To predict what tomorrow brings, is it reasonable to assume only the present isrelevant?

This report will focus on understanding and evaluating the implementation ofHidden Markov models (HMMs) for predicting a football team’s form. HMMs areuseful in systems where the true state - in this case, a team’s performance trend,or form - is hidden, and must be inferred from some observable output, such asin this case; expected goals (xG). The purpose of the model is to then unveil theprobabilities which govern transitions between hidden states, and how likely eachstate is to produce a particular observation. To achieve this, the probabilities areestimated through an expectation-maximization algorithm.

For this project, the training data for the model consisted of games that spanseveral seasons, from 2020 until 2025; with a focus on applying it to a team thatretained the same manager throughout the period, ensuring a relatively consistentplay style. Arsenal F.C in the English Premier league (EPL) was chosen. Thisallows us to assume the process is time-homogeneous meaning the probabilitiesassigned by the model are constant over time.

The model was subsequently refined by selecting the most appropriate number ofhidden states, followed by an analysis evaluating its predictive accuracy and howwell it fits the historical data.

This study demonstrates that it is possible to capture underlying long-term formtrends in football using HMMs, as for predictive power in the short term, it failsin beating a naive baseline.