Abductive reasoning assigns special status to the explanatory power of a hypothesis. But what determines explanatory power remains unclear. Our study clarifies this issue by asking: How does the explanatory power of a hypothesis cohere with other cognitive factors? How does probabilistic information affect explanatory judgments? To answer these questions, we conducted an experiment, where participants made judgments about a potentially explanatory hypothesis and its cognitive virtues. In the responses, we isolated three constructs: Explanatory Value, Rational Acceptability, and Entailment. While explanatory judgments strongly cohered with judgments of causal relevance and with a sense of understanding, Explanatory Value was sensitive to manipulations of statistical relevance relations between hypothesis and evidence, but not to explicit information about the prior probability of the hypothesis. These results indicate that probabilistic information about statistical relevance is a strong determinant of Explanatory Value, and that abductive and probabilistic reasoning are two distinct modes of inference.