Football (soccer) is arguably one of the most unpredictable sports. Countless variables play a role in determining the outcome of a certain football match. Due to the high complexity of the entire set of involved parameters, the results of football matches may seem pretty random at the first glance. However, there are mathematical theories enabling us to model and analyze the behavior of such complex systems (e.g. chaos theory, probability, and dynamical systems). 


Also, just like the case of financial markets, there is a great commercial and social motivation behind predicting football matches. For instance, if you are in charge of a company sponsoring a certain football team in an elimination tournament, you might be concerned with the number of matches that your team can play before its elimination so that you can estimate the amount of public attention and profit that you can obtain by sponsoring this certain team.


During my search I came across the following interesting papers in which some methods from dynamical systems and probability theory are used for analyzing football matches. 


* K. Davids, D. Araújo and R. Shuttleworth, *Applications of Dynamical Systems Theory to Football*. ([Link to the paper](http://www.ff.ul.pt/~lgouveia/dmproj/DavidsAraujoShuttleworthSoccer.pdf))
* L. Bastos; J. da Rosa, *Predicting probabilities for the 2010 FIFA World Cup games using a Poisson-Gamma model*. J. Appl. Stat. 40 (2013), no. 7, 1533–1544. ([MR3286258](https://mathscinet.ams.org/mathscinet-getitem?mr=3286258))
* G. Angelini and L. De Angelis, *PARX model for football match predictions*.
J. Forecast. 36 (2017), no. 7, 795–807. ([MR3714406](https://mathscinet.ams.org/mathscinet-getitem?mr=3714406))


Also, based on the following paper, I guess some chaos theoretic approaches might be relevant to this problem.


* M. G. Mack, S. Huddleston, K. E. Dutler, and J. K. Mintah, *Chaos Theory: A New Science for Sport Behavior?* ([Link to the article](http://www.athleticinsight.com/Vol2Iss2/ChaosPDF.pdf))


I wonder whether there is any known *really successful* and *practically applicable* mathematical method for predicting football matches or not. 



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> **Question.** What are examples of research papers modeling football matches/tournaments using mathematical tools (from chaos theory, dynamical systems or probability) which particularly suggest methods for **predicting** the results of the football matches/tournaments? 
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On Mathematical Foundations of Football
Typing "mathematics of soccer" into the internet led to J.A. Tenreiro Machado, António M.Lopes, On the mathematical modeling of soccer dynamics, Communications in Nonlinear Science and Numerical Simulation, Volume 53, December 2017, Pages 142-153: 


Abstract


This paper addresses the modeling and dynamical analysis of soccer teams. Two modeling perspectives based on the concepts of fractional calculus are adopted. In the first, the power law behavior and fractional-order integration are explored. In the second, a league season is interpreted in the light of a system where the teams are represented by objects (particles) that evolve in time and interact (collide) at successive rounds with dynamics driven by the outcomes of the matches. The two proposed models embed implicitly details of players and coaches, or strategical and tactical maneuvers during the matches. Therefore, the scale of observation focuses on the teams behavior in the scope of the observed variables. Data characterizing two European soccer leagues in the season 2015–2016 are adopted and processed. The model leads to the emergence of patterns that are analyzed and interpreted.


Also, [this](https://www.fourfourtwo.com/features/soccermatics-how-maths-will-change-your-understanding-football) article, Soccermatics: How maths will change your understanding of football, on the 442 website, reporting on the work of Professor [David Sumpter](https://www.bloomsbury.com/uk/soccermatics-9781472924124/). Sumpter has several math/soccer videos online. 


