Many higher education institutions use a policy for academic dismissal. In the Netherlands, the academic dismissal policy is such that students with fewer credits than a certain threshold after their first year, are expelled. This article employs the beta-binomial model to assess whether this method succeeds in filtering those who have potential from those who do not and what the optimal level of the threshold is. The model considers 13,234 students in three consecutive cohorts from around fifty different bachelor's degree programmes at the University of Groningen. We found that demanding 45 out of 60 credits constitutes a fair threshold for this institution. Although a strict dismissal policy has only a minor effect on cohorts, it can have a major effect on specific groups of students. The software employed here is made available.