Chapter 5 of Brian Hayes's Group Theory in the Bedroom and Other Mathematical Diversions is an interesting, if cursory, chapter on "The Statistics of deadly quarrels". The bulk of the piece conveys the idea that there is really nothing we have found that seems to correlate with the magnitude of deadly quarrels. That is to say that when we run the "numbers" of wars through various statistical schemes mathematicians have found nothing that really correlates with the magnitude of quarrels. (Magnitude being defined as a function of the number of deaths.) So there is no correlation, for example between a country's population, and the magnitude of the wars they fight.
But there are numerous problems with such studies. Beside the methodological problems setting an ontology for a war - which is an interesting philosophical problem in itself and given the statistical studies there now seems like there is a good excuse for philosophers to think about this - there has been no significant correlation between wars and a country's religion, economics, politics, or anything like that. Mathematicians, or at least statisticians like the pioneer Lewis Fry Richardson, have not been able to correlate war with anything too significant.
So the mathematics of war is a field that still needs a lot of work if it is to be informative.
One thing Hayes wrote toward the end of the article caught my eye: <blockquote>Even if Richardson's limited data were all we had to go on, one clear policy imperative emerges: at all costs avoid the clash of the titans. However painful a series of brushfire wars may seem to the participants, it is the great global conflagrations that threaten us most. As noted above, the two magnitude-7 wars [wars that have a death toll in the neighborhood of 10,000,000] of the twentieth century were responsible for three-fifths of all deaths that Richardson recorded. . . </blockquote> But the lesson hardly fits the data that Hayes nicely synopsizes.
The fact that titans clashed and had a high death-toll hardly suggests that they are the cause of the death toll (as is certainly suggested by the quoted passage). In the case of WWII for example (one of the Mag-7 wars), I am not certain who the titans were (Germany? Russia? The United States? All of the above?) But the fact is that the US would not have been involved were it not for the the already high death toll and the threat of an even higher one, and had they not been involved, there is certainly a case to be made that the death toll, especially in the long run, would have just kept going up.
Sometimes it is conceivable that if there is a war between one "titan" and some small groups or countries, it completely justifies, by some reasonable moral standard anyway, a second titan stepping in to stop the first. The aggregate death toll, especially given that the first titan may have no qualms about sacrificing their own soldiers or civilians for the sake of killing the more vulnerable populations. I am not convinced that utilitarian considerations really ought to be the main focus. The body-count of a war is hardly an indication of its moral status. And as the author points out in the final sentence "would a war be only half as bad if half as many people died?"
If there is an agressor in a war, justice seems to dictate that it is worth sacrificing some resources, including human life, to stop him. If that brings the death-toll up, then so be it. It is not the titans clashing that needs to be avoided, but unjustified agression that ought to be the focus.
Granted, Hayes may have been merely pointing out that when you have great powers participating in a war it is a more deadly war. But one must be particularly careful about suggesting causality when discussing statistics.