Large-scale events like the UEFA Euro 2020 football (soccer) championship offer a unique opportunity to quantify the impact of gatherings on the spread of COVID-19, as the number and dates of matches played by participating countries resembles a randomized study. Using Bayesian modeling and the gender imbalance in COVID-19 data, we attribute 840,000 (95% CI: [0.39M, 1.26M]) COVID-19 cases across 12 countries to the championship. The impact depends non-linearly on the initial incidence, the reproduction number R, and the number of matches played. The strongest effects are seen in Scotland and England, where as much as 10,000 primary cases per million inhabitants occur from championship-related gatherings. The average match-induced increase in R was 0.46 [0.18, 0.75] on match days, but important matches caused an increase as large as +3. Altogether, our results provide quantitative insights that help judge and mitigate the impact of large-scale events on pandemic spread.