Assessing the power and influence of states on the world arena has always been one of the most pressing tasks in political science and international relations. Nevertheless, the problem of creating a universally recognized tool for measuring national power remains unsolved. The article presents one of the strategies of such an evaluation - discriminant analysis, which, in our opinion, has several advantages compared with its analogs. One of the obvious advantages of this method is the use of computational algorithms for finding the optimal «weights» of indicators in the index of national power based on training samples. The latter are sets of countries with maximum and minimum influence, obtained on the basis of expert assessments. In other words, using training samples gives researchers the opportunity to formalize mathematically the exact combination of indicators applied to estimate a state’s international power. Basing upon methodology developed in the project «Political Atlas of the Modern World», we apply it to the analysis of a wider data set, which includes 1995, 2005 and 2015. We track the dynamics of changes in the determinants of power and influence potential from 1995 to 2015, and come to an unexpected conclusion about the absence of any «tectonic» shifts in its components. Two dimensions of power potential, related, on the one hand, to economic and institutional factors, and, on the other hand, to military force, have remained the key ones over the past twenty years. Another empirical result of the study is a set of concrete estimations of international power potential for more than 190 countries during the period mentioned above.