We show that the relative isomer stability of fullerene anions is essentially governed by a few simple structural motifs, requiring only the connectivity information between atoms. Relative energies of a large number of isomers of fullerene anions, C(2n)(q) (2n = 68-104; q = -2, -4, -6), can be satisfactorily reproduced by merely counting the numbers of seven kinds of hexagon-based motifs. The dependence of stability on these motifs varies with the charge state, which reflects the fact that the isomeric form of the carbon cage in endohedral metallofullerenes (EMFs) often differs from that in neutral empty fullerenes. The chemical origin of the stabilization differences between motifs is discussed on the basis of electronic and strain effects as well as aromaticity. On the basis of this simple model, the extraordinary abundance of the icosahedral C80 cage in EMFs can be easily understood. We also provide an explanation for why the well-known isolated pentagon rule is often violated in smaller EMFs. Finally, simple topological indices are proposed for quantitatively predicting the relative stability of fullerene anions, allowing a rapid determination of suitable hosting cages in EMFs by just counting three simple structural motifs.