This paper studies the relative importance of teacher-student match effects and general teacher effectiveness in producing student learning, and quantifies gains from alternative teacher assignments. We estimate a framework that separates these components, allowing match quality to vary with observable student characteristics and unobservable teacher-school factors. Using more than a decade of administrative data from a large urban district, we address endogenous sorting with quasi-random assignment variation induced by differences in driving time between teachers and schools. Match effects are similar in magnitude to general effectiveness. Teacher-acceptable reassignments can raise average test scores by about 0.13 standard deviations.