Much of the evidence for quantum mechanics is statistical in nature. Close agreement between Born-rule probabilities and observed relative frequencies of results in a series of repeated experiments is taken as evidence that quantum mechanics is getting something --- namely, the probabilities of outcomes of experiments --- at least approximately right. On the Everettian interpretation, however, each possible outcome occurs on some branch of the multiverse, and there is no obvious way to make sense of ascribing probabilities to outcomes of experiments. Thus, the Everett interpretation threatens to undermine much of the evidence we have for quantum mechanics. In this paper, I will argue that the Everettian evidential problem is indeed one that Everettians should take seriously, and explain why, in order to deal with it successfully, it is necessary to go beyond existing approaches, including the Deutsch-Wallace decision-theoretic approach.