•A method suitable for comparisons of observed asteroids with N-body simulations is presented, which does not rely on the hierarchical clustering (HCM).•Size-frequency distribution of the synthetic family and background matches the observed SFD. Colours and albedos are used to decrease the contamination.•The Eos family shape in the space of proper elements is fully explained, including the distribution of pole latitudes.•Traces of the original velocity field are detectable even 1.3 Gyr after the impact. In order to fully understand the shapes of asteroids families in the 3-dimensional space of the proper elements (ap, ep, sin Ip) it is necessary to compare observed asteroids with N-body simulations. To this point, we describe a rigorous yet simple method which allows for a selection of the observed asteroids, assures the same size-frequency distribution of synthetic asteroids, accounts for a background population, and computes a χ2 metric. We study the Eos family as an example, and we are able to fully explain its non-isotropic features, including the distribution of pole latitudes β. We confirm its age t=(1.3±0.3)Gyr; while this value still scales with the bulk density, it is verified by a Monte-Carlo collisional model. The method can be applied to other populous families (Flora, Eunomia, Hygiea, Koronis, Themis, Vesta, etc.).