  We identify the asymptotic distribution of $p$-rank of the sandpile group of
a random directed bipartite graphs which are not too imbalanced. We show this
matches exactly that of the Erd{\"o}s-R{\'e}nyi random directed graph model,
suggesting the Sylow $p$-subgroups of this model may also be Cohen-Lenstra
distributed. Our work builds on results of Koplewitz who studied $p$-rank
distributions for unbalanced random bipartite graphs, and showed that for
sufficiently unbalanced graphs, the distribution of $p$-rank differs from the
Cohen-Lenstra distribution. Koplewitz \cite{K} conjectured that for random
balanced bipartite graphs, the expected value of $p$-rank is $O(1)$ for any
$p$. This work proves his conjecture and gives the exact distribution for the
subclass of directed graphs.
