A relative of Palestinian boy Mohammed Eweda, whom medics said was killed in an Israeli air strike, mourns during his funeral in Rafah in the southern Gaza Strip August 4, 2014. (REUTERS/Ibraheem Abu Mustafa)

In yesterday’s New York Times, reporter Anne Barnard delved into the trauma of a Gaza psychologist. In a passage describing the violence in the current Israel-Hamas conflict, she wrote:

Now, with the death toll for the last three weeks exceeding 1,500 Palestinians — relative to the population, the equivalent of nearly 200,000 deaths in the United States — nearly every Gazan has heard or witnessed shelling, and most know someone personally who was killed or injured.

Jordan Ellenberg, a math professor at the University of Wisconsin-Madison, counseled us to be expecting such proportional reporting. In his recent book “How Not to Be Wrong: The Power of Mathematical Thinking,” Ellenberg includes a chapter titled “How Much Is That in Dead Americans?” It debunks precisely the calculation that Barnard unfurls in her New York Times article.

The gripe isn’t with the calculation itself — proportions are proportions, after all. Rather, Ellenberg takes aim at the logic behind the calculation: “Any time a lot of people in a small country come to a bad end, editorialists get out their slide rules and start figuring: how much is that in dead Americans.”

The book cites one counterterrorism specialist who had calculated that Palestinians had killed 1,074 Israelis in the first half of the 2000s, “the proportional equivalent of more than 50,000 dead…for the United States.” Ellenberg jumps in:

The Israeli victims are equivalent to 7,700 Spaniards or 223,000 Chinese, but only 300 Slovenes and either one or two Tuvaluans. Eventually (or perhaps immediately?) this reasoning starts to break down. When there are two men left in the bar at closing time, and one of them coldcocks the other, it is not equivalent in context to 150 million Americans getting simultaneously punched in the face.

The author then embarks on a detailed explanation of the Law of Large Numbers, which states that the more times you test something, the closer the actual results come to the “expected value.” Take coin-flipping: If you do 10 flips, notes Ellenberg, it’s possible that seven or eight or even nine will turn up heads. If you do 100 flips, the number of heads will inevitably hew closer to the expected 50 percent.

More Ellenberg:

What applies to coins…applies to massacres and genocides, too. If you rate your bloodshed by proportion of national population eliminated, the worst offenses will tend to be concentrated in the smallest countries. Matthew White, author of the agreeably morbid Great Big Book of Horrible Things, ranked the bloodlettings of the twentieth century in this order, and found that the top three were the massacre of the Herero of Namibia by their German colonists, the slaughter of Cambodians by Pol Pot, and King Leopold’s war in the Congo. Hitler, Stalin, Mao, and the big populations they decimated don’t make the list.

So there, all you proportionalists!