It is well known that in vitro muscles maximize their power output when acting against a moderate resistance regarding their maximum strength. Similar behavior has been observed from in vivo muscular systems in both single-joint and most of the multi-joint maximum performance tasks. We refer to that phenomenon as a strength-dependent behavior, since the optimum external load that maximizes the mechanical power output of particular muscle(s) or neuro-musculoskeletal system corresponds to a certain percent of maximum strength. In this review paper, we present evidence that the optimum load in maximum vertical jumps is one's own body mass, regardless of the strength of the lower limb muscles (i.e., the strength-independent behavior). Although the discussed phenomenon is still underexplored, we believe that several neuro-mechanical mechanisms are involved. Among these are a long-term adaptation of the muscular force-velocity relationship to the body weight and inertia, alteration of the jumping technique, load-specific muscle activation and jumping skills. Further exploration of the discussed strength-independent behavior of the lower limb muscles is of importance for refining various training and rehabilitation procedures, as well as for understanding the design and function of lower limb muscles.