Globular star clusters that formed at the same cosmic time may have evolved rather differently from the dynamical point of view(because that evolution depends on the internal environment) through a variety of processes that tend progressively to segregate stars more massive than the average towards the cluster centre(1). Therefore clusters with the same chronological age may have reached quite different stages of their dynamical history (that is, they may have different 'dynamical ages'). Blue straggler stars have masses greater(2) than those at the turn-off point on the main sequence and therefore must be the result of either a collision(3,4) or a mass-transfer event(5-7). Because they are among the most massive and luminous objects in old clusters, they can be used as test particles with which to probe dynamical evolution. Here we report that globular clusters can be grouped into a few distinct families on the basis of the radial distribution of blue stragglers. This grouping corresponds well to an effective ranking of the dynamical stage reached by stellar systems, thereby permitting a direct measure of the cluster dynamical age purely from observed properties.