This article aims to maximize the reliability of presidential power scores for a larger number of countries and time periods than currently exists for any single measure, and in a way that is replicable and easy to update. It begins by identifying all of the studies that have estimated the effect of a presidential power variable, clarifying what scholars have attempted to capture when they have operationalized the concept of presidential power. It then identifies all the measures of presidential power that have been proposed over the years, noting the problems associated with each. To generate the new set of presidential power scores, the study draws upon the comparative and local knowledge embedded in existing measures of presidential power. Employing principal component analysis, together with the expectation maximization algorithm and maximum likelihood estimation, a set of presidential power scores is generated for a larger set of countries and country time periods than currently exists, reporting 95 per cent confidence intervals and standard errors for the scores. Finally, the implications of the new set of scores for future studies of presidential power is discussed.