What does it mean for analogy to be rational? John Stuart Mill described a probabilistic underpinning for analogical inference based on the the odds of observing systemic pairwise correspondence across otherwise independent systems by mere chance. Although proponents and critics have debated its validity, Mill’s approach has yet to be implemented computationally or studied psychologically. In this paper we examine Mill’s approach and show how it can be instantiated using Bayes theorem. Then we describe two experiments that present subjects with partially-revealed, aligned binary strings with varying degrees of intra- and inter-string regularity. Experimental results are compared to a formal rational analysis of the stimuli revealing conditions whereby participants exhibit confidence patterns consistent and inconsistent with Mill’s rational basis of analogy.