Outside the Beltway

Are Hamas Death Figures Fake?

Damned if I know.

James Joyner · Monday, March 18, 2024 · 15 comments

YahooNews points me to a March 16 Telegraph column by Jake Wallis Simons titled “This could be the devastating proof that Hamas is faking its death figures.”

One of the marks of anti-Semitism, George Orwell observed in 1945, is “an ability to believe stories that could not possibly be true”. Which brings us smartly to Hamas and how the broadcast media, aid organisations, international bodies and world leaders take its disinformation as gospel. Last week it became clear that this gullibility may have led to a crime against reality.

A new analysis of the group’s casualty statistics indicates that the rag-tag terror army may have pulled off one of the biggest propaganda coups of modern times. The figures, repeated by everyone from the White House to the BBC, are freighted with familiarity: 30,000 dead in Gaza, 70 per cent of whom are women and children. Yet it now seems overwhelmingly likely that these statistics are fabricated.

Professor Abraham Wyner, a data scientist at the University of Pennsylvania, has conducted a thorough analysis. He found that Hamas’s official civilian death toll was statistically impossible. “Most likely, the Hamas ministry settled on a daily total arbitrarily,” he wrote in an incendiary essay in Tablet. “We know this because the daily totals increase too consistently to be real. Then they assigned about 70 per cent of the total to be women and children, splitting that amount randomly from day to day. Then they in-filled the number of men as set by the predetermined total. This explains all the data observed.”

The giveaways were many. For example, the reported death toll mounted “with almost metronomical linearity”, Prof Wyner found, showing little daily variation. Obviously, this bore no resemblance to any plausible version of reality. Then there was the fact that, according to Hamas data from 29 October, 26 men came back to life; and the fact that on several days, no men were apparently killed at all, but only women. Were we really supposed to believe any of this?

In February, Hamas admitted to losing 6,000 of its fighters, representing more than 20 per cent of the total casualties reported. Given its claims that 70 per cent of the dead were women and children, there were two possible conclusions: either almost no male civilians had died, or almost all the men in Gaza were fighting for Hamas. Both were obviously absurd.

Therefore, the number of women and children killed was likely grossly exaggerated. If that is the case – if, as Prof Wyner suggests, “the casualties are not overwhelmingly women and children, and the majority may be Hamas fighters” – where does that leave western outrage? Has the West fallen victim to a monstrous con?

The true ratio of civilian casualties to combatants is likely to be exceptionally low, “at most 1.4 to 1 and perhaps as low as 1 to 1”. This, Prof Wyner says, is a “successful effort to prevent unnecessary loss of life while fighting an implacable enemy that protects itself with civilians”.

While I had been naturally skeptical of casualty reports issued by a terrorist group (and, frankly, I tend to be skeptical of any party to a war’s real-time numbers given both the very real propaganda incentives for misrepresentation and the “fog of war” making these assessments fraught even for honest brokers), I had seen enough claims by experts that we should take them seriously that I more-or-less stopped asking.

Looking at Wyner’s bio, CV, and Google Scholar pages, I consider him a highly qualified expert data scientist. He earned his PhD in Statistics from Stanford in 1993, has won multiple awards, and is a prolific and well-cited scholar. Judging from the handful of articles he’s published at Tablet and Forward, he seems to be an ardent Zionist and something of a COVID and climate change skeptic but there aren’t enough red flags to overcome his stature as a top-rate scholar.

Still, that works both ways. He published the above-referenced essay (“How the Gaza Ministry of Health Fakes Casualty Numbers“) on March 6. Even granting that he’s a statistician rather than an International Relations or Security Studies scholar, you’d think such devasting findings from someone of his stature would have made it to my attention in the intervening two weeks.

Wyner’s main evidence is in this chart:

About which he observes,

This regularity is almost surely not real. One would expect quite a bit of variation day to day. In fact, the daily reported casualty count over this period averages 270 plus or minus about 15%. This is strikingly little variation. There should be days with twice the average or more and others with half or less. Perhaps what is happening is the Gaza ministry is releasing fake daily numbers that vary too little because they do not have a clear understanding of the behavior of naturally occurring numbers. Unfortunately, verified control data is not available to formally test this conclusion, but the details of the daily counts render the numbers suspicious.

I stumbled on Caltech computational biologist Lior Pachter‘s March 8 post (“A note on ‘How the Gaza Ministry of Health Fakes Casualty Numbers’“) responding to Wyner’s analysis.

Wyner’s plot shows cumulative reported deaths over a period of 15 days from October 26, 2023 to November 10, 2023. The individual reported deaths per day are plotted below. These numbers have a mean of 270 and a standard deviation of 42.25:

The coefficient of determination for the points in this plot is R² = 0.233. However, the coefficient of determination for the points shown in Wyner’s plot is R² = 0.999. Why does the same data look “extremely regular” one way, and much less regular another way?

If we denote the deaths per day by , then the plot Wyner shows is of the cumulative deaths . The coefficient of determination R², which is the proportion of variation in the dependent variable (reported deaths) predictable from the independent variable (day), is formally defined as  where  is the sum of squares of the residuals and and  is the variance of the dependent variable. Intuitively, R² is a numerical proxy for what one perceives as “regular increase”.

In the plots above, the  are roughly the same, however  is much, much, higher for the y_i in comparison to the x_i. This is always true when transforming data into cumulative sums, and is such a strong effect, that simulating reported deaths with a mean of 270 but increasing the variance ten-fold to 17,850, still yields an “extremely regular increase”, with R² = 0.99:

Sadly, I must confess that my long-ago statistical training has atrophied, and I likely never would have fully understood Pachter’s equations. In response to a commenter, though, he adds this bit of clarity:

There could be many reasons for these correlations. Maybe it’s an artifact of the age threshold for children and the distribution of age in Gaza. Maybe it’s the result of lags in recording deaths. Maybe it’s a happenstance arising from so few datapoints. Maybe the data was indeed faked.

I’ll note that there are all sorts of anomalies one can grasp onto. I noticed, for example, that the average, 270 is an integer. Adding up 15 random numbers and then dividing by 15 is unlikely to yield an integer. But it can happen (7% of the time). When one starts floating tons of hypotheses, especially with little data, evidence for one of them doesn’t carry significance.

Additionally, commenter Ken M adds this insight:

If you look at the numbers, it’s very clear that they update fatalities faster than the update #women or #children (and they don’t specify #men, that is just (#fatalities – #women-#children)). On some days fatalities update but there is no change in the #w or #c; on other days the increase in (#w+#c) exceeds the increase in #f. In other words, in the conditions of war, it is hard to get information. The Gazan Ministry of Health (GMH) makes a list of the name and ID # of every identifiable death; Israel maintains the registry of ID #’s so GMH can’t fake that. That’s why their numbers come out accurate. But in real time, they may get a number of fatalities from a hospital and get the names, which allow identification of #w or #c, only later, maybe much later. And if they get the list of names, they have to go through the registry to determine who is a child or an adult, and maybe for ambiguous names who is a woman or a man, and that probably takes time too. So #w and #c get updated with arbitrary lags, sometimes multiple days worth may suddenly get updated at once. So looking at day-by-day movements of these #’s is meaningless.

I’ll add two other things. First, he says there is no correlation between increment in #women and increment in #children, just like Lior showed that there is no correlation between increment in #fatalities and time. But if you look at the cumulative #women vs the cumulative #children, you get perfect correlation, R^2=0.99 (I checked), just like he finds perfect correlation between cumulative #fatalities and time. Second, for his day-by-day anticorrelation between women and men: because they don’t specify men, only #w and #c, and because they may update in bunches, when there is an update of a lot of women, it will look like there’s not many men (i.e. change in fatalities – change in (women + children) is small, or even negative). When there’s an update where they don’t know the identities so it looks like there’s no increase in the #women, it will look like there’s a big increase in men – all the fatalities will appear to be men. So that’s why you get an anticorrelation between #women & #men.

Looking at the numbers as a lapsed data scientist but as a still-engaged Security Studies scholar, my immediate problem with Wyner’s analysis was his assumption that the daily correlation between males and/or Hamas fighters killed and those of women and children ought to be pretty consistent. But there’s no reason that should be the case. The battlefield isn’t a constant, after all. Air strikes are likely to kill a much high percentage of noncombatants than commando raids, for example.

Further, Wyner himself acknowledges the fog of war and says, “The truth can’t yet be known and probably never will be.” Yet, the whole tone of the piece is one of certitude: Hamas is obviously faking the numbers.

• “The numbers are not real. That much is obvious to anyone who understands how naturally occurring numbers work. The casualties are not overwhelmingly women and children, and the majority may be Hamas fighters.”
• Only a bit of caveating here: “Perhaps what is happening is the Gaza ministry is releasing fake daily numbers that vary too little because they do not have a clear understanding of the behavior of naturally occurring numbers. Unfortunately, verified control data is not available to formally test this conclusion, but the details of the daily counts render the numbers suspicious.”
• And here: “While the evidence is not dispositive, it is highly suggestive that a process unconnected or loosely connected to reality was used to report the numbers. Most likely, the Hamas ministry settled on a daily total arbitrarily.”

All in all, I would be much more comfortable with “Be Cautious About Gaza Ministry of Health Casualty FIgures” than “How the Gaza Ministry of Health Fakes Casualty Numbers.”