Academic failure among first-year university students has long fuelled a large number of debates. Many educational psychologists have tried to understand and then explain it. Many statisticians have tried to foresee it. Our research aims to classify, as early in the academic year as possible, students into three groups: the "low-risk" students, who have a high probability of succeeding; the "medium-risk" students, who may succeed thanks to the measures taken by the university; and the "high-risk" students, who have a high probability of failing (or dropping out). This article describes our methodology and provides the most significant variables correlated to academic success among all the questions asked to 533 first-year university students during November of academic year 2003/04. Finally, it presents the results of the application of discriminant analysis, neural networks, random forests and decision trees aimed at predicting those students' academic success. Technical background to the different methods of prediction is appended. (Contains 4 tables and 2 figures.) [This research is funded by the Belgian State through the Inter-University Attraction Pole project.]