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

2026-04-18

AI Summary

This study addresses the accurate conversion of betting odds into outcome probabilities for sports forecasting and market efficiency analysis. It proposes two approaches: first, an odds-only expected profit-consistent (OO-EPC) method that requires no historical data and is grounded in the assumption that bookmakers set odds such that their expected profit is equal across all possible outcomes; second, a frequency-learning generalized linear model (FL-GLM) that incorporates historical data and corrects the favorite–longshot bias by estimating only a single calibration parameter. OO-EPC introduces a novel perspective by modeling odds conversion through the lens of bookmaker profit confidence, while FL-GLM enhances interpretability and simplifies existing frameworks. Evaluated on a dataset of 90,014 football matches, OO-EPC outperforms existing odds-only methods, and FL-GLM consistently surpasses traditional multinomial and logistic regression models across multiple bookmakers, demonstrating successful application in six basketball prediction contests.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

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.

Problem

• sports forecasting
• betting odds
• probability conversion
• market efficiency
• favorite-longshot bias

Innovation

• Odds-Only Conversion
• Equal Profitability Confidence
• Favourite-Longshot Bias
• Generalised Linear Model
• Market Efficiency