Value-added measures of teacher quality may be useful tools to help manage the teacher workforce and improve the efficiency of schools. But this requires that they be reliable estimates of teacher effectiveness. Because value-added scores are based on observational data, they may be biased by systematic patterns in the assignments of students to teachers. Whether assignment processes permit unbiased estimation of teacher value-added is a matter of great dispute. In this paper, I loosen the assumption from past research that assignment processes are identical at all schools. I develop a method for measuring the heterogeneity in school-level assignment practices, and I leverage the variation in practices to learn about the magnitude of biases in teacher value-added estimates. I show that about 60% of elementary schools in North Carolina systematically sort students with higher and lower scores on previous year’s tests to different classes – a pattern of student “tracking”. About half of these schools also allocate the classes of high and low achievers to the same teachers year after year – a pattern of “matching” teachers to certain students. Biases in value-added estimates are most likely in these matching schools, and least likely in school that are neither tracking or matching. Using data on teachers who move between the two types of schools, I document strong evidence of systematic and substantial biases in value-added measures. Importantly, these biases are negatively correlated with teachers’ true effects, so would not be detected by prior estimates of value-added. Overall, I conclude that the quality of value-added assessments is likely to depend on the nature of the student-teacher allocation process used at specific schools or school systems.