arXiv:cond-mat/0110605v2 [cond-mat.stat-mech] 19 Feb 2002Football 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 1Introduction 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.Theshort-termpredictabil- 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-ratedependenceonboth 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 Science29 May 2018
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