Sports betting's recent federal legalisation in the USA coincides with the golden age of machine learning. If bettors can leverage data to accurately 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 forecasting 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. Evaluating various betting systems, we show that optimising the forecasting model for calibration leads to greater returns than optimising for accuracy, on average (return on investment of $110.42\%$ versus $2.98\%$) and in the best case ($902.01\%$ versus $222.84\%$). These findings suggest that for sports betting (or any forecasting problem where decisions are made based on the predicted probability of each outcome), calibration is a more important metric than accuracy. Sports bettors who wish to increase profits should therefore optimise their forecasting model for calibration.

翻译：近期美国联邦层面将体育博彩合法化，恰逢机器学习的黄金时代。若投注者能通过数据准确预测赛事结果的概率，便能识别博彩公司赔率中蕴含的有利机会。鉴于仅美国体育博彩业就价值数十亿美元，发现此类机遇将极具盈利潜力。众多研究者已将机器学习应用于体育赛事结果预测问题，通常采用准确率评估预测模型性能。我们提出假设：在体育博彩问题中，模型校准性比准确率更为重要。为验证该假设，我们基于多个赛季的NBA数据训练模型，并利用公开赔率对单个赛季进行投注实验。通过评估不同投注系统，我们证明：平均而言，优化校准性的预测模型比优化准确率的模型带来更高回报（投资回报率$110.42\%$对比$2.98\%$），最佳情况下差异更显著（$902.01\%$对比$222.84\%$）。这些发现表明，对于体育博彩（或任何依据各结果预测概率进行决策的预测问题），校准性比准确率更重要。因此，希望提升盈利的体育博彩者应优化其预测模型的校准性。