The Empirical Attainment Function is a 2D empirical distribution function, which is actually a distribution of convergence trajectories. It can be efficiently computed, using the monotonic nature of those trajectories. We argue that it extends both the classical fixed-target and fixed-budget ECDF, which are the current gold-standard to assess black-box heuristic search performances. We argue that, in addition to capturing more information, if is also less prone to approximation error, as it does not need a pre-defined target set.