Stop Simulating! Efficient Computation of Tournament Winning Probabilities

TL;DR

This paper introduces a method for exact computation of tournament winning probabilities that is significantly faster than traditional simulation, applicable to major sports tournaments like the FIFA World Cup.

Contribution

The authors demonstrate that leveraging tournament structure allows for exact probability calculations, outperforming simulation-based methods regardless of the match outcome model.

Findings

Exact computation is faster than simulation for tournament probabilities.

Applicable to real-world tournaments like FIFA World Cup.

Independent of the match outcome model used.

Abstract

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.