Welcome to the Measurement of National Power Project

The purpose of this website is to introduce the statistical foundation for creating and assessing indices of national power and to introduce a new simple quantitative index of national power (NPI) that satisfies tests of external validation. Because our approach deviates radically from the existing practices and the new index introduces information that contradicts some conventional wisdom on the relative power of nations, we introduce, defend, and illustrate several conceptual and methodological innovations that require careful examination.

It will be useful to keep in mind some fundamental assumptions we make and several new features that we introduce before embarking on the exploration of this website.

  1. There is a need for a simple quantitative index of national power
    • The existing quantitative indices fail to provide any test of validity of their scale values — we do not know what the differences in quantitative values mean
    • There is clear evidence that these indices exaggerate the relative power of powerful nations
    • Therefore, both scholars and policy makers are likely to be exposed to potentially misleading information about the relative power of nations
    • The continuing quest for complex and sophisticated measures of national power does not obviate the need to have a simple index of national power that counters the widespread misperception of relative power of nations
  2. There is a need for a new conceptual and methodological foundation for constructing indexes of national power
    • Our starting assumption is that the relative power of a nation has no meaning unless it is systematically related to the winning and losing probabilities when two nations compete, in wars, business, or sports
    • A new statistical model for relating power to winning probabilities is developed and introduced
    • The connection between the power differences and winning (and losing) probabilities is not well-known, but, once learned, can provide a powerful means for evaluating the validity of existing measures of national power
  3. The proposed new index is based on the fundamental assumption that the basic or core power of a nation can be obtained by considering only the most basic and enduring components of a nation’s power – its human resources
    • It is likely to be a monotonic increasing function of the population size (quantity)
    • It is likely to be a monotonic increasing function of the quality of manpower (the level of human development)
    • It is likely to be an interactive function of these two components
  4. Despite its simplicity, the new index is credible and informative
    • The scale of the new index is credible because it passes the test of external validation, and it has clear and credible connection to winning probabilities
    • It can be used as points of reference to reveal important information that is hard to obtain without such a frame of reference
    • Its simplicity has its own virtues, and it can be shown that adding more components or making the index more comprehensive may not increase its usefulness or informativeness
    • It can be used as an external criterion for indices of national power and any sub-component (indicator) of such indices
  5. The test of external validation is an essential step in establishing the validity of scales of any index, but finding an external criterion variable is extremely difficult
    • The Winner-Take-All (WTA) distortion effects are ubiquitous in almost all human affairs and have serious implications for constructing and validating indices of national power
    • It is natural to seek for indicators of power that are based on competitive outcomes, but the outcome-based indicators of power are likely to introduce distortions into the scale values because of the WTA-distortion effect
    • The factor-analytic measurement model can provide a critical means for finding an external criterion variable and testing external validity
    • Fortunately, several soccer-power indexes turn out to be credible external criterion variables
    • In order to provide easier access to the technical information and the nature and extent of the WTA distortions, we rely on extensive computer simulations
Power Ranking with Maximum Possible Limit of Power
Power Ranking with Maximum Possible Growth

Here is a brief introduction to the overall organization of this website. There are several different sections, and some sections have additional subsections. For those who are new to this website or who are unfamiliar with index construction of national power or capacity, we recommend to browse the pages in the following order.

  • This page with the outline of the project website.
  • Index of National Power
    • Power Hierarchy : Three different graphic displays of the power hierarchy of 187 nations, as measured by the new and simple National Power Index (NPI)
    • Winning Probability: Linking winning and losing probabilities in bilateral competitions to scales of the power index — building a conceptual and methodological foundation for the new index
    • External Validation: the scale properties of the new index is validated against credible external criterion variables — a first and unique attempt to do so
    • Decomposition: The construction of the index and a graphic display of the connection between the NPI and its two components: one sub-index based on the quantity of human resources and the other based on the quality of human resources
  • Index Comparisons: an interactive graph shows the real meaning of index values by displaying winning probabilities implied by the four different indices: NPI, GNI, CINC, and log-GNI. The results of bilateral competition for 187 nations can be examined, using one of the four indices.
  • WTA (Winner-Take-All) Distortions: This page explores the effects of WTA phenomenon and its many implications on measurement, perception of power, and the creation of social inequality
  • Index Construction: This page explores both well-known and rarely-discussed practical problems in constructing indices of national power, and more generally, other types of indices
  • Tables: This page contains many tables of national rankings
    • Indices of National Power
      • NPI
      • GNI & logGNI
      • CINC
    • Indices of Soccer Power:
      • FIFA
      • ELO
      • SPI
    • Olympics-Fortune500-NobelPrizes
  • It is highly recommended that the users download and install the freely available CDF Player from Wolfram Research in order to view the interactive graphs in these pages, from https://www.wolfram.com/cdf-player/.