dorsal/arxiv
View SchemaFootball fever: goal distributions and non-Gaussian statistics
| Authors | Elmar Bittner, Andreas Nussbaumer, Wolfhard Janke, Martin Weigel |
|---|---|
| Categories | |
| ArXiv ID | physics/0606016 |
| URL | https://arxiv.org/abs/physics/0606016 |
| DOI | 10.1140/epjb/e2008-00396-1 |
| Journal | Eur. Phys. J. B 67, 459 (2009). |
Abstract
Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. Instead, a good effective description of the data is provided by less basic distributions such as the negative binomial one or the probability densities of extreme value statistics. To understand this behavior from a microscopical point of view, however, no waiting time problem or extremal process need be invoked. Instead, modifying the Bernoulli random process underlying the Poissonian model to include a simple component of self-affirmation seems to describe the data surprisingly well and allows to understand the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments, including data from all past tournaments of the ``FIFA World Cup'' series, and found the proposed models to be applicable rather universally. In particular, here we analyse the results of the German women's premier football league and consider the two separate German men's premier leagues in the East and West during the cold war times and the unified league after 1990 to see how scoring in football and the component of self-affirmation depend on cultural and political circumstances.
{
"annotation_id": "b9c1e717-d5ed-46ef-b802-e64909b38db3",
"date_created": "2026-03-02T18:01:07.612000Z",
"date_modified": "2026-03-02T18:01:07.612000Z",
"file_hash": "b6b29186c9fb7020955456137ba5f70d82db678ff110df94bb0dbcc73aa7e703",
"private": false,
"record": {
"abstract": "Analyzing football score data with statistical techniques, we investigate how\nthe not purely random, but highly co-operative nature of the game is reflected\nin averaged properties such as the probability distributions of scored goals\nfor the home and away teams. As it turns out, especially the tails of the\ndistributions are not well described by the Poissonian or binomial model\nresulting from the assumption of uncorrelated random events. Instead, a good\neffective description of the data is provided by less basic distributions such\nas the negative binomial one or the probability densities of extreme value\nstatistics. To understand this behavior from a microscopical point of view,\nhowever, no waiting time problem or extremal process need be invoked. Instead,\nmodifying the Bernoulli random process underlying the Poissonian model to\ninclude a simple component of self-affirmation seems to describe the data\nsurprisingly well and allows to understand the observed deviation from Gaussian\nstatistics. The phenomenological distributions used before can be understood as\nspecial cases within this framework. We analyzed historical football score data\nfrom many leagues in Europe as well as from international tournaments,\nincluding data from all past tournaments of the ``FIFA World Cup\u0027\u0027 series, and\nfound the proposed models to be applicable rather universally. In particular,\nhere we analyse the results of the German women\u0027s premier football league and\nconsider the two separate German men\u0027s premier leagues in the East and West\nduring the cold war times and the unified league after 1990 to see how scoring\nin football and the component of self-affirmation depend on cultural and\npolitical circumstances.",
"arxiv_id": "physics/0606016",
"authors": [
"Elmar Bittner",
"Andreas Nussbaumer",
"Wolfhard Janke",
"Martin Weigel"
],
"categories": [
"physics.soc-ph",
"cond-mat.stat-mech"
],
"doi": "10.1140/epjb/e2008-00396-1",
"journal_ref": "Eur. Phys. J. B 67, 459 (2009).",
"title": "Football fever: goal distributions and non-Gaussian statistics",
"url": "https://arxiv.org/abs/physics/0606016"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "dffceb3e-e0d6-439c-827b-9d7cb6190d6d",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}