Abstract  The main result of the paper contains an exact formula for the rate of regularity of a set-valued mapping with a convex graph. As a consequence we find an exact expression for the rate of regularity of set-valued mappings associated with so-called constraint systems. It turns out that the rate is equal to the upper bound of Robinson-type estimates over all norms in the graph space of the homogenized mapping majorizing the norm of the underlying space. We further introduce a concept of a perfectly regular mapping and find some criteria for perfect regularity.