Hard spherical particles may exhibit a variation in impact damage on a softer target depending on the particle diameter and particle velocity. In this paper quantitative equations will be derived for these transitions in material behaviour. These equations have been presented in an erosion map of particle size against impact velocity. The equations used for the erosion map presented here resembles the mathematical relationships presented by others. The difference with earlier reports is that in this paper not only proportionalities are given but also the prefactors are determined. The theoretically derived erosion map has been validated for spherical particle impacts on borosilicate glass. The results show that the theoretical derived erosion map is generally correct. Most remarkable is the existence of cone cracks in the plastic regime.