One way to reconstruct the miracle argument for scientific realism is to regard it as a statistical inference: since it is exceedingly unlikely that a false theory makes successful predictions, while it is rather likely that an approximately true theory is predictively successful, it is reasonable to infer that a predictively successful theory is at least approximately true. This reconstruction has led to the objection that the argument embodies a base rate fallacy: by focusing on successful theories one ignores the (...) vast number of false theories some of which will be successful by mere chance.In this paper, I shall argue that the cogency of this objection depends on the explanandum of the miracle argument. It is cogent if what is to be explained is the success of a particular theory. If, however, the explanandum of the argument is the distribution of successful predictions among competing theories, the situation is different. Since the distribution of accidentally successful predictions is independent of the base rate, it is possible to assess the base rate by comparing this distribution to the empirically found distribution of successful predictions among competing theories. (shrink)