In the run-up to any major sports tournament, winning probabilities of participants are publicized for engagement and betting purposes. These are generally based on simulating the tournament tens of thousands of times by sampling from single-match outcome models. We show that, by virtue of the tournament schedule, exact computation of winning probabilties can be substantially faster than their approximation through simulation. This notably applies to the 2022 and 2023 FIFA World Cup Finals, and is independent of the model used for individual match outcomes.

翻译：在任何重大体育赛事开赛前，参赛者的获胜概率都会被公布以吸引关注和用于博彩。这些概率通常基于从单场比赛结果模型中采样，对赛事进行数万次模拟得出。我们证明，由于锦标赛的赛程安排，精确计算获胜概率的速度可显著快于通过模拟进行近似计算。这一结论尤其适用于2022年和2023年国际足联世界杯决赛阶段，并且独立于用于单场比赛结果的模型。