The Poisson Distribution was developed by the French mathematician Simeon Denis Poisson in 1837. It’s one of the most popular (and effective) statistical methods applied in mathematical football predictions.
This video explains the Poisson process. Definitely worth watching! Read more about the Poisson process on this Khan Academy learning page.
Betting predictions
Predicting Football Results With Statistical Modelling – David Sheenan’s post explains how to predict football matches using the Poisson distribution, combining the world’s most popular sport with everyone’s favourite discrete probability distribution.
Football Prediction Models – this is probably the best online article on how to use Poisson distribution in football betting predictions. It’s a step-by-step explanation for beginners on “how do we actually create a predictive model for football games based on Poisson distribution?” You can actually build your own betting prediction model using Excel (which has the Poisson formula built in, anyway, you just need to follow the steps in this article to fill in the data properly).
A Bivariate Weibull Count Model for Forecasting Association Football Scores – an academic paper written by researchers Georgi Boshnakov, Tarak Kharrat and Ian G. McHale (School of Mathematics, University of Manchester, UK, Centre for Sports Business, Salford Business School, University of Salford, UK.) presenting a forecasting model for association football scores. The model uses a Weibull-inter-arrival times based count process and a copula to produce a bivariate distribution for the number of goals scored by the home and away teams in a match. They test it against a variety of alternatives, including the simpler Poisson distribution-based model and an independent version of their model. The out-of-sample performance of their methodology is illustrated first using calibration curves and then in a Kelly-type betting strategy that is applied to the pre-match win/draw/loss market and to the over-under 2.5 goals market. The new model provides an improved fit to data compared to previous models and results in positive returns to betting.
Online sources
Wikipedia – if you are new to the topic, check out the fundamentals first.
This Wikipedia article on Statistical association football predictions also provides a great overview of the most common method used in sports betting to predict the outcome of football matches by means of statistical tools and outperform the predictions of bookmakers. They dedicate a section to the Time-Independent Poisson Regression and the Time-Dependent Markov Chain Monte Carlo models each.
How to Make Accurate Soccer Predictions – a useful blog post on Trading with Data: Sports Trading Using Data and Systems to Create an Edge
Wolfram.com – an explanation published on Wolfram MathWorld, the most extensive math resource on the Web.
Online Stat Book – this is a GREAT educational resource in online statistics education. An Interactive Multimedia Course of Study developed by three universities: Rice University, University of Houston Clear Lake and Tufts University, with high-profile academic contributors and partial support of the National Science Foundation.
NIST/SEMATECH e-Handbook of Statistical Methods, also called the “Engineering Statistic Handbook”, is a very useful resource for scientists and engineers to use statistical methods in their work. NIST is an agency of the US Commerce Department.
Interactive Mathematics – a good explanation for beginners, it covers the very basics and it’s easy to understand.
Investopedia’s “Free Term of the Day” helps you gain a better understanding of all things financial with technical and easy-to-understand explanations. Refine Your Financial Vocabulary and Gain the Financial Knowledge You Need to Succeed.
MathWorks (“Accelerating the pace of engineering and science”) is one of the leading developers of mathematical computing software for engineers and scientists. Founded in 1984, MathWorks employs over 3000 people in 15 countries, with headquarters in Natick, Massachusetts. It has plenty of useful web pages explaining statistical methods for free. Definitely worth checking out!
Poisson Distribution: Predict the score in soccer betting – this is a useful article by Benjamin Cronin (2017) on Pinnacle.com, explaining: 1) how to use Poisson Distribution to predict soccer scores, 2) using Defence Strength & Attack Strength values, 3) how to calculate the most likely score-line, and 4) converting estimated chance into odds.
Mathematics is fun
University pages
University of Massachusetts Amherst – this page is part of the Warring States Project. It explains a couple of “classic” Poisson problems, such as The King’s Coiner, Ozzie’s Risk, The Gwodyen Problem, The Birthday Problem, The Prisoner’s Dilemma.
University of Alabama in Huntsville – this page explains the basic theory through not-so-basic examples. Intermediate level, not the first source to start with.