The literature on the relationship between socioeconomic background (SES) and university education is inconsistent. Some studies conclude SES is important to university entry and course completion, others find trivial SES effects, net of students' prior performance, and a third group concludes that SES effects are important and policy relevant even when considering prior performance. Parallel arguments apply to demographic, school sector, and institutional differences in the university career, that is, are they unimportant when considering student performance? Using comprehensive and accurate measures of SES and student performance, and a statistical method that utilizes all non-missing data, this study quantifies the effects of socioeconomic, demographic, and institutional factors and prior student performance. SES has only weak effects on university entry and attrition, and no effects on course completion. Student performance has strong effects on entry and has moderate effects on attrition and completion. Demographic other differences mostly disappear when controlling for student performance.