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We demonstrate that the gain attained by network coding (NC) on the multicast capacity of random wireless ad hoc networks is bounded by a constant factor. We consider a network with n nodes distributed uniformly in a unit square, with each node acting as a source for independent information to be sent to a multicast group consisting of m randomly chosen destinations. We show that, under the protocol model, the per- session capacity in the presence of arbitrary NC has a tight bound of Theta (1/radic(mnlog(n))) when m = O(n/(log(n))) and Theta(1/n) when m = Omega(n/(log(n))). Our result follows from the fact that prior work has shown that the same order bounds are achievable with pure routing based only on traditional store-and-forward methods.