In a situation in which several explanations compete, is the one that is better qua explanation also the one we should regard as the more likely to be true? Realists usually answer in the affirmative. They then go on to argue that since realism provides the best explanation for the success of science, realism can be inferred to. Nonrealists, on the other hand, answer the above question in the negative, thereby renouncing the inference to realism. In this paper I separate the two issues. In the first section it is argued that a rationale can be provided for the inference to the best explanation; in the second, that this rationale cannot justify an inference to realism. The defence of the inference rests on the claim that our standards of explanatory power are subject to critical examination, which, in turn, should be informed by empirical considerations. By means of a comparison of the realist's explanation for the success of science with that of conventionalism and instrumentalism it is then shown that realism does not offer a superior explanation and should not, therefore, be inferred to.