SIAM Journal on Financial Mathematics, Volume 12, Issue 1, Page 295-317, January 2021.
We provide a fast and scalable numerical algorithm for inferring the distributions of participant scores in a contest under the assumption that each participant's score distribution is a translation of every other's. We term this the horse race problem, as the solution provides one way of assigning a coherent joint probability to all outcomes and pricing arbitrarily complex horse racing wagers. However, the algorithm may also find use anywhere winning probabilities are apparent, such as with e-commerce product placement, in Web search, or, as we show, in addressing a fundamental problem of trade: who to call, based on market share statistics and inquiry cost.

中文翻译：

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从多人竞赛中的获胜概率推断相对能力

SIAM Journal on Financial Mathematics，第 12 卷，第 1 期，第 295-317 页，2021 年 1 月。
我们提供了一种快速且可扩展的数值算法，用于在假设每个参与者的分数分布是每个人的。我们将此称为赛马问题，因为该解决方案提供了一种方法，可以为所有结果分配一致的联合概率并为任意复杂的赛马投注定价。然而，该算法也可以在任何获胜概率明显的地方使用，例如电子商务产品植入、网络搜索，或者，正如我们所展示的，在解决贸易的一个基本问题时：根据市场份额统计，给谁打电话和查询费用。