Thu 2023-Mar-02

Another Grim Anniversary

Tagged: MathInTheNews / Politics / Sadness

As if the world weren’t bad enough, today there’s evidence that Russian casualties in Ukraine have topped 150,000 dead.

Ok, so who says that?

Twitter: Defense of Ukraine Here at Chez Weekend, we – along with 1.8 million others – have been following the Twitter account Defense of Ukraine, which is official reporting from the Ukrainian Ministry of Defense.

Now, you could argue that since this is a Ukrainian source, we’re susceptible to being propagandized here. On the one hand, sure; but on the other hand nobody believes a single word of what the Russians say. The Ukrainian MoD has said a couple times that these body counts are the result of actual counts in the field, so the true number is probably higher. OSInt sources seem to believe that, based on spot-checking where feasible. They’re at least consistent with outside sources, while the Russian sources appear to be, at best, orthogonal to the truth.

We also tend to believe the high Russian casualty numbers because many other news sources confirm Russian use of human wave tactics involving badly equipped, badly trained former convicts sent forth en masse, without combined-arms tactics.

To be fair, this would be better from a statistical point of view if we also had Ukrainian casualty figures, preferably from the Ukrainians themselves as a reliable source. But, of course, there would be intense Russian scrutiny of those numbers to estimate the effectiveness of their tactics. And nobody wants to help the invaders do better at invasion.

So, one-sided as it is, these seem to be about the best data we’ll get unless there’s a UN investigation post-war, or a war crimes investigation, or something of that order.

The grim facts

Ukraine MoD @ Twitter: RUS deaths & equipment losses, 2022-Feb-24 to 2023-Mar-02


Shown here is their report: now over 150,000 confirmed Russian casualties. Yesterday alone, 715 deaths.

This is utterly crazy. Not just in the moral or legal sense, though it is definitely crazy there. It’s crazy in the pragmatic sense to lose 700 lives/day just holding in place, not taking any new territory.


Take a look at another eye-popping fact: 3397 tanks lost in about 12 months of fighting. That works out to 3397 tanks / 12 months = 283 tanks lost / month. (Not quite 10 tanks/day, but almost.) Well, ok… but is that a lot, or a little? What’s the scale here? (Scientists, especially statistically literate ones, always have to ask that. Every. Single. Time.)

Zitser @ BI: Russia produces 20 tanks/month A good summary source here is an article in Business Insider by Joshua Zitser [1], drawing on investigations by The Economist into tank production rates in Russia and the Dutch open-source intelligence platform Oryx on tank loss rates.

  1. Oryx has estimated the loss rate at 150 tanks/month, much lower than what the Ukrainians are claiming based on battlefield counts (they’re claiming a total of 1779 tanks lost over the last year, which works out to just below 150 tanks/month). This makes sense, since Oryx only wants to count “real” tank losses that have independent verification by some means or other, so that’s probably an undercount.

    You might want to assume the Ukrainians are exaggerating for propaganda purposes (though I see no evidence of that, so either they’re telling the truth or they’re very skilled propagandists). Then their rate of 283 tanks/month may be an overcount.

    So we should believe somewhere in the range of 150 - 280 tanks/month, and I’m personally inclined toward the upper end of that range.

  2. The Economist thinks there’s basically 1 single operational tank production facility in Russia, whose output is 20 tanks/month.

    On the other hand, they grant that the Russians have a large number – $O(10^4)$ – of older, somewhat obsolete tanks in storage that may possibly be refurbished. However, the usual Russian “storage” means many of those tanks will be a total loss (due to poor maintenance, weather exposure, looters, or all those). Even the refurbished ones will have to do without semiconductors that are harder to get in Russia (so very elementary/short-range sights, for example, thereby reducing range of fire).

    Doubtful maintenance & refurbishing, lack of modern electronics, and obsolete tanks at the start are… a bit of a handicap! Still, The Economist thinks they might squeeze out 90 refurbished tanks/month.

    Let’s go with 90 tanks/month total, instead of 20 new tanks + 90 refurbished, to account for the difficulties of repairing old tanks with scarce materials.

That all adds up to losing 150 - 280 tanks/month, while producing maybe 90 tanks/month, for a net deficit of 60 - 290 tanks/month lost permanently without replacement. (Also, they usually lose the tank crew when the tank is destroyed, and training a new tank crew – even on an older tank – takes a long time.)

So they’re bleeding tanks at a rate of 60 - 290 tanks/month.

Baker @ BI: Russian tanks in Ukraine Again, we have to ask: is that a lot, or a little? How many tanks do they have in Ukraine, anyway? For that, we turn to Sinéad Baker, again writing in Business Insider and basing her report on data from Oryx and a CNN report from military analyst Jakub Janovsky. [2]

While there are of course no official numbers known outside the Kremlin, the estimates seem to converge to starting out the invasion with about 3,000 Russian tanks:

  • If you believe the overestimate from the Ukraine MoD data above, all of those are wiped out and Russia is left only with whatever reinforcements they’ve brought in over the last year. At 20 - 90 new tanks/month for 12 months, that’s 240 - 1080 tanks left.
  • If you believe the underestimate from visually confirmed tanks via Oryx above, then they started out with about 3000 tanks, lost about 1800, so about 1200 of the originals remain. Add in the reinforcements they’ve undoubtedly shipped for the last 12 months, and you get something like 1440 - 2280 tanks left.

At a burn rate (net of continuing reinforcements) of 60 - 290 tanks/month, that means the Russians run out of tanks in:

  • ( 240/290) — (1080/60) months = 1 — 18 months (Ukrainian MoD data)
  • (1440/290) — (2280/60) months = 5 — 38 months (Oryx data)

(Yes, I got those intervals by the very crude method of dividing high and low tank estimates by low and high tank loss rate estimates, respectively. This is Not The Way. I should model each set of numbers by a shifted binomial distribution, then employ the methods of ratio distributions which say the ratio is approximately lognormally distributed. (The math here is similar to estimating the probability distribution of a vaccine efficacy!) But in my currently post-COVID-19-brain-fog-addled brain, I just can’t summon up the oomph to flog the damn recalcitrant neurons any harder than this. Better in the future as I heal, I promise… but you are permitted – and encouraged – to hold this one example of bad behavior against me to make sure I do better in the future.)

Well, that’s a couple of wide ranges. We expect the Oryx data to lead us to believe it will take longer, since they have much lower tank destruction estimates. They want independent visual confirmation on every tank destroyed. So I’m gonna go with the Ukrainian data here, and (crudely!) estimate about 9 months until Russia runs out of tanks in Ukraine.

It could be faster, if Ukrainians are able to deploy Challenger, Leopard-2, and maybe even Abrams tanks from the west. Each of those should be able to hunt Russian tanks pretty well.

The Weekend Conclusion

Disclosure: My military knowledge and experience is negligible. I’ve read a bit, and I’ve consulted (very) occasionally for military customers some decades ago, but that’s it. In other words, to a very good approximation I know nothing.

Also, still working through persistent post-COVID-19 brain fog and waiting for anti-depressants to kick in. So down-rate your estimate of my credibility accordingly.

But it looks like around 9 months, maybe up to 18 months, and then Russia runs out of tanks.

Now, Russian analysts in the Kremlin know this, and know it much more reliably than some dumb guy with a keyboard at Château Weekend using business publications to estimate force levels!

  • Are they telling Putin this stuff already, or will it come as a surprise?
  • Will Putin escalate, potentially to nuclear threats, if he (reasonably) feels cornered by this outcome?

The rational outcome would be to look at all this, shrug, issue some bizarre propaganda statement, and withdraw to Russia.

When I were just a wee tad, I had great faith in human rationality: if only I could nail down all the details mathematically, and speak clearly & forcefully to the decision makers, surely they would do the rational thing, right? Now that I’m a grizzled old scientist, bearing the scars of many battles with irrational corporate managements, I no longer have much faith in human rationality.

I don’t like this world line. Can I speak with The Management about switching to another?

Notes & References

1: J Zitser, “Russia has just one tank factory churning out 20 tanks a month, with demand outstripping production by a factor of ten, says report”, Business Insider, 2023-Feb-28.

2: S Baker, “Russia has lost at least 1,500 tanks since the start of the Ukraine war, more than half of its invasion force: report”, Business Insider, 2023-Feb-09.

Published Thu 2023-Mar-02

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