Self-affirmation model for football goal distributionsE. Bittner1, A. Nußbaumer1, W. Janke1 and M. Weigel2
1 Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig Postfach 100 920, D-04009 Leipzig, Germany
2 Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University Riccarton, Edinburgh, EH14 4AS, UK
received 14 February 2007; accepted in final form 12 April 2007; published June 2007
published online 16 May 2007
Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out that in particular the tails of the distributions are not well described by independent Bernoulli trials, but rather well modeled by negative binomial or generalized extreme value distributions. To understand this behavior from first principles, we suggest to modify the Bernoulli random process to include a simple component of self-affirmation which seems to describe the data surprisingly well and allows to interpret 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 and found the proposed models to be applicable rather universally. In particular, here we compare men's and women's leagues and the separate German leagues during the cold war times and find some remarkable differences.
89.20.-a - Interdisciplinary applications of physics .
02.50.-r - Probability theory, stochastic processes, and statistics .
© Europhysics Letters Association 2007