From individual-level data for nine entire cohorts of undergraduate students in UK universities; we estimate the probability that an individual will drop out of university during their first-year. We examine the 1984-85 to 1992-93 cohorts of students enrolling full-time for a 3 or 4-year course; and focus on the sensitivity of the probability of withdrawal to the individual's prior qualifications relative to those of the other students in their university course. We show not only that weaker students are more likely to withdraw but also that the extent of variation in prior qualifications within the student's university degree course also exerts an influence on the individual's probability of withdrawal. We also find that withdrawal behaviour varies across universities according to a measure of average university student quality.