Paweł Krawczyk

In 2023 a complexity scientist Peter Turchin had published an Attrition Warfare Model for the war in Ukraine^1 which attempted to predict its outcome based on mathematical modeling.

Turchin is a scientist working in the area of complex systems. The latter had in the past gained some publicity as chaos theory – modeling systems so complex internally that their states are usually only described in statistical terms and their behaviour is described as “chaotical”, even when it really isn’t.

In 2020 Turchin made some fame when people dug up his 2010 prediction that in a decade US may be hit by a wave of large civil unrests. He came to this conclusion based on modeling a combination of numerous economic and social factors which seemed to converge to a state usually resulting in unrest.^2 Turchin later extended his theory which can be summarised as “workers stagnate while elites multiply” to the election of Trump, the MAGA movement and general wave of antidemocratic movements.^3

In 2023 Turchin also attempted to model the war started by Russia and his team created a mathematical model that includes economic (military industry output) and demographic parameters (number of soldiers).^1 The model has evolved over the last two years but the latest version is probably best described, including its limitations, by the 2023 article “Empirically Testing Predictions of an Attrition Warfare Model for the War in Ukraine”^4. I was surprised to see people like MacGregor and Ritter quoted there, but Turchin seems to use them as the proponents of the most possibly cynical scenario for the purpose of modeling. If you read the whole model description, which I encourage everyone to do, Turchin’s assumptions are quite impartial and as realistic as a simplified model can be.

The baseline scenario is quite pessimistic: to make the long story short, Russia has economy and population so large that it will simply not deplete before Ukraine’s does. That’s as cynical as it can be, and as a matter of fact this is the core argument Russians are always raising: they’re just too big to lose and therefore they always win. The original 2023 model predicted ~150k Russian losses and ~400k Ukrainian losses after 36 months of war, which was February 2025:

Please note the input parameters – casualty per shell, because it's key to understanding how such result was even possible. In short, the model assumes that both sides suffer equal casualty ratio, but because Russia fires much more shells and has more people, it wins.

Turchin also looks at alternative scenario where Ukraine’s economy (represented by ammunition production rate) is really equivalent to the whole EU and US, in which case the roles reverse.

The model in theory should not be interpreted as a real-world forecast, as clearly stated in the article’s disclaimer. But you really cannot avoid comparing it against the real world, because all the time it refers to actual numbers of real people in real countries (this was very much the same case with Club of Rome Limits to Growth model published in 1972).

When I first looked at the model in 2024, the primary issue I had was specifically the unrealistic prediction of losses. After two years of war (February 2024) the model predicted Ukraine’s losses to reach almost 300’000 while Russian were 3x less. This, if anything, was the opposite of real estimates. Three years into the war, as of 2025, the divergence is even larger.

The secret really lies in two factors: the number of shells fired (function of economy) and the “casualties per shot”, which is kind of arbitrary and set to 0.03 (30 shells fired kill one soldier). The number is, again, kind of estimated based on real Russian loses, but then, on page 8, Turchin wrote the key phrase “I set d2 = d1”. This statement essentially assumes that Russian losses per shell are the same as Ukrainian. Why? Because.

If you try to play with these parameters in the live model^1 you can actually get losses modelled closer to the real estimates^6. When setting the casualties per Ukrainian shell to 0.06 and Russian to 0.006 we will get ~120k Ukrainian casualties and ~250k Russian which are the latest conservative estimates of KIA.

Of course, this is just one parameter. The original 2023 model assumptions have many factual issues – for example, Russia's army size is not 200k, it's now closer to 600k while Ukraine's is close to 1m. These could be also modified in the respective recruitment tab if we had reliable estimates, which I don't.

All of the above model’s deficiencies are prominently mentioned by Turchin in the article. The primary Turchin’s conclusion from the model’s outputs seems to be that the critical condition for Ukraine’s victory is economical and industrial support of its allies. Also, in terms of model’s parameters, as Turchin himself notes, human losses suffer from very high uncertainty as both sides actively obscure them. At the same time, OSINT provides equipment losses which were in the past confirmed to cover up to 80% the actual losses, which could make the case for further improvement of the model’s output.

Personally, I believe the losses ratio is a critical parameter, because it's precisely what counterweights the popular Russian narrative that they're “doomed to win because they're larger”. Russia may indeed have population 4x larger than Ukraine but with losses at ratio 1:13 (confirmed armour losses) or 1:7 (declared by Ukraine) this advantage is going to diminish fast. Which clearly hints that any strategy that incurs such losses at Russia is preferable, which most likely implies a defensive strategy.

Another important thing to note here is the chart showing size of Ukraine's army – according to the model, with its original recruitment ratio and the above losses, it will continue to grow, increasing rather than decreasing Ukraine's military potential. You may not agree with the exact numbers, but it's empirically true and explains why Russia has invested enormous resources into information war targeting Ukraine's army mobilisation. If you have never heard of it, it's because you are not the target of it, but believe me – the Russian campaign to discredit mobilisation is very much visible in Ukraine. The same factor on Russian side explains its desperate measures to attract recruits without a countrywide official mobilisation.^5

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Paweł Krawczyk https://krvtz.net/
Fediverse @kravietz@agora.echelon.pl