<p>Referee assignments for tournament matches are crucial decisions in sports, influenced by numerous factors. The assignment process involves inherent uncertainty due to fluctuations in referee performance and the varying challenges of different games. This work introduces the Stochastic Referee Assignment Problem using a multi-stage stochastic programming framework where each stage corresponds to a block of consecutive rounds. The developed model encompasses several constraints that are relevant to the assignment process in practice. It comprises two sets of variables: one that determines the set of referees for each round of the game schedule based on long-term planning criteria, and another that assigns referees to the games of the rounds so that game difficulty levels are met as much as possible. Because solving the full multi-stage model is computationally prohibitive, we propose a two-stage approximate solution methodology that is based on sample average approximation. With numerical experiments, we quantify the value of the stochastic solution, and provide and interpret the results of our approximate method.</p>