A credible index of national power or capacity can be used in many different ways. One of the most important uses is to use it as an external criterion for any index of national capacity. Another important use is to use it as points of reference. For instance, we may examine whether a nation is doing well relative to its basic power or capacity. A third use is to use it as a means of controlling the hidden impact of national capacity while considering relationships between other variables. We will start with the use of NPI as points of reference.


As Points of Reference

We start with with a bubble chart in which the x-axis represents NPI2012 and the y-axis represents the average Olympic Medal points, OLY6Ave. A bubble chart allows to show four dimensional information on a two-dimensional space. In addition to the two (x and y) axis’s, the size of the bubbles and the colors of bubbles can represent different information. The default graph shown below shows geographical location of a nation by color coding, and the information on the relative population size by RPI (one may use also actual raw population size).


  • NPI2012: Index of National Capacity for 2012
  • logGNI12: Log of Gross National Income for 2012
  • GNI2012: Raw Gross National Income for 2012
  • RPI2012: RPI is log-transformed and normed index of population
  • Pop2012: Raw Population Size for 2012
  • OLY6Ave: Average Medal Points for six Summer Olympics (1992-2012)
  • FIFA6: Composite FIFA index, using old ranking scheme used until 2006
  • CommExp: Nations with Communist political experience

First, you may note that the relationship between the basic national capacity and the Olympics performance outcome is non-linear: there is a severe WTA (Winner-Take-All) distortion, as expected.

Second, you may notice that some countries deviate from the expected non-linear pattern– either out performing or under performing. Clear examples of over-achievers are Russia and China, and clear examples of under-achievers are Japan, and Mexico. (By moving the mouse pointer over a dot, you can get the necessary information.)

If you now choose the logged values of Olympic performance (logOLY6Ave) as your y-axis, you will see the pattern of under- and over-performance more clearly through the full range of NPI power spectrum. You can see the pattern and tooltips if you use the interactive graph. Below is a static graph for easy access to those without a functioning CDF Player.

Countries floating at the top of the linear trend are the over-achieving countries relative to their basic national capacity, and at the bottom are under-achieving countries. If you use, the interactive graph, you will be able to see that many countries in Africa, and almost all former or current communist countries over-perform, and many Asian and some Latin American countries under-perform.

Now click on the “CommExperience” button (while keeping logOLY6 as y-axis), you will see more clearly that almost all countries with Communist past (except Vietnam, Albania and Macedonia-FYR) are over-achievers.

To see the identifying information, you should go back to the interactive graph. This static graph shows only the over-all pattern without identifying information.

The most important point is that without the availability of a credible index of national power, it will be very difficult to get the kind of information we obtained: for example, that Japan is a significant under-achiever in the Olympics despite its substantial average medal points.

Now switch back to the interactive graph (at the top), and reset the y-axis with Fortune500, and the Color Code category with Continents. If you do, you will see another severely non-linear relationship between NPI and Fortune500 (2012). Here is a static graph.

The United States is at the top with 140 companies, followed by a distant second, Japan, with 68 companies. The next three countries are closely bunched together – France, Germany and China, respectively, with 40, 39, and 37 companies. Great Britain is at the sixth place (with 26 companies), followed by Switzerland (with 15), then by Korea and Canada, which are tied for the 8th position (with 14 companies), and the Netherlands at the 10th place with 12 companies. From the graph, you can see that Switzerland is a clear over-achiever relative its basic national capacity.

As An External Criterion Variable for Other Indexes of National power

We have shown elsewhere how GNI and CINC produce unacceptable winning probabilities between some nations — a clear indication that something is amiss with their scale values. If GNI and CINC are credible indexes of national capacity, they should have linear relationship with credible external criterion variables, such as ELO and SPI indexes. But there is no need to rely on them any more because NPI can be used as much more powerful external criterion for these indexes of national power. If you go back to the beginning interactive graph, you can inspect whether these two indices have linear relationship with NPI. As you can see, the relationship between NPI and GNI is severely non-linear, while that between NPI and log-GNI is fairly linear.

This is why we argued elsewhere (Kim et al, 2013) that the log-GNI can be used as a quick and rough indicator of basic national capacity. If you examine the relationship more carefully, using the interactive graph, you will notice the following:

  • Some large countries in Asia, such as China, India, Pakistan, and Bangladesh, have relatively higher GNI relative to their NPI index — largely due to their relatively low human development index.
  • Many countries in Africa have relatively higher GNI relative to their NPI index, here again, owing to their low human development index.
  • So if one were to use GNI, instead of NPI, one will be discounting the impact of human development.

CINC index fails the external validity test in the same way the GNI fails. You may see the nonlinearity between NPI and CINC in “Validation” subpage.

Checking Reasonableness of Potential Components of any Power Index

In principle, the scale admissibility of any component must be examined before including them into a composite index. There is one test that is easy to apply but often neglected: the examination of the distribution pattern of a raw component index. If the distribution of a component variable is extremely skewed, as are the case with the population size, the GNI, the total energy consumption, the size of military personnel and many other raw variables, it is NOT likely that such raw values can be assumed to have a reasonable relationship with winning probabilities. If we cannot assume that there is at least a rough correspondence between the raw values and winning probabilities in national contest, then there is no justification for adding them as components of any power index. One must transform the raw values into a credible scale before including them into a composite index.

Sometimes, the suggested transformation may be obvious; sometimes, they may not be. The NPI can be used for testing the credibility of the transformed scales: if the relationship between the transformed scale values and NPI is roughly linear (at least not severely non-linear), such components can be included in the construction of composite index. Suppose that one is creating a composite index of national power, and one is willing to accept the idea that population, GNI, total energy consumption are reasonable candidates for inclusion. The first inspection will show that all three raw variables are extremely skewed:

If one were to try a log-transformation of these raw variables, and one would check the acceptability of these transformed variables against NPI, one will find the following relationships (some of them we have already examined in a different context):

The left side panel shows two graphs for raw population size: an irregular pattern of relationship at the top, and extremely skewed distribution at the bottom. In contrast, the right side panel for logged values of population shows a linear pattern at the top, and a distribution much closer to a normal one at the bottom. Of course, one could try some other transformations. But the simple log-transformation passes the test of reasonableness of its scale. There are so many raw variables, that are mentioned as possible candidates for a inclusion in the index construction of comprehensive national power, all of which have equally severe skews and require some transformation: total energy consumption, size of military personnel, size of military budget, territorial size, GDP, total number of scientific patents, and so on.

Credible External Criteria for Power Indexes

Now we return to the first external criterion variable we have identified — a composite index of Soccer Power, based on the old FIFA scheme, used until 2006. This particular graph is based on only 166 nations. Note that the pattern of relationship between NPI and FIFA06 is clearly linear. The size of each bubble is proportional to the population size of a nation.

Bubble chart showing the relationship between NPI and FIFA

Since FIFA switched to a new scheme of power rating, the new FIFA index is no longer a credible external criterion variable. The new index is not linearly related to the old FIFA index (the first graph below), but it is not linearly related to two other Soccer Power indexes (ELO, in the middle, and SPI on the right.) We have elsewhere shown that FIFA is not a credible index for evaluating a competitive strength of national teams, in terms of winning or losing probabilities. See section on Winning Probability. In a way, the availability of NPI allow us to reveal certain defects in the FIFA official index.

Luckily we have two soccer power indexes that are available as external criterion variables for NPI. See the linearity of relationships between NPI on one hand and, on the other, ELO2014 and SPI2014. In the right-most graph, the pattern of the relationship between NPI2012 and FIFA2014 is slightly curvilinear.