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.A large body of work has estimated the outcome of variation in presidential power. To identify studies of presidential power systematically, we searched a selection of leading comparative politics journals 1 and identified a total of forty-nine studies that included an estimation of presidential power.2 The distribution of this work confirms that scholars are increasingly choosing to estimate the effect of presidential power generally. Four were published from 1995-99 inclusive and ten from 2000-04 inclusive, whereas twenty-five articles were published from 2005-09 inclusive with ten in 2010 and 2011 alone. In all but four of these studies, presidential power was operationalized explicitly or implicitly as an explanatory variable. In these forty-five studies, the dependent variable ranged widely across topics such as economic reform, democratic consolidation, the level of protectionism, the effective number of parties, cabinet composition, voter turnout and many others. In thirty of these forty-five studies, variation in presidential power was confirmed to have a significant effect on the outcome under investigation.What are scholars trying to capture when they estimate the effect of presidential power? In eleven of the forty-nine studies we identified, scholars focused only on a specific aspect of * Department of Politics and International Relations, University of Oxford, UK (email: david.doyle@politics. ox.ac.uk); School of Law and Government, Dublin City University, Ireland (email: robert.elgie@dcu.ie). We would like to acknowledge the three anonymous referees and the editors of the journal. We would also like to thank the participants at the ECPR Joint Sesssions of Workshops, Johannes Gutenberg Universität Mainz, 2013. Data replication sets and online appendices are available at http://dx.doi.org