859",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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      "plos",
      "/Biology and life sciences/Physiology/Biological locomotion/Running"
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      "plos",
      "/Biology and life sciences/Physiology/Biological locomotion/Swimming"
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  "pdf_url": "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0359859&type=printable",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/0abrk8nmshee0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:30Z",
      "native_id": "10.1371/journal.pone.0359859",
      "source": "plos",
      "url": "https://doi.org/10.1371/journal.pone.0359859"
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  "subjects": [
    {
      "field": "biology",
      "origin": "plos:neuroscience",
      "subfield": "neuroscience"
    },
    {
      "field": "mathematics",
      "origin": "plos:geometry",
      "subfield": "geometry-topology"
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    {
      "field": "medicine",
      "origin": "plos:physiology",
      "subfield": "physiology"
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  "title": "World-record envelopes: The speed-distance trade-off in racing events",
  "title_text": "World-record envelopes: The speed-distance trade-off in racing events",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:30Z",
  "url": "https://research.draconitic.com/paper/0abrk8nmshee0",
  "venue": "PLOS One",
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}