{
  "annotation_id": "93d43cb6-3765-4947-8d1f-bd4710ae2090",
  "date_created": "2026-03-02T18:01:11.494000Z",
  "date_modified": "2026-03-02T18:01:11.494000Z",
  "file_hash": "d8654b0bb2f9b063352f17605ebc0dd83cc1a516afeb58790241b6cf66c7fa95",
  "private": false,
  "record": {
    "abstract": "We present an extensive statistical analysis of the results of all sports\ncompetitions in five major sports leagues in England and the United States. We\ncharacterize the parity among teams by the variance in the winning fraction\nfrom season-end standings data and quantify the predictability of games by the\nfrequency of upsets from game results data. We introduce a novel mathematical\nmodel in which the underdog team wins with a fixed upset probability. This\nmodel quantitatively relates the parity among teams with the predictability of\nthe games, and it can be used to estimate the upset frequency from standings\ndata.",
    "arxiv_id": "physics/0608007",
    "authors": [
      "E. Ben-Naim",
      "F. Vazquez",
      "S. Redner"
    ],
    "categories": [
      "physics.soc-ph",
      "cond-mat.stat-mech"
    ],
    "journal_ref": "J. Quant. Anal. Sports Vol. 2: No. 4, Article 1 (2006).",
    "title": "Parity and Predictability of Competitions",
    "url": "https://arxiv.org/abs/physics/0608007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a9645d0c-9f02-4177-93d6-37559e35d7ef",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}