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Football goal distributions and extremal statistics

Authors
J. Greenhough,P. C. Birch
S. C. Chapman,G. Rowlands,Mark Godley,kyoungtae kim,Paolo Manghi,Shannon Johnson,Olga Shlykova,Hafid ANANE,Paul Bobrowski,Sergey E. Mikhailov,Jolanta Opacka-Juffry,Emanuele Leonardi,Beth Middleton,Christopher Nicklin,Marek Moszyński,Dolores del Mar Sánchez-González,Gabriele GIULI,Steven Pomerantz,Anatoli Chigarev,Ekaterina A. Shibaeva,PASCUAL ROMAN POLO,Nobuhiro Kuriyama,Konstantin Smirnov,Maggi Savin-Baden,Verónica Custodio Ramírez,Philippe Bergonzo,S Gnanakaran,Reiner Lenz,Michael Cropper,José Luis Gómez Urdáñez,James Suliburk,Gregory Tyson,Sid Becker,Vladimir Kharchenko,David Lide,Rowena Maguire,José Luis PIZARRO SANZ,Alan Goldin,Adam Godzik,Leandro Tessler,John Michael Conlon,Mikael Togeby,Bengt Steen,Jason Rivers,Viktor Mikla,Fernando Silva,Catherine Zandonella,Robert Pike,Dieter Böning,James Lowe,Martin Pavlas,David Ranson,Tatiana Kalinina,Ekkard Brinksmeier,Anil Taku,Vitalij Danilchenko,Wolfgang Marquardt,Janet Bradbury,Randall Morck,Patrizia Baraldi,Giuseppe Ranieri,Gabriele Simi,Michele Bellantoni,Runhua Tan,Paola Arias,JOSEFA ALVAREZ-FUENTES,Jean-Marc Seigneur,Wenping Li,Mikhail Pyatibratov,,Sebastian Böck,Jun Takahashi,Piet Van Nuffel,Amanda Weinstein,Richard Van de Water,Danny MacKinnon,Raymond Frey,David Asner,Daniel Červenkov,Jong-Seok Lim,James Russ,Bruno Breitmeyer,Andrew Onderdonk,Giorgio Sberveglieri,Eric Guittet,Thierry Roger,Corey Brady,Babajide Familoni,Jeffrey Silverstein,Yanhong Liu,Hong Lu,Ashu M. G. Solo,Patrick Edwards,Jonathan Benthall,Chris McSweeney,Andrea Sarkozy,Prof. Dr. Ellouze Mohamed,Lowell Fryman,Greg Watchmaker,Joan Bosch,Tomasz Staszewski,José Enrique Martín Domínguez,john reilly,Diego Restuccia,Antonio Siccardi,Shiliang Sun,Ronald Tallarida,Gregory Hendey,Jorge Juan Vilches,Wladimir SOUGAKOFF,J. 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arXiv:cond-mat/0110605v2 [cond-mat.stat-mech] 19 Feb 2002 Football goal distributions and extremal
statistics
J. Greenhough , P. C. Birch, S. C. Chapman, G. Rowlands
Department of Physics, University of Warwick, Coventry CV4 7AL, UK
Abstract
We analyse the distributions of the number of goals scored by home teams, away
teams, and the total scored in the match, in domestic football games from 169
countries between 1999 and 2001. The probability density functions (PDFs) of goals
scored are too heavy-tailed to be fitted over their entire ranges by Poisson or negative
binomial distributions which would be expected for uncorrelated processes. Log-
normal distributions cannot include zero scores and here we find that the PDFs are
consistent with those arising from extremal statistics. In addition, we show that it
is sufficient to model English top division and FA Cup matches in the seasons of
1970/71 to 2000/01 on Poisson or negative binomial distributions, as reported in
analyses of earlier seasons, and that these are not consistent with extremal statistics.
Key words: football, extremal statistics
1 Introduction
Few authors have considered foot-
ball scores from a statistical point of
view. Moroney [1] showed that the
numbers of goals scored by individual
teams, and the total goal scores, were
well described by a “modification of
the Poisson”; Reep et al. [2] later
identify this as the negative bino-
mial distribution, and found similar
results for other ball games. Maher
[3] then pointed out that a negative
Corresponding author.
Email address:
greenh@astro.warwick.ac.uk
(J. Greenhough).
binomial distribution may arise from
the aggregate of Poisson-distributed
scores with a different mean for each
team. The short-term predictabil-
ity of results has subsequently been
modelled using independent Poisson
distributions with means dependent
on teams’ past performances [4,5];
an improved model [6] includes the
scoring-rate dependence on both
time and the current score.
Other aspects of the game have been
examined including the effects of cer-
tain conditions on the scores - see [7]
for a review. Seeking a broader un-
derstanding, it has been suggested
[8] that the distribution of goals per
Preprint submitted to Elsevier Science 29 May 2018
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