Introductions of non-indigenous species in ballast water are one of the greatest threats to freshwater and marine ecosystems worldwide. New approaches to reducing the release of organisms from ballast water are under consideration nationally and internationally. Unfortunately, the development of scientifically defensible policy for controlling introductions from ballast water has been retarded by the lack of relevant ecological theory and a shortage of information about the identity and numbers of organisms in ballast. Here, we present a novel quantitative approach to estimating the risk of species establishment by combining a model for population spread with known allometric correlations between body size and population growth rate for broad taxonomic categories. Our approach is applicable to sexually reproducing, planktonic taxonomic groups including ctenophores, cnidaria, arthropods, annelids, mollusks and (as an approximation) echinoderms and fishes. As expected, the allowable volume of ballast discharge depends strongly on the acceptable level of risk (which is a societal decision), the taxonomic group of concern and the characteristics of the receiving environment. For example, for a risk tolerance equivalent to establishment of one in one hundred introduced species, independent releases of untreated ballast water should not exceed around 50,000 metric tons. Because of differences in horizontal mixing in different environments, releases in harbors are more risky than releases in open water. These results provide quantitative guidelines that could immediately lower the risk of species invasion while other more permanent technological solutions are developed.