The first part of this series gave an introduction to the Osipov-Lanchester (OL) model and illustrated the ideas with the example of the American Civil War. In this second part, my aim to extract a prediction from the OL model for the War in Ukraine. A few general points/reminders:

• I am not taking sides and I am not discussing the rights and wrongs.
• War is evil, but needs to be studied.
• I am interested in a scientific prediction, not prophecy.
• The model is very simple and its prediction is not a statement of what will be, but a way to find out how reality deviates from its prediction.
• I am not basing this prediction on a direct analogy with the American Civil War (ACW); I use it only as an illustrative example.

In fact, and as some people pointed out in the comments to the previous post, the ACW may not be a good example of the Square Law (while being a good illustration of a more general OL approach). More generally, a few studies, I am aware of, that attempted to test the OL model came to the conclusion that the actual exponent relating numerical advantage to war advantage is almost never 2, but is typically between 1 and 2. But this is not going to affect what follows.

The core of the OL approach is to model the dynamics of casualty rates inflicted by each army shooting projectiles at the enemy. It’s a model of attrition warfare (although the model is usually applied to a single battle, I use it to model the course of an entire war). Since over 80 percent of casualties in the Ukrainian conflict are inflicted by artillery, to a first degree of approximation we need to know how many shells are fired by each side. There is a general agreement by all sides that the Russians expend many more munitions than the Ukrainians. Specific numbers might be something like 5,000 shells per day fired by the Ukrainians as compared to 20,000 shells fired by the Russians. These numbers primarily refer to heavy guns, shooting 152 mm ammunition (USSR/Russian standard) or 155 mm (NATO standard). The numbers represent averages. For example, the Russian ammunition expenditure has varied between 10,000 and 50,000 shells per day, or even more. The overall conclusion is that Russians have roughly a 4:1 advantage in artillery, although it could be easily 3:1, 5:1, and even 2:1 or 10:1 (I’ve seen all such ratios mentioned by different sources).

The main assumption I am going to make is that the rate of casualties inflicted on the enemy is proportional to the number of projectiles expended. In the numerical example worked out in Ultrasociety (p. 157) I assumed that the ratio of arrows shot to casualties inflicted (killed or wounded) is 10:1. In the Ukrainian war it is more like 20-30, or even 40 shells per casualty (it also depends on whether casualties are defined as KIA or also include wounded), but the general principle of proportionality is the same. Thus, according to this model, the prediction is that Ukrainian casualties must be roughly 4 times that of Russians (but the range could be 3–5, or even 2–10). Once we have better data on the ammunition expended by each side during the course of the war (after the war ends), we will be able to tighten up this prediction.

This prediction comes from a very simple model, and reality can deviate from it due to a number of factors (remember, this is not a prophecy). Let’s consider some such complicating factors. Note, depending on how important these factors are, the prediction could be substantially different. In other words, we have alternative predictions resulting from different assumptions—finding out which of these alternatives matches the data best is what the scientific method is about.

• The prediction assumes that neither side has a serious technological edge. There are diverse opinions on whose guns/tanks/airplanes are better. A post-war assessment will show how accurate this simplifying assumption is.
• Skill. Because the war actually started in 2014, by February 2022 the Ukrainian artillerists had an advantage in skill as they have been fighting against the Donetsk and Lugansk militia for eight years. But as the conflict lengthened, they lost this advantage as Russian gunners increasingly gained experience.
• Morale. There are conflicting reports on this aspect. Furthermore, in an attrition warfare morale plays less important role than in mobile warfare. In the absence of a compelling argument one way or the other, we stick with the simplifying assumption of no advantage for either side.
• Defense/offense. Both sides have conducted defensive and offensive operations. Furthermore, in attrition warfare, there is no clear difference between offense and defense, as the same piece of territory may change back and forth due to attacks and counter-attacks.
• Although artillery dominates, it is not the only force that inflicts casualties. Air force, guided missiles, land mines, and drones are also important. It’s an open question how adding them to the equation may change the prediction.
• Variations in time and space. Unlike a mathematical model, with its smooth curves, actual casualty rates will fluctuate in time with the intensity of conflict. There are “battles” when fighting is intense, and lulls between them when casualty rates are low. Space can also be important. One side achieving a local numerical advantage could shift the relative casualty ratio in its favor.
• Logistics. The OL model doesn’t include space, but in order to be shot, munitions need to be delivered to the front lines.
• Production. This is the most important factor affecting the long-term course of the conflict, and it requires more detailed discussion (which I defer to a future installment).
• War goals of each side and their determination to achieve them. Again, this is very important, and I will devote a separate post to it.

To summarize, what we have here is a clear and specific prediction coming from a simple model. And there are many ways in which it can go off track. The goal of this exercise is to determine how close the prediction is to the actual outcome, once the war ends; and, even more importantly, which of the factors listed above will have a significant effect on this outcome.

In the next installment I plan to provide an interim assessment of the state of this war; at least, as much as we know about it.