The market for English Premier League (EPL) odds

Abstract

This paper employs a Skellam process to represent real-time betting odds for English Premier League (EPL) soccer games. Given a matrix of market odds on all possible score outcomes, we estimate the expected scoring rates for each team. The expected scoring rates then define the implied volatility of an EPL game. As events in the game evolve, we re-estimate the expected scoring rates and our implied volatility measure to provide a dynamic representation of the market's expectation of the game outcome. Using a dataset of 1520 EPL games from 2012-2016, we show how our model calibrates well to the game outcome. We illustrate our methodology on real-time market odds data for a game between Everton and West Ham in the 2015-2016 season.We show how the implied volatility for the outcome evolves as goals, red cards, and corner kicks occur. Finally, we conclude with directions for future research.

On the probability of Magnus Carlsen reaching 2900

“…There is a large literature on the choice of $$$ K $$$‐factor in chess and in other sports 6–8 as the Elo rating system is used extensively to great effect. The problem of lack of volatility in a players' rating changes when $$$ K=10 $$$ has been the center of much debate.…”

“…Stern 9 provides a model for addressing the probabilities of winning a sports contest. Feng et al 7 extend this model to discrete outcomes using a Skellam process for EPL football matches. This is more appropriate given that chess has a similar outcome distribution profile with $$$ \left( win, draw, loss\right) $$$.…”

“…Section 2 provides a simple Brownian motion model for assessing the two fundamental questions of how likely is it that Magnus Carlsen will reach 2900, and at what level of play would he have to achieve to have a reasonable chance of achieving 2900? To do this we use the Brownian motion model for sports scores as originally developed by Stern 6 and extended by a number of authors, Feng et al 7 for EPL, Polson and Stern 8 for implied volatility of a sports game. Then we provide an empirical analysis of Magnus Carlsen's games and changes in Elo ratings.…”