An analytically solvable model for soccer: further implications of the classical Poisson model

Fry, John and Hastings, Tom and Serbera, Jean-Philippe (2017): An analytically solvable model for soccer: further implications of the classical Poisson model.

Abstract

In this paper we discuss an exactly soluble statistical model for soccer. By taking into account key features of soccer matches (goals are rare, goal-scoring patterns are not well understood) we arrive at a version of the classical Poisson model but with constraints on the expected total number of goals in a game. Closed form expressions are derived for expected scores and match outcomes. We are also able to reconstruct an empirically observed inverse strike-back effect pertaining to teams scoring consecutive goals. We produce analytical results for perfectly competitive soccer leagues where draws are tied to the average number of goals in a game. An empirical application to the 2016 UEFA European Championships is also discussed.

• Item Type: MPRA Paper
• Language: English
• Keywords: Forecasting; Gaming; Sports; Stochastic Processes
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General

References

[1] Baker R D and McHale I G (2015). Time varying ratings in association football: the alltime greatest team is ... Journal of the Royal Statistical Society A178: 481-492.

[2] Boshnakov G, Kharrat T and McHale I G (2015). Are goals Poisson distributed? STN Journal of Sports Modelling and Trading (forthcoming)

[3] Cain L P and Haddock D D (2006). Measuring parity: Tying into the idealized standard deviation. Journal of Sports Economics 7: 330-338.

[4] Cain M, Law D and Peel D (2000). The favourite-longshot bias and market efficiency in UK football betting. Scottish Journal of Political Economy 47: 25-36.

[5] Campbell J Y Lo A and MacKinlay A C (1997) The econometrics of financial markets, Princeton University Press: Princeton.

[6] Clarke S T and Norman J M (1995)Home ground advantage of individual clubs in English soccer. Journal of the Royal Statistical Society D 44: 509-526.

[7] Constantinou A C and Fenton N E (2017) Towards smart-data: Improving predictive accuracy in long-term football team performance. Knowledge-Based Systems 124: 93-104.

[8] Constantinou, A C., Fenton N E and Neil, M. (2012) pi-football. A Bayesian network model for forecasting Association football match outcomes. Knowledge-Based Systems 36:322-329.

[9] Dixon, M J and Robinson M E (1998). A birth process model for association football matches. Journal of the Royal Statistical society D 47: 523-538.

[10] Dyte D and Clarke S R (2000). A ratings based Poisson model for World Cup soccer simulation. Journal of the Operational Research Society 51: 993-998.