  We study the large $N$ limit of the matrix models associated with the
superconformal indices of four-dimensional $\mathcal{N}=1$ superconformal field
theories. We find that for a large class of $\mathcal{N}=1$ superconformal
gauge theories, the superconformal indices in the large $N$ limit of such
theories are dominated by the 'parallelogram' saddle, providing $O(N^2)$ free
energy for the generic value of chemical potentials. This saddle corresponds to
BPS black holes in AdS$_5$ whenever a holographic dual description is
available. Our saddle applies to a large class of gauge theories, including ADE
quiver gauge theories, and the theories with rank-2 tensor matters. Our
analysis works for most $\mathcal{N}=1$ superconformal gauge theories that
admit a suitable large $N$ limit while keeping the flavor symmetry fixed. We
also find 'multi-cut' saddle points, which correspond to the orbifolded
Euclidean black holes in AdS$_5$.
