Forecast Sports Outcomes under Efficient Market Hypothesis: Theoretical and Experimental Analysis of Odds-Only and Generalised Linear Models

TL;DR

This paper introduces novel odds-only and generalized linear models for converting betting odds into accurate outcome probabilities, validated through extensive datasets and real-world sports forecasting competitions.

Contribution

It proposes the OO-EPC odds-only method that aligns with bookmakers' profitability goals and the FL-GLM model that captures the favourite-longshot bias with a single parameter, improving accuracy.

Findings

OO-EPC outperforms existing odds-only methods in empirical tests.

FL-GLM outperforms traditional models in football match probability estimation.

Both models demonstrate effectiveness in real-world sports forecasting scenarios.

Abstract

Converting betting odds into accurate outcome probabilities is a fundamental challenge in order to use betting odds as a benchmark for sports forecasting and market efficiency analysis. In this study, we propose two methods to overcome the limitations of existing conversion methods. Firstly, we propose an odds-only method to convert betting odds to probabilities without using historical data for model fitting. While existing odds-only methods, such as Multiplicative, Shin, and Power exist, they do not adjust for biases or relationships we found in our betting odds dataset, which consists of 90014 football matches across five different bookmakers. To overcome these limitations, our proposed Odds-Only-Equal-Profitability-Confidence (OO-EPC) method aligns with the bookmakers' pricing objectives of having equal confidence in profitability for each outcome. We provide empirical evidence from our betting odds dataset that, for the majority of bookmakers, our proposed OO-EPC method outperforms the existing odds-only methods. Beyond controlled experiments, we applied the OO-EPC method under real-world uncertainty by using it for six iterations of an annual basketball outcome forecasting competition. Secondly, we propose a generalised linear model that utilises historical data for model fitting and then converts betting odds to probabilities. Existing generalised linear models attempt to capture relationships that the Efficient Market Hypothesis already captures. To overcome this shortcoming, our proposed Favourite-Longshot-Bias-Adjusted Generalised Linear Model (FL-GLM) fits just one parameter to capture the favourite-longshot bias, providing a more interpretable alternative. We provide empirical evidence from historical football matches where, for all bookmakers, our proposed FL-GLM outperforms the existing multinomial and logistic generalised linear models.