This paper explores differences in the frequency with which students from different schools reach high levels of math achievement. Data from the American Mathematics Competitions is used to produce counts of high-scoring students from more than two thousand public, coeducational, non-magnet, non-charter U.S. high schools. High-achieving students are found to be very far from evenly distributed. There are strong demographic predictors of high achievement. There are also large differences among seemingly similar schools. The unobserved heterogeneity across schools includes a thick tail of schools that produce many more high-achieving students than the average school. Gender-related differences and other breakdowns are also discussed.