  We investigate the distribution of the lowest-lying energy states in a
disordered Andreev billiard by solving the Bogoliubov-de Gennes equation
numerically. Contrary to conventional predictions we find a decrease rather
than an increase of the excitation gap relative to its clean ballistic limit.
We relate this finding to the eigenvalue spectrum of the Wigner-Smith time
delay matrix between successive Andreev reflections. We show that the longest
rather than the mean time delay determines the size of the excitation gap. With
increasing disorder strength the values of the longest delay times increase,
thereby, in turn, reducing the excitation gap.
