In this installment I will use the ideas discussed in previous posts to make projections. A projection is different from a forecast (and, certainly, from a prophecy) in that it is not an attempt to predict what will happen. Rather, it is a description of what would happen given certain hypotheses and assumptions. Typically, we want to make several projections, using different assumptions. This gives us some idea of how different assumptions result in different possible future trajectories.

A good rule of thumb is that we should start with the simplest possible model, but one that captures the most important feature of the dynamical process. Selecting which features to focus on, and which to ignore (at least, in the first, simplest version of the model), is as much art as science. I will follow my intuition, but others, of course, can disagree with me. In which case, they should propose an explicit alternative and show how that affects the projection.

These projections assume that this conflict in Ukraine will continue (and end) as a war of attrition. If the nature of war changes, all bets are, of course, off. I revisit this point briefly at the end, and plan to address it in more detail in a future post.

In a war of attrition there are two key processes that determine the eventual outcome. First, each army shrinks as a result of soldiers getting killed, seriously wounded, or captured by the enemy. Second, these losses are replenished by drawing on a finite pool of recruits. Whichever side runs out of recruits first is the one that loses the war.

I am going to short-circuit these two processes and sum the dynamics up with just one equation for each side. The equation tracks how the pool of recruits is diminished by non-replaceable losses. This approach doesn’t track the size of each army because I assume that each side attempts to maintain sufficient troops to hold the front by replacing the losses from the pool of recruits—as long as there are recruits in the pool. This approach ignores any territorial gains or losses, because what matters is running out of recruits, not land.

Next, I need an estimate of loss rates. As we saw in Part II, these are primarily caused by projectiles such as shells, mines, kamikaze drones, etc. Let’s assume that the Russians will fire shells at a constant rate of 20,000 per day = 600k/month. For each 50 shells there is 1 KIA, but the overall loss rate (including seriously wounded and captured) is at least double that. This works out to 24k casualties/month. The Ukrainians continue firing 5,000 shells per day with the same rate of casualties per shell.

Finally, we need an estimate of the sizes of recruit pools. This Twitter thread proposes a useful way of thinking about this quantity. Although its author, Armchair Warlord, tends to argue for the Russian side, the argument he makes is transparent and is not affected by any such bias. He points out that during World War II Germany started collapsing once the level of casualties reached 3 million out of population of 80 million. Arguing by analogy, Ukraine should find itself in the same situation when it loses 750,000 killed, wounded, or captured. Some commenters to his tweet argued that the base population number he uses for Ukraine (20 mln) is too low. On the other hand, he points out that Ukraine has a deep demographic hole where it comes to the prime military age, men in their twenties and thirties. For a projection, thus, 750k is as good estimate as any (and in a moment, we will vary it to see how much it affects the end point). 

This (extremely) simplified model yields the following projection of the course of the conflict:

Here solid lines track the dynamics of cumulative casualties for the two sides. The brown broken line indicates the size of the recruitment pool for Ukraine.

According to this projection, Ukraine’s losses exceed its available recruit pool (solid brown line crossing the broken line) on Month 32 after the start of the conflict. In other words, as of July 2023, we are about half way there.

But of course, this is false precision. When we vary the rate of attrition and the overall sizes of recruit pools, the end point comes either much faster, or much slower:

Here we are looking only at Ukraine’s trajectories, because the Russian trajectory never gets into the danger territory. It would take a lot of months (and shells) to exhaust the roughly 300,000 soldiers yielded by the partial mobilization in the Fall of 2022, which were later supplemented by more than 100,000 of additional volunteers since then (and, according to the Russian Ministry of Defense, this is an ongoing process).

What these projections suggest is that under this inertial scenario of war of attrition Ukraine loses. The only question is how long it would take.

There are two major assumptions that can overturn this result.

First, this calculation assumes that Russia can sustain the heavy expenditure of munitions for the time necessary to bring this war to a conclusion. A detailed analysis by this anonymous Substack argues that this is, indeed, the case: On Shells And Armor: The War Of Sustainment. In fact, it appears that the assumption that Ukraine can continue firing 5,000 shells per day may not be tenable. Again, this argument comes from a self-professed pro-Russian blog, but the argument Simplicius makes and his numbers appear to make sense.

Second, this projection assumes that the macro-structure of conflict will not undergo an abrupt shift. Russia is, undoubtedly, under a huge political and economic strain, and several pundits have suggested that it can crumble from within in one way or another. Other possible scenarios include NATO or some NATO members putting actual “boots on the ground.” Any such event would make these projections completely irrelevant.

Summing up, there are many ways in which these projections can be invalidated. But the overall conclusion is that the inertial scenario—a static war of attrition—heavily favors a win by Russia.

Note on the margins: I will be on vacation and, for this reason, turn off all comments.