Saturday, June 23, 2012

Measuring Military Capabilities

There have been some interesting discussions about how to measure the position of the United States relative to China in the past few months (see here for an earlier take).

One point that has been made a few times, particularly by Beckley, is that we put too much weight on the sheer size of a country. If you took a middling power and added 50 million or so desperately poor, illiterate, starving people, both their GDP and CINC scores (available here, under the National Material Capabilities page of Available Data Sets) would increase dramatically. Yet none of us really believe that such a nation would grow appreciably stronger as a result. It's high time someone proposed a measure that is immune to this criticism.

I doubt it's perfect (in fact, I'm sure it's not), but I'd like to propose such a measure. It focuses exclusively on military components, and so I'm imaginatively calling it M.


This is a little messy. Math-phobes are going to want to skip this section. But for those who are interested in the details, here's how I constructed my measure.

\mbox{M}= ln(\mbox{milper}_{i,t})\displaystyle\left(\frac{ln(\mbox{qual}_{it})}{\delta_t}\right),
where \(\mbox{milper}_{i,t}\) is country \(i\)'s total military personnel in year \(t\), \(\mbox{qual}_{i,t}\) is \(i\)'s quality ratio (military expenditures per personnel) in year \(t\), and \(\delta_t\) is a time-varying discount factor that I constructed to adjust for changes in military technology.

\delta_t = 2.2^{\left((\mbox{year}-1700)/100\right)},
which ensures that \(\delta\) takes on a value fairly close to the average quality ratio among the major powers in any given year, without exhibiting the fluctuations found in the actual average.

My goal was to account for the size of a military as well as it's sophistication. I also wanted a measure that didn't correlate so highly with time (as GDP does) nor require that the total of capabilities in the international system always sum to 1 (as CINC does). There are various other technical concerns I had in mind that I'm glad to discuss in the comments if anyone is interested.

But enough technical details. Let's look at some colorful graphs.


Here's a graph of the CINC scores for the United States, United Kingdom, Russia/Soviet Union, and China from 1945 to 2007 (the last year with available data).

And here's M for the same states over the same time period.

I don't know about you, but it looks to me like M has more face validity. According to CINC, China has already surpassed the United States. For all the debate between "alarmists" or "declinists" on the one hand, and "polyannas" on the other, no one seems to believe that the US has already ceased to be the dominant military power in the international system. We don't get that from M. CINC also tells us that the UK was a second rate power even in 1946, whereas M has the UK looking stronger even than the US in 1940 (not shown), soon to be eclipsed by their Atlantic ally during WWII, yet still quite formidable in 1946, though quickly dropping off from there. Finally, M makes the Soviet Union look like a real challenger to the US during the Cold War, whereas CINC suggests that the Soviet Union was far weaker than the US during the early decades of the Cold War. YMMV, but all of those things make me think that M does a better job of capturing the military might of these four powers.

That said, there are some patterns in M that stand out. China sees a big slump before the end of the Cold War and a smaller but still considerable one in the past few years. Do these reflect real changes in the relative military capabilities, or are they signs that something is wrong with the measure? I don't know enough about China to say.

Let's take a look at the European powers from 1816 to 1910.

Compared to CINC, M paints a picture of a much more evenly balanced continental system, particularly after 1850 or 1860. The CINC score points to a century of fairly pronounced British dominance that only begins to break down at the very end of the century. I think there are those who would argue that CINC gets it right here, but I don't know. Do we really believe that Germany was basically a nobody until 1890 or so? That Austria was never even one of the top 3 European powers? That France was never remotely close to as strong as the UK? If anyone is more familiar than I am with 19th century Europe, please feel free to chime in, but my sense is that M actually looks pretty good here too.

At any rate, this is all very preliminary, and only speaks to face validity. I'm excited enough about this measure that I just might decide to try to validate this measure in other ways. If it outperforms CINC in terms of explaining patterns of international conflict, both in terms of onset and outcome, I may start relying on it in my academic work. Maybe. For now, it's mostly just food for thought.

What M Is Not

Power is multi-faceted. It's also typically defined in a manner that's damn near tautological ("the ability to get others to do what you want them to do when they would otherwise not be inclined to do so"). I was careful above not to refer to M as a measure of "power", because I'm not at all sure that it is one. No more so, at any rate, than CINC is. It's a measure of military capabilities (as opposed to a broad basket of material capabilities that includes demographic and industrial components). One might argue that a measure based solely on nuclear or naval power might be more meaningful. Or one might argue that any debate about whether the future belongs to China should reflect measures of soft power and the growing dominance of the English language and American culture; the centrality of the United States in the global economy and the role of the dollar as the international system's reserve currency; or various other concerns. I have no principled argument to offer against such claims. All I set out to do was construct a measure of military might that would draw upon the same publicly available data that scholars of international relations are used to using but might be considered superior to CINC in certain respects. And I think I have done that...though if you ask me again in a month or so, my opinion may have changed.


  1. I like it. Certainly an improvement on CINC, which is so bad that any article that uses it should be rejected immediately.

  2. Heh. I'm not sure I'd go that far, but yes, CINC has got some serious issues.

    Glad you like it. I was wondering what you're reaction would be.

  3. This is pretty cool, and long overdue. I'm also happy to see I'm not the only one that spends a portion of my Friday night working.

  4. Thanks, Mike.

    Ha ha. No, you are definitely not.

  5. Glad to see you're actively blogging again, Phil. I'd like to know more about how you derived this - it's kind of rare to see a product of logarithms, isn't it? It's also a bit concerning that to a first approximation (Taylor expanding the logs) the measure is really just military expenditures scaled by year (an implicit GDP deflator?).

    Similarly, I think this is something that could probably be estimated, perhaps with a Bradley-Terry model? As in, war outcomes are determined by strengths, which are unknown functions of the CINC components. I know another grad student at Rochester is doing some work on estimating changes in military technology from battle outcomes, based on estimating components of Lanchester models. I now forget whether his results would give you individual state strengths by year or not, but it might be something to look into (I can give more details over email etc).

    1. Hey Brenton.

      The measure actually correlates more highly with military personnel (about 0.6) than expenditures (0.3). There are probably better ways of achieving the same outcome, and you're right that it's a bit unusual to be working with the product of logarithms, so I'll continue to play around with this, but I don't think it's just milex scaled by year...

      You're certainly right that one could try to estimate military might by looking at war outcomes.

  6. Hi Phil,

    Quick thought. Is it the case that your measure is more volatile than CINC? Or is this just an artifact of the vertical scale on the graph?

    This presumes, of course, that these measures are comparable in the sense that if CINC shows the US has twice the capabilities of Russia in a given year we can compare this to ration provided by M.

    1. Hi Jeff.

      The measure is more volatile, yes. CINC includes a lot of things that change very slowly (like population) and so isn't very prone to short term fluctuations. Since M only includes information from military expenditures and military personnel, which do sometimes change quite a bit from year to the next (particularly during war), it bounces around a bit more.

  7. This is great. But CINC is supposed to measure residual national capability, no? Not saying I like it, but just that' there might be an a-to-o comparison.

    1. Thanks, Dan.

      You're absolutely right. It's not entirely a fair comparison. I probably should have been clearer that I wasn't trying to construct a "better" measure, but one that might be more suitable for answering a specific question.

      I suppose CINC is probably best thought of as measure of how capable a state would be of defending itself in a war of national survival. Having a large population and strong industrial base would become relevant in such a conflict. And insofar as such an interpretation would suggest that China is currently the last country anyone would ever want to try to conquer, that's probably right. Insofar as people are often interested in the ability to project power to far-flung areas of the globe, it's less clear that CINC is useful. I'd like to think my measure, while still imperfect, does a better job of telling us the relative capacity of the major powers for doing that. When we talk about who dominates the international system, I think we're more interested in who has the short-term capacity to exert influence over other actors, even when the survival of the state isn't in question. At least, that's my read of these debates.

  8. Hey Phil,

    Is there anyway ( formula, mathematics approach) or other empircal ways that I can use to evaluate the balance of power between two given countries and assert that there is or not a balance of power between these two countries?

    Thanks in advance for any assistance

    1. Eddy,

      There are a number of ways, all of which are imperfect. One common way of determining this is to calculate (m_1)/(m_1 + m_2), where m_1 is some measure of the military capabilities of the stronger of the two states and m_2 is a measure of the military capabilities of the weaker state. This will always give you a number between 0.5 and 1, with values closer to 0.5 indicating a balance of power and values closer to 1 indicating that the stronger state has a preponderance of power. Thus far, scholars have mostly used GDP or the Correlates of War Project's CINC scores for the measures of military capabilities. I hope to eventually convince people to use my measures instead.

    2. This comment has been removed by the author.

  9. This comment has been removed by the author.

  10. Hey Phil and thanks for the reply.
    Indeed I found your approach very much interesting and more convincing. However, I do not really understand the basic trends in how can I use your formula to evaluate whether there is or not a balance of power between two chosen countries? For instance if I have the following three examples:
    1. Democratic Republic of Congo and Rwanda
    2. USA and Mexico
    3. Turkey and Syria
    Can you, please, explain how you can go by, step by step, in order to get the result for these three above mentioned countries and confirm whether there is or no a balance of power between each couple? If you can assist me with these three couple of countries, that will definitely give me a better understanding of your approach. In my research I have twenty bordering countries that I need to measure the balance of power between each two bordering countries using a convincing and reliable approach as yours.

    Hope you provide me with some clean and clear explanations and illustrations for the three examples that I have stated here.

    Your assistance is highly appreciated.


    1. Eddy,

      You can find the M scores for each country in each year on my personal website ( The countries are listed by country codes rather than names. These are the country codes used by the Correlates of War ( You can download the spreadsheet by clicking on the Available Data Sets tab on the left and then on the State System Membership link (which is send from the top). The file you are looking for is states2011.csv, which is the third one down in the box with all the hyperlinks.

      Once you have the country codes (2 for the US, for example) you can find the M scores in my spreadsheet that you need. Once you have the M scores, you use the formula I mentioned above: (m_1)/(m_1 + m_2).

      I hope that helps. If not, let me know and I'll see if I can make it clearer.

  11. Hey Phil,

    Thanks for explaining again. I followed the way you directed me and found all the information you have explained. However, the problem still persist on how I can use this formula and the values that I am going to insert for m_1 and for m_2. What I can see clearer here is only the code representing the country. From your spreadsheet, I can even see the value representing the m for each country. I understand well as you explained ealier that:
    m_1 is some measure of the military capabilities of the stronger of the two states and m_2 is a measure of the military capabilities of the weaker state. Is it the m value that is standing for each country at your spreadsheet that I am supposed to use for each country? Respectively as m_1 and m_2? About when I am pretty unsure which one is or should be the stronger or the weaker country?

    Thanks in advance for durter clarifications.

    1. Eddy,

      Yes, the m scores in my spreadsheet are what I'm suggesting you use for m_1 and m_2. To determine which is stronger, just look at which m score is bigger. For the US and Mexico, I'm pretty sure the US's m score will be bigger than Mexico's in each year. Assuming I'm right, that means that your measure of whether there is a balance of power between the US and Mexico in any given year would be (US's M score for that year in Phil's spreadsheet)/(US's M score for that year in Phil's spreadsheet + Mexico's M score for that year in Phil's spreadsheet).

      I hope that helps.

    2. Hey Phil,

      Once more I tank you a lotfor the explanations. I have tried to use the formula you have shown ((m_1)/(m_1 + m_2), while on the other side trying even to control the outcome with othe facts like the annually military expenditures. I have noticed in general that in using the above mentionned formula, one can claim that there is a balance of power when the result gives a value that is > 0 but ≤ 0.5, and there is no balance of power when the answer is > 0.5 but ≤ 1. Seems to be quite ok to use it in that context as most of the cases that in my research can intuitively fullfill this requirements. What I just wanted to ask you this time is where does this formula come from?Is there any credible and trustworthy link, book, author, or organisation that have created this formula? I just would like to have a reference for this formula in order for me to show that it is not something that I have created myself.

      Thanks a lot in advance and hope to hear from you soon.

      Great regards

    3. Eddy,

      If you follow the instructions I provided, you will never get numbers below 0.5. The larger of the two m scores goes on top. The closer the number you get from the fraction is to 0.5, the more balanced power is. The closer the fraction is to 1, the less balanced it is, because that would indicate that the more powerful of the two states has almost all the power in their relationship.

      Annual military expenditures are already accounted for by the m scores. I wouldn't add them in separately.

      This formula, or one very much like it, has been used in many works. You'll often see people using CINC scores instead of my m scores, but the formula is the same. Or sometimes they'll use 1 minus that fraction, which would mean that numbers closer to 0 mean power is imbalanced while numbers closer to 0.5 indicate balance, instead of numbers closer to 1 meaning power is imbalanced. You can do that instead of what I said above if you prefer. Just remember, the larger m score goes on top. If you aren't consistent about that, the interpretation changes dramatically.

      Bennett and Stam's Behavior Origins of War includes a measure of the balance of power that is equal to 1 - ((cap_1)/(cap_1+cap_2)), if I recall correctly.