Does access to four-year colleges affect degree completion for students who would otherwise attend two-year colleges? Admission to Georgia’s four-year public sector requires minimum SAT scores. Regression discontinuity estimates show that access to this sector increases four-year college enrollment and college quality, largely by diverting students from two-year colleges. Access substantially increases bachelor’s degree completion rates for these relatively low-skilled students. SAT retaking behavior suggests students value access to four-year public colleges, though perhaps less than they should. Our results imply that absolute college quality matters more than match quality and suggest potential unintended consequences of free community college proposals.