Comparing two methods for testing the efficiency of sports betting markets

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Abstract

Sports betting markets can be considered strongly efficient if expected returns on all possible bets on an event are equal. If this form of efficiency holds, then there is a direct mapping from betting odds into probabilities of outcomes of sporting events. We compare two regression-based methods for testing this form of efficiency that have been used in previous research: One that uses normalized probabilities as the explanatory variable for event outcomes and one that uses the inverse of the decimal odds. We show that the normalized probability method produces good tests of the null hypothesis of strong market efficiency but that the inverse odds method does not, with results biased against finding favorite-longshot bias. We illustrate this finding using large datasets of bets and outcomes for tennis and soccer and also with realistic simulations.
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比较检验体育博彩市场效率的两种方法
如果对某项赛事的所有可能投注的预期收益都相等,那么体育博彩市场就可以被视为具有很高的效率。如果这种效率形式成立,那么投注赔率就可以直接映射到体育赛事结果的概率。我们比较了之前研究中使用的两种基于回归的方法来测试这种效率形式:一种是使用归一化概率作为赛事结果的解释变量,另一种是使用十进制赔率的倒数。我们的研究表明,归一化概率法可以很好地检验强市场效率的零假设,但赔率倒数法则不然,其结果偏向于发现偏好-长投偏差。我们使用网球和足球的大型投注和结果数据集以及现实模拟来说明这一发现。
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