It is well known that average pupil-teacher ratios (PTRs) are higher in poorer countries. This paper shows that PTR variation is also higher, and this helps explain cross-country differences in educational attainment. I build a new global school-level data set that comprises nearly two million schools and represents the public primary education sector in 86 countries. This allows me to uncover three new stylized facts. First, variation in school-level PTRs is negatively correlated with per capita income, both across countries and within countries across time. Second, PTR variation is negatively correlated with educational outcomes across countries and districts. Third, school remoteness can only explain a negligibly small share of PTR variation within lower income countries. To assess the relevance of these facts, I build and calibrate a model of teacher allocation. Through simulations, I show that educational attainment gains from implementing counterfactual teacher allocations would be substantial in many lower income countries, closing up to 9% of the attainment gap with the US. I project that obtaining equivalent attainment gains through reductions in aggregate PTRs, holding the relative distribution of teachers between schools fixed, would require teacher workforce increases of up to 40%.