Sports betting's recent federal legalisation in the USA coincides with the golden age of machine learning. If bettors can leverage data to reliably predict the probability of an outcome, they can recognise when the bookmaker's odds are in their favour. As sports betting is a multi-billion dollar industry in the USA alone, identifying such opportunities could be extremely lucrative. Many researchers have applied machine learning to the sports outcome prediction problem, generally using accuracy to evaluate the performance of predictive models. We hypothesise that for the sports betting problem, model calibration is more important than accuracy. To test this hypothesis, we train models on NBA data over several seasons and run betting experiments on a single season, using published odds. We show that optimising the predictive model for calibration leads to greater returns than optimising for accuracy, on average (return on investment of $+34.69\%$ versus $-35.17\%$) and in the best case ($+36.93\%$ versus $+5.56\%$). These findings suggest that for sports betting (or any probabilistic decision-making problem), calibration is a more important metric than accuracy. Sports bettors who wish to increase profits should therefore optimise their predictive model for calibration.

翻译：美国近期对体育博彩的联邦合法化恰逢机器学习的黄金时代。若投注者能借助数据可靠预测赛果概率，即可识别庄家赔率对自身有利的情形。鉴于仅美国体育博彩市场即价值数十亿美元，识别此类机会可能带来巨额收益。众多研究者已将机器学习应用于赛果预测问题，通常以准确率评估预测模型性能。我们假设：在体育博彩问题中，模型校准度比准确率更为关键。为验证该假设，我们基于NBA多个赛季数据训练模型，并利用公开赔率对单个赛季进行博彩实验。结果表明：优化预测模型校准度所带来的平均投资回报率（$+34.69\%$）显著优于优化准确率的回报率（$-35.17\%$），最佳情况下前者（$+36.93\%$）亦远超后者（$+5.56\%$）。这些发现表明，对于体育博彩（或任何概率决策问题），校准度是比准确率更重要的评估指标。因此，希望提升收益的体育博彩者应优先优化预测模型的校准度。