The proportion of human genetic variation due to differences between populations is modest, and individuals from different populations can be genetically more similar than individuals from the same population. Yet sufficient genetic data can permit accurate classification of individuals into populations. Both findings can be obtained from the same data set, using the same number of polymorphic loci. This article explains why. Our analysis focuses on the frequency, omega, with which a pair of random individuals from two different populations is genetically more similar than a pair of individuals randomly selected from any single population. We compare omega to the error rates of several classification methods, using data sets that vary in number of loci, average allele frequency, populations sampled, and polymorphism ascertainment strategy. We demonstrate that classification methods achieve higher discriminatory power than omega because of their use of aggregate properties of populations. The number of loci analyzed is the most critical variable: with 100 polymorphisms, accurate classification is possible, but omega remains sizable, even when using populations as distinct as sub-Saharan Africans and Europeans. Phenotypes controlled by a dozen or fewer loci can therefore be expected to show substantial overlap between human populations. This provides empirical justification for caution when using population labels in biomedical settings, with broad implications for personalized medicine, pharmacogenetics, and the meaning of race.