By invoking a result originally due to G. Shimura, we give a new proof of a generalization of a theorem of Deuring concerning supersingular elliptic curves, namely, a mass formula for superspecial abelian varieties with PEL-structures in characteristic p. This mass formula is then applied to estimate the dimension of Siegel modular cusp spaces modulo p and count the number of irreducible components in the supersingular region of the Siegel modular variety.