Positive allometry of secondary sexual traits (whereby larger individuals have disproportionally larger traits than smaller individuals) has been called one of the most pervasive and poorly understood regularities in the study of animal form and function. Its widespread occurrence is in contrast with theoretical predictions that it should evolve only under rather special circumstances. Using a combination of mathematical modeling and simulations, here we show that positive allometry is predicted to evolve under much broader conditions than previously recognized. This result hinges on the assumption that mating success is not necessarily zero for males with the lowest trait values: for example, a male who lacks horns or antlers might still be able to copulate if encountering an unguarded female. We predict the strongest positive allometry when males typically (but not always) compete in large groups, and when trait differences decisively determine the outcome of competitive interactions.