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.