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.

翻译：将博彩赔率转化为准确的比赛结果概率，是将其作为体育预测基准和市场效率分析依据的关键挑战。本研究提出两种方法以突破现有转化方法的局限性。首先，我们提出一种仅依赖赔率的方法，无需历史数据拟合模型即可将赔率转化为概率。尽管现有仅赔率方法（如乘法模型、Shin模型和Power模型）存在，但它们并未针对我们构建的包含90014场足球比赛、横跨五家博彩公司的数据集所发现的偏差或关系进行调整。为克服上述局限，我们提出的"等盈利置信度仅赔率模型"（OO-EPC）遵循博彩公司对各比赛结果保持同等盈利置信度的定价目标。基于该数据集的实证结果表明，对多数博彩公司而言，OO-EPC模型优于现有仅赔率方法。除受控实验外，我们将OO-EPC模型应用于年度篮球赛果预测竞赛的六轮实际场景，验证其在真实不确定性下的表现。其次，我们提出一种利用历史数据拟合模型再转化赔率的广义线性模型。现有广义线性模型试图捕捉有效市场假说已涵盖的关系，针对这一不足，我们提出的"热门冷门偏差调整广义线性模型"（FL-GLM）仅通过拟合单一参数来捕捉热门冷门偏差，提供了更具可解释性的替代方案。基于历史足球比赛的实证表明，对所有博彩公司而言，FL-GLM模型均优于现有多项式与逻辑斯谛广义线性模型。