Wed 2024-Apr-10

Casualties in Ukraine: Grief Piles Higher & Deeper

Tagged: MathInTheNews / Politics / R / Sadness / Statistics

The Russian invasion of Ukraine just keeps getting worse. Predictably.

Russian Casualty Data: Is It Consistent Over Time?

We’ve been following the dire and dispiriting Ukraine invasion for some time now, writing about it occasionally on this Crummy Little Blog That Nobody Reads (CLBTNR). [1] [2] [3] [4] [5] [6] [7]

Some of those articles are more philosophical, like the one on Tacitus. Others are more our usual hard-nosed look at the best data we can get. We previously found that Russian casualty rates (as reported by the Ukraininan Ministry of Defence) are amazingly constant, fitting a linear model quite well. Other things are more bursty, as targets of opportunity present themselves. For example, Ukraine has sunk several Russian ships, and that’s an opportunity that does not occur daily for a small nation with no navy.

We haven’t looked much at the data over the past year, since it’s been too depressing and we’ve had too much Long COVID-19 brain fog. However, today came an update from the Ukrainians that demands a look:

Ukraine MoD: 450,080 Russian casualties on 2024-Apr-10

450k dead. The mind boggles; this is a crime against humanity, inflicted by Russians upon themselves. In addition, of course, let alone all the death, mutilation, and misery they have inflicted upon Ukrainians.

Now, previously we’d done some regression models on the first 116 days of the conflict (as well as a more fine-grained analysis on days 60 - 116, chasing a small trend). That established that a linear regression model was a good fit at 200k casualties, with $R^2 \sim 99.43\%$.

Here we are, at 2024-Apr-10, which is now day 443 of the conflict: about a year later, and 250k more Russians dead. How has that model held up?

Russian soldiers killed in Ukraine over time: outperforming the regression trend Here’s a plot of the original model, showing:

  • Time in days since the start of the conflict on the horizontal axis, and Russian casualty figures on the vertical axis.
  • The blue dots are the training data, Russian casualties on days 1 - 116.
  • The black dashed line is the excellent linear regression fit, whose regression coefficients report about 699.6 $\pm$ 4.98 deaths/day.
  • The gray bands show some uncertainty bands, which I’ve explained elsewhere. Basically we’re 95% sure the true regression line is in there somewhere, and the black dashed line is our best estimate.

We’ve extended the range of the plot, both horizontally and vertically, to reach the present day and the present casualty rates.

Look closely (click on the image to embiggen) at the upper right corner: there’s a single red dot, representing 450k dead on day 443 of the conflict. What to make of its position?

  1. It’s pretty close to the trend line of the previous regression, especially since we’re extrapolating so far away from the training data. We had 100ish days of training data, and now we’re still on trend at 450ish days!
  2. If anything, the Russian casualty rate is slightly above the trend, i.e., Russians have been dying at slightly higher than previous rates.

The Weekend Conclusion

Ukrainians have been doing rather well, and rather consistently over time. This is especially impressive given that they are under-armed for pretty much the entire conflict so far. Russia has enormous resources, but severe problems doing logistics and combined arms fighting to use them.

Even more shameful is the reluctance of Western nations to provide sufficient arms for Ukrainians to defend themselves! I’m incandescently angry at Republicans in the US for blocking Ukraine aid, hoping to gain political advantage by enabling Putin. The only reasonable response is to fund Ukraine’s weapons.

We desperately need to neuter such Republicans. The reasonable course seems to me to employ the fact that most of them were complicit in the Jan 6 insurrection, so should be judged ineligible for office under the 14th Amendment.

As for Trump himself, the words of Goethe apply:

The truth must be repeated over and over again, because error is also repeatedly preached among us…

(… man muß das Wahre immer wiederholen, weil auch der Irrtum um uns her immer wieder gepredigt wird…)

— Johann Wolfgang von Goethe, Conversations of Goethe with Eckermann and Soret, 1827-Dec-16.

Translation by Goethe Global, based on translation by John Oxenford.

So it can only be repeated:

Ceterum censeo, Trump incarcerandam esse.

Notes & References

1: Weekend Editor, “Another Grim Anniversary”, Some Weekend Reading blog, 2023-Mar-02.

2: Weekend Editor, “Do the Ukrainian Reports of Russian Casualties Make Sense?”, Some Weekend Reading blog, 2023-Apr-15.

3: Weekend Editor, “Update: Ukrainian Estimates of Russian Casualties”, Some Weekend Reading blog, 2023-May-01.

4: Weekend Editor, “Updated Update: Ukrainian Estimates of Russian Casualties”, Some Weekend Reading blog, 2023-May-09.

5: Weekend Editor, “Updated${}^3$: Ukrainian Estimates of Russian Casualties Hit 200k”, Some Weekend Reading blog, 2023-May-17.

6: Weekend Editor, “Ukraine Invasion: 250k Russian Dead”, Some Weekend Reading blog, 2023-May-17.

7: Weekend Editor, “Tacitus in Ukraine”, Some Weekend Reading blog, 2023-May-25.

Published Wed 2024-Apr-10

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