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Football goal distributions and extremal statistics

Author

Listed:
  • Greenhough, J
  • Birch, P.C
  • Chapman, S.C
  • Rowlands, G

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 1970/71–2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics.

Suggested Citation

  • Greenhough, J & Birch, P.C & Chapman, S.C & Rowlands, G, 2002. "Football goal distributions and extremal statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 615-624.
    • Handle: RePEc:eee:phsmap:v:316:y:2002:i:1:p:615-624
    DOI: 10.1016/S0378-4371(02)01030-0
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    Cited by:

    1. Martín-González, Juan Manuel & de Saá Guerra, Yves & García-Manso, Juan Manuel & Arriaza, Enrique & Valverde-Estévez, Teresa, 2016. "The Poisson model limits in NBA basketball: Complexity in team sports," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 182-190.
    2. Mueller-Langer, Frank & Andreoli-Versbach, Patrick, 2013. "Leading-effect vs. Risk-taking in Dynamic Tournaments: Evidence from a Real-life Randomized Experiment," Discussion Papers in Economics 15452, University of Munich, Department of Economics.
    3. Narizuka, Takuma & Yamamoto, Ken & Yamazaki, Yoshihiro, 2014. "Statistical properties of position-dependent ball-passing networks in football games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 157-168.
    4. A D Fitt & C J Howls & M Kabelka, 2006. "Valuation of soccer spread bets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(8), pages 975-985, August.
    5. G. K. Skinner & G. H. Freeman, 2009. "Soccer matches as experiments: how often does the 'best' team win?," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(10), pages 1087-1095.
    6. S Lessmann & M-C Sung & J E V Johnson, 2011. "Towards a methodology for measuring the true degree of efficiency in a speculative market," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(12), pages 2120-2132, December.
    7. Mueller-Langer Frank & Andreoli-Versbach Patrick, 2017. "Leading-Effect, Risk-Taking and Sabotage in Two-Stage Tournaments: Evidence from a Natural Experiment," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 237(1), pages 1-28, February.
    8. Jeon, Gyuhyeon & Park, Juyong, 2021. "Characterizing patterns of scoring and ties in competitive sports," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    9. Loek Groot, 2009. "Competitive Balance in Team Sports: The Scoring Context, Referees, and Overtime," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 165(3), pages 384-400, September.

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    Keywords

    Football; Extremal statistics;

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