What Osipov and Lanchester Tell Us about the War in Ukraine

Peter Turchin


Join 36.6K other subscribers

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.

Most Voted
Newest Oldest
Inline Feedbacks
View all comments

Excellent – can’t wait to read the next post


How much of this also depends on the percentage of the population which is able to be mobilized to fight ?

For example as a hypothetical Russia has the potential manpower advantage but maybe cant mobilise a similar percentage of its population as Ukraine because its politically not possible , therefore the absolute manpower advantage is not as pronounced.

Meanwhile the Ukrainians can mobilise a higher percentage of their lower population which somewhat equalizes the potential manpower advantage

Roger Cooper

There are some problems with your comments. Lanchester’s law is almost complete nonsense on the battlefield. If you have numerical superiority, that does not mean you can bring all your forces to bear. More soldiers also means more targets for the enemy.

In what military historians call the Age of Gunpowder (roughly 1600-1900) battlefield losses were roughly even in battles, even if there was some disparity in numbers. This was true for most American Civil War battles, save a few were armies frontally assaulted entrenched positions.

The problem the South was facing by 1864, was that Northern armies had become large enough that they could advance even if beaten or the North could split its forces without fear of counterattack. In the decisive Overland campaign (Virginia 1864-1865), the South won most of the battles, but they were still force into an untenable position. Numbers won but indirectly.

I have never seen a Civil War historian claim that blockade runners were what kept the South going. The South was quite successful at producing gunpowder. There was no ACW battle that was lost by the South due to lack of powder.

The lack of food was a bigger issue. With so many able-bodied men under arms, food production fell. Slaves fled their plantations, increasing the agricultural labor shortage.

As for the War in the Ukraine, it is worth the noting that initial Russian invasion force only had 190,000 men, hardly enough to defeat Ukraine’s 200,000 strong army (without an advantage in quality). Once things settled down to trench warfare, military quality and morale matter more than the number of artillery shells.

We now so Russia starting to crack. A large-scale mutiny involving high-ranking officers is sign of failing morale. Already, Russia has resorted to recruiting from prisons. Where will the Russians get the next 200,000 men from?


I think it’s better to wait the next chapter. lanchester law Is write even in the post above that it’s true for hand to hand combat not for gunpowder Age. Also the point Is not on single Battle, but on the full war. The south win a lot of battles but at the end lose the war: suppose a nord vs sud war fought by hand to hand combat: the sud need to kill/pow 4 time more nord soldiers than sud casualty in the war (not the single Battle) to win. With rifle and artillery the sud need to kill 16 time more enemy, again in the full war. Translate this to 2023 war: the quality and morale matter by can kill ratio arrive at 16:1? for internal stability, military coup, i think that we all have to wait next chapter i disagree with you but this is a very good question. And i’m a bad student here, nothing more. Sorry if my english Is not good: i read well but write is another question,

Steven Johnson

The observation that no Civil War battle was lost due to the lack of powder assumes even Confederate slaveholders would decide to give battle without counting the powder stocks at hand. This is a big ask, even given the usual pro-Confederate stance. More to the point, how many battles, did the Confederate generals forego because of lack of artillery and other key supplies. Would a small fleet of river going iron clads prevented Grant from crossing the Mississippi to invest Vicksburg? Would the artillery barrage before Pickett’s charge have succeeded if there had been twice as many guns and enough powder to keep it up twice as long?

My confidence in your dismissal of Lanchester et al. would be stronger if it was clear what you mean by saying the Confederates won all the battles but still lost the Overland Campaign. Nor is it obvious what an indirect victory by mere numbers is, much less why such fake victories don’t really count. If that’s not what you mean to say, please clarify, because it’s not clear at this point.

John Strate

The ideas in the post are similar to the views of Col. Douglas MacGregor, Russia has a manpower advantage and a huge artillery advantage. Ukraine is running out of shells and NATO can’t p;roduce them fast enough. There are few men left to recruit. The new recruits do not have sufficient training to employe combined arms. Presumably, Russia is waiting for Ukraine to exhaust itslef. Will it then go on the offensive? I look forward to the next installment.


The numbers of casualty Is higher becouse around half of pow don’t go in captivity but free on promise that don’t fight again before Pow exchange. so a lot are counted as pow and as dead or wounded.


I am interested to see where you go with this. Lanchester’s laws are often difficult to actually use – what level of analysis (tactical, operational, strategic, grand strategic) to employ, how to measure “quality” – and getting good numbers on troop strength and (especially) casualties is hard enough after a conflict ends, let alone while it is going on and each side is trying to spin the numbers. Subjective factors are even harder to model, true, but that doesn’t mean they don’t matter, often critically. For example Clausewitz’s trinity framework suggests Ukraine has something Russia does not – cohesion between the three elements of people, government, and armed forces.

Specific material factors can be key as well – fortifications, terrain (including rivers as obstacles to advance), and of course sustainment – you can’t use materiel that you can’t get to the front, due to bad roads or enemy interdiction.

Steven Johnson

By this point, there is a general agreement that the War in Ukraine is a conflict between NATO and Russia.”

I’m not sure this is true at all. In popular media, it is Russia invading Ukraine in a war that began in 2022. And it’s pretty much deemed an aggressive attack meant to lead to world conquest.

I think a good many more serious analysts do see a war between NATO and Russia, but even those circle still harbor the people who serve as talking heads or writers in the popular media version. Worse, I’m not sure how many of these more serious analysts are aware that attributing independence of action to NATO is a question to answer, not a reliable assumption.


Меня удивляет, что Вы не взяли в качестве кейса войну СССР против Третьего Рейха. Была бы более прямая аналогия. Превосходство населения в 3,4 раза на стороне СССР по А, Тузу при явном технологическом преимуществе Рейха. И немцы едва не выиграли.

Vladimir Dinets

While we are waiting for the second part, it’s worth keeping in mind that nobody knows what Russia’s population currently is. I’ve seen claims that it’s less than half of the official number.

Taksu Cheon

Excellent article as we expect from Prof. Turchin. Cannot wait till the sequel.
On top of the numerical and framework-wise (relience on outside help for one side) similarities between this war and american civil war, we cannot help noticing the deeper similarity in that this war really is a civil war between “brotherly” peoples sharing culture, history and tradition (I understand many Ukrainians aren’t pleased to be reminded of this, but brothers often hate one another which doesn’t stop them being brothers) I wonder whether Prof. Turchin might expand on this aspect in the next post…

Chris Morris

Numbers of soldiers and war materials are different aspects of the same thing, material force. Lots of troops with little material don’t amount to very much (think of the queues of Russians in World War I waiting to use the one rifle available when their colleague is incapacitated) and lots of material without soldiers is no more than a supply dump,

Material force is the first ‘M’ of conflict. The second ‘M’ is Morale/determination, and the third ‘M’ is Manoeuvre.
The skill of the combatants in manoeuvre and in using what they have is important too. The ability of certain Northern commanders to snatch defeat from the jaws of victory added quite a lot to the length of the US Civil War, I feel.

In the Russo-Ukraine conflict, Russia has the hand down advantage on the first ‘M’ as it has in most of its wars since the Romanovs came to power, but it seems to be performing pretty badly on the other two ‘M’s (again very much as it has since the Romanovs came to power).

Material advantage only starts to count if a power can hold its own as regards Morale and Manoeuvre. Russian performance on these two has been less than stellar. Bands of mercenaries taking time off for a march to the capital? Constructing 40 mile traffic jams for the enemy to attack at leisure (rather like 1939 Finland)?

So the question is: Can the Ukrainian advantages in Morale and Manouevre result in a victory (or at least a peace after someone in Moscow has fallen through their 6th floor window) before the Russians can use their Material advantage to grind their way to Kiev?

It’s worth remembering that Lincoln thought that he’d lost the 1864 Presidential election and the US Civil War. The capture of Atlanta came just in time,

Steven Johnson

It is not generally held that Grant’s casualties in the Overland Campaign nearly lost the war while Joseph Johnston’s brilliant defensive campaign against Sherman’s advance into Georgia nearly lost it. In fact, this implied position of yours is vehemently rejected.

Lincoln’s (likely sincere) belief that if McClellan was elected, the war would be lost is a counterfactual. I think McClellan would have found great difficulty in making peace and keeping what was left of the Union intact. The war for the Union was also a war for democracy (bourgeois if you wish, but democracy nonetheless) and compelling surrender would have required I think a true tyranny in the North. I suspect those who like to portray Lincoln as a power-mad doctrinaire despot, an unholy anticipation of Lenin, are basically sore losers.

Chris Morris

McClellan might indeed have experienced difficulty in making peace (stopping wars is much harder than starting them), but my point is that as late as 1864, Northern victory was not inevitable. Highly likely, but not inevitable.
If I were asked to suggest a crunch point within the year, it would be May 5-7, 1864 when Grant didn’t respond to Confederate successes like Hooker had done a year earlier at Chanchellorsville.
Even so, the casualties that he was incurring in the Overland Campaign were not exactly conveying an air of victory, hence Lincoln’s unease about his prospects of electoral success. Sherman’s activities around Atlanta were much more clearcut victories.

I believe that President Putin has a date with the Russian electorate on March 17, 2024, which is only eight months away. At the current rate of progress, I don’t think he will be campaigning on the basis of “The man who brought the special military operation to a successful conclusion”.
The question is whether the apparatchniks will be happy to expend time and effort adjusting the electoral results to give victory to “The man who didn’t bring the special military operation to any conclusion at all”.

Steven Johnson

It seems to me false lessons from previous history can derail the analysis of the current hybrid WWIII (which is how I think of it) so perhaps this won’t be too much of a diversion? People who live by the West Point version of the Civil War are not I think well equipped to follow events.

McClellan to make peace would have had to knife the economic interests of the western states by ceding control of the Mississippi to the CSA. Railroads had already some utility in binding the North together from Minnesota to Maine, but they weren’t magic and river traffic was still a big deal. McClellan would have had to purge the army and navy of its Black soldiers. McClellan would have had the “problem” of suppressing the escaped non-combatant ex-slaves, possibly re-enslaving them or mass deportations (which would have in themselves bordered on genocide.) McClellan would have had to remove Morton in Indiana, regime changing an entire state. McClellan would had to revisit the existence of West Virginia, though maybe he could have rebuffed Virginian revanchism. Whatever mix of concessions he made to the CSA would have required a corresponding mix of repressions in the rump US, assuming the rump didn’t break up. CSA independence would have meant more wars later on, if only from clashes over CSA expansionism in Mexico, the Caribbean and Latin America.

And no, he could not have made peace on a status quo platform, because the Mississippi River bisected the CSA. CSA peace demanded territorial concessions. McClellan’s official program as a War Democrat was absolute nonsense.

Northern victory was “inevitable” from Antietam on, if—-a big if—the North chose to pay the price. If it did, the South had no hope of matching it. The South couldn’t win, they could only be let off the hook.

As for the alleged crunch point? More than anything it was the huge casualties from the Overland Campaign that threatened Lincoln’s re-election, that might have persuaded the North to give upLee never was in a position to take the offensive against Grant/Meade, so he never handed Grant a defeat in the sense Lee kept the field and Grant retreated. Lee didn’t have the same army he damaged so badly at Gettysburg and he couldn’t. In popular politics of the time, keeping the field was the only sign of victory in battle, so in that sense Grant was perceived as a victor. But politically, victory was taking Richmond and in that sense Grant was a loser, hence Lincoln’s worries.

We could argue about whether Grant’s persistent refusal to keep in field but actually take time to recuperate and really prepare an effective new offense was wise. I suspect Grant’s continued failure to flank Lee wasn’t just Lee’s superior generalship but Grant jumping the gun. He could have learned something from George Thomas, perhaps. (Insofar as a single general matters, Thomas was why Chickamauga wasn’t West Chancellorsville.)

Chris Morris

Certainly there were many more fault lines in the USA than the North/South one, and the collapse of the Union rump might have resulted from a McClellan attempt at Peace without Total Victory. Or maybe not. The Union had survived the Peace of Ghent after the War of 1812-14, and the option of “Fifty-Four Forty or Fight” was quietly forgotten after the Oregon Treaty in 1846. LIfe was possible without an overwhelming clearcut victory in an encounter, even if not everyone was happy.
A peace with the CSA would quite likely have resulted in later wars, but that is another story.
The point of the “alleged crunch point” is that if Grant had retreated after the Wilderness, as Hooker had done after Chancellorsville, Jubal Early’s 1864 raid on Washington or something akin to it would have looked a lot less like the forlorn hope that it was, and a lot more like “Maybe, we’ll be third time lucky”. And that would not have gone down well electorally.

In the current Russo-Ukraine war, there are a great many groupings who have different views on how things are going, and should a trip to Moscow by one or other of them result in gunfire, the clearcut material advantage of Russia could evaporate. As the saying has it, “The Russian army started as the second army in the world. Then it became the second army in Ukraine and ended as the second army in Russia.”

It’s fair to say that in the long run, the strongest power will win – but it can be a very long run. China was far more powerful than its nomad neighbours, but nomads ended ruling chunks (or all) of China on at least four occasions in the last 1800 years (Liao, Chin, Yuan, Ching)

  1. Home
  2. /
  3. Cliodynamica
  4. /
  5. Regular Posts
  6. /
  7. What Osipov and Lanchester...

© Peter Turchin 2023 All rights reserved

Privacy Policy

%d bloggers like this: