  At nonzero quark chemical potential dynamical lattice simulations of QCD are
hindered by the sign problem caused by the complex fermion determinant. The
severity of the sign problem can be assessed by the average phase of the
fermion determinant. In an earlier paper we derived a formula for the
microscopic limit of the average phase for general topology using chiral random
matrix theory. In the current paper we present an alternative derivation of the
same quantity, leading to a simpler expression which is also calculable for
finite-sized matrices, away from the microscopic limit. We explicitly prove the
equivalence of the old and new results in the microscopic limit. The results
for finite-sized matrices illustrate the convergence towards the microscopic
limit. We compare the analytical results with dynamical random matrix
simulations, where various reweighting methods are used to circumvent the sign
problem. We discuss the pros and cons of these reweighting methods.
