Animal contests often involve the use of repeated signals, which are assumed to advertise stamina, and hence fighting ability. While an individual may be predicted to give up once it has crossed an energetic threshold, costs inflicted by its opponent may also contribute to the giving-up decision. Therefore, physical strength should be of key importance in contests, allowing high signal magnitude as well as potentially inflicting costs. We investigated this using hermit crab shell fights, which employ a ‘hybrid signal’ of shell rapping, which advertises stamina but also imposes potentially deleterious consequences for the receiver. We examined the links between contest outcomes and two proxies for strength; the protein content and relative mass of hermit crab abdominal muscles, the main muscle group used in shell rapping. Our results indicate that there was no difference in muscle protein between winners and losers, whereas winners had significantly greater muscle mass : body mass ratios. Thus, while stamina has been assumed by theory to be an important determinant of agonistic success, the present results demonstrate the importance of muscle size and thereby strength.