Large males are solitary or occur in small groups in numerous ruminants. I propose that large males may become less social because of differences in costs and benefits of aggression as they age and increase in size and social status. Outside the mating season, large males have little to gain from sparring and interacting aggressively with other large males. I examined if large male Roosevelt elk (Cervus elaphus roosevelti) were more solitary or in smaller groups than other size or sex classes, associated with other large males, directed more aggression to small males, and displayed behaviors that reduced aggression when in groups. Large males were in the smallest groups and solitary more than twice as often as small males and females, and groups with large males had ≥50% of the group composed of large males. In relation to small males, large males sparred less frequently, were more dispersed in groups, and directed more aggressive behaviors toward them. Differences in costs and benefits of aggression between small and large males may help explain the asocial nature of large males.