We show that in a general four-dimensional N=1 supergravity with M >> 1 scalar fields, an exponentially small fraction of the non-supersymmetric critical points are metastable vacua. For a random superpotential and Kaehler potential, we construct a matrix model for the mass matrix and compute the eigenvalue spectrum analytically. We find that in generic configurations a significant fraction of the eigenvalues are negative. We then determine the probability p of a fluctuation in which all the eigenvalues become positive. Strong eigenvalue repulsion makes such a fluctuation extremely unlikely: we find p ~ e^(-c M^q), with q>1. We conclude that in string compactifications in which the superpotential and Kaehler potential are accurately described as random functions, almost all the non-supersymmetric critical points are saddle points and not metastable vacua. Our results have significant implications for the counting of de Sitter vacua in string theory.