Population-level theories of evolution - the stock and trade of population genetics - are statistical theories par excellence. But what accounts for the statistical character of population-level phenomena? One view is that the population-level statistics are a product of, are generated by, probabilities that attach to the individuals in the population. On this conception, population-level phenomena are explained by individual-level probabilities and their population-level combinations. Another view, which arguably goes back to Fisher (1930) but has been defended recently, is that the population-level statistics are sui generis, that they somehow emerge from the underlying deterministic behavior of the individuals composing the population. Walsh, Lewens, and Ariew (2002) label this the statistical interpretation. We are not willing to give them that term, since everyone will admit that the population-level theories of evolution are statistical, so we will call this the emergentist statistical interpretation (ESI). Our goals are to show that (1) this interpretation is based on gross factual errors concerning the practice of evolutionary biology, concerning both what is done and what can be done; (2) its adoption would entail giving up on most of the explanatory and predictive (i.e., scientific) projects of evolutionary biology; and finally (3) a rival interpretation, which we will label the propensity statistical interpretation (PSI), succeeds exactly where the emergentist interpretation fails.