The concept of flow competence is generally employed to evaluate velocities and bed stresses of river floods from the sizes of the largest sediment particles transported. For the most part, this evaluation has been empirical, combining data from a number of separate flood events in different river systems. Those data are re-examined and compared with empirical equations for the selective entrainment of gravel from deposits of mixed sizes. It is found that the competence relationships trend counter to those obtained for selective entrainment, indicating that the competence evaluations are affected by varying degrees of selective size entrainment. Individual data sets which have been employed to establish the flow-competence relationships either show no trend on their own or yield a trend which runs counter to the competence equation, instead being more compatible with the selective-entrainment relationships. In most instances, the empirical competence equations greatly overestimate the hydraulics of flood flows, and it is suggested that the better established selective entrainment equations be used for competence evaluations as well. Empirical equations are available for this purpose, relating the dimensionless Shields entrainment function or the bed shear stress to the diameter of the largest grain moved and to the median diameter of the deposit as a whole.