In Part 1 of this series, I briefly explained the Elo rating system along with the two key parameters involved. In Part 2, I described how a Bayesian model could be setup to estimate the Elo parameters and the Elo ratings of teams. In this post, I discuss how we can use the model and simulations to estimate the win probabilities of future matches, including the tournament outcome. I assume that the you are familiar with the notations I have used in Part 1 and 2 and hence, will not explain it again here. The source code for this work can be found here.

In Part 1 of this three-part series, I presented an introduction to the Elo rating system. In this post, I describe the specifics of the Bayesian model used to infer the Elo parameters $K$ and $\tau$. I also illustrate how the parameter uncertainty is reflected in Elo ratings by showing the posterior distribution of the ratings for two teams (St. Kilda and West Coast Eagles) as the season progressed. Instead of a single point estimate for a team’s Elo rating, we can get a more informative view by looking at plausible values of Elo expressed as a probability distribution. This is a precursor for the final piece of the puzzle, covered in the Part 3, where I estimate the win probabilities for future matches, including the Premiership title. The source code for this work can be found here.

In this three-part series, I want to share some of the work I did for fun during the 2018 AFL season. In particular, this work is about using a Bayesian model to estimate AFL team ratings. In Part 1, I give a brief introduction to a rating system known as Elo. In Part 2, I will share how a Bayesian approach can be used to estimate the parameters of the Elo system. I will also share some results on how the model tracked the changes in team ratings as the 2018 AFL season progressed. One of the advantages of using a Bayesian Elo framework is that it allows us to capture the uncertainty or the randomness in team ratings. Incorporating this uncertainty in the ratings is crucial for avoiding over confident win/lose predictions for matches. What exactly I mean by this would become clearer in Part 2. In Part 3, I will show how we can use simulations to estimate the probabilities of the tournament outcome (of course, before the tournament ends). The source code for this work can be found here.