Probably the most consequential currently unfolding geopolitical event is the war in Ukraine. When I wrote about Ukraine in End Times the latest phase of this conflict had just started (I turned the completed text to the publisher in August 2022). During the year since then, many people have asked me what I think of this war.

As my readers know, I don’t take partisan or ideological sides—whether it is the Democrats versus Republicans, or Russians versus Ukrainians (and NATO). One thing I will not be talking about is the rights and wrongs of this war. Instead, the question that I want to address is, what is the dynamic of this conflict? And how is it likely to end? Approaching war in the spirit of scientific inquiry, evenhanded and dispassionate, is hard because war is such an ugly thing. I think the great majority of people will agree with me that abolishing war should be one of the most important goals for the humanity as a whole. But to do it effectively, we need to study it — see more on this in Why Social Scientists Need to Study War.

Another thing I won’t do is pronounce a prophecy. I am making a scientific prediction. The difference is explained here: Scientific Prediction ≠ Prophecy; see also “The Mad Prophet of Connecticut”. In any case, as this amusing historical anecdote shows, people believe prophets at their own risk.

In 560 BC, Croesus, King of Lydia, asked the Oracle at Delphi about the outcome of the war he wanted to prosecute against Persia. The Oracle replied that if he made war on the Persians, he would destroy a mighty empire. Unfortunately for Croesus, the empire that was destroyed was his.

Predicting the outcome of a war is notoriously difficult. Croesus is not an isolated case; history abounds with examples of states that started wars in expectations of victory, instead ending in defeat.

Still, granted that absolute certainty in predicting war outcomes is not attainable, can we assess the probabilities of different outcomes? As I wrote in End Times, cliodynamic models can help answering this questions.

One such approach is discussed in Chapter A1 of End Times in the context of the American Civil War. There, I describe a mathematical model, independently proposed during World War I by the Russian military officer Mikhail Osipov in 1915 and the English engineer Fredrick Lanchester in 1916. Although the model is very simple, it yields an unexpected insight into the probabilities of either side winning. Yielding novel insights, of course, is one of the reasons we value mathematics.

Generally speaking, the probability of winning a war depends mainly on three factors: (1) how many soldiers are recruited in each army; (2) how much war material (weapons, ammunition, etc) can each side supply to their army; and (3) morale/determination to win. The argument that I made in my book, was that once the North was determined to fight as much (and as long) as necessary to win, the South was doomed.

The reason is simple: a great disparity in the military capacities of the adversaries. First, the population of the Union outnumbered the Confederates (once we subtract the slaves) by a factor of 4 to 1. Second, the dis-balance in the capacity to produce arms and munitions was even more lop-sided: for every rifle produced in the South, Northern factories churned out 32. However, the second number is of lesser importance to the calculation, because the bulk of weapons with which the Confederates fought was produced not in the South, but in Britain (I’ll return to this important point later).

The American Civil War is one of the most studied conflicts, and the consensus by historians is that, really, the South had no chance against the North. What the Osipov-Lanchester model adds to this consensus is that the 4 to 1 advantage in population (and the corresponding advantage in army size) translates into 16 to 1 warfare advantage.

This mathematical result is known as the Lanchester Square Law (thus, 16 is the square of 4). It doesn’t apply to all conflicts. For example, if armies fight with hand-held weapons, then 4:1 numerical advantage translates merely into 4:1 warfare advantage (this is the Lanchester Linear Law). But in conflicts fought primarily by projectiles—whether it is bows and arrows, rifles, or artillery—the Square Law rules. (I explain this with a numerical example in Ultrasociety, page 157).

And now I return to the question with which I started: what is the probability of a Ukrainian win against Russia? Interestingly, the balance of power in the War in Ukraine is similar to that in the American Civil War. In 2022 Russia had about 4:1 advantage in population and 10:1 advantage in GDP. On the basis of these numbers, Ukraine has about as much chance of winning the conflict as the Confederacy did.

But things are, of course, more complicated. Most importantly, Ukraine is not fighting alone. By this point, there is a general agreement that the War in Ukraine is a conflict between NATO and Russia. This is the rhetoric coming from both Russia and US/EU. A comparison of population and productive capacities of NATO versus Russia (for example, here) results in an equally lopsided dis-balance, but this time against Russia.

Here again the American Civil War offers a useful historical comparison. As I mentioned above, the Confederacy could not produce enough arms and munitions to sustain its military operations against the Union. These military supplies were produced in Europe (mainly, in Britain) and then smuggled into the South by blockade runners. At least 600,000 rifles were supplied in this way (to give an idea of the scale of this effort, the Confederacy mobilized 880,000 soldiers). Blockade runners also brought in artillery pieces, powder, percussion cups, and other war material. Even the fast ships, used by blockade runners, were built by the British. Historians estimate that the military aid provided by European countries to the Confederacy extended the war by two years and cost additional 400,000 casualties. But, despite this enormous aid, the South still lost. After all, rifles had to be wielded by soldiers, and the Confederacy had to rely on its own population resources to replace casualties. They simply ran out of recruits. Here’s the breakdown of the Confederate casualties, according to Wikipedia:

• 94,000 killed in action
• 164,000 disease deaths
• 194,026 wounded in action
• 462,634 captured (including 31,000 who died as POWs)

Total: 914,660. Curiously, the casualty count is larger than the official number of soldiers mobilized (880,000), but keep in mind that all these numbers are estimates with substantial levels of error.

This historical example suggests that a crude comparison based on GDPs is not the way to go. In 1860, the GDP of Great Britain was substantially larger than that of both the Union and the Confederacy, combined (see here, for example). Yet it only helped to extend the conflict and made it more costly in human life.

Unlike economists, professional military analysts focus not on the overall economy, but on the sectors that are devoted to producing arms and munitions. Of particular importance in this conflict are artillery pieces and shells they fire, because most—more than 80 percent—of casualties in the War in Ukraine are due to artillery. If we want to understand the course and potential outcomes of this conflict, then, we need to track the dynamics of arms production and loss, as well as army recruitment and casualties. This is where an Osipov-Lanchester approach is very useful. Details in the next post.