Last week we started evaluating Donald Trump’s stated positions in light of facts and sober analysis (at least the best I could find). As it turns out, his immigration policy is way too big for one post, so for the time being, let’s look at one of its cornerstones: building a wall on the Mexican border—in part to stop all those dangerous Mexican criminals from entering the U.S.

(Warning: there is math involved, and math is not my strong suit. If it’s yours, and you spot a flaw in my calculations below, please speak up.)

Trump’s statement claims that “for many years, Mexico’s leaders have been taking advantage of the United States by using illegal immigration to export the crime and poverty in their own country.” He supports his claim with this statement:

In 2011, the Government Accountability Office found that there were a shocking 3 million arrests attached to the incarcerated alien population, including tens of thousands of violent beatings, rapes and murders.

The Math

For starters, the figure is wrong. The GAO study estimates 1.7 million arrests for 2.9 million offenses (apparently you can be arrested for multiple offenses at the same time, a fact I have no intention of verifying firsthand). It also attributes these offenses to 249,000 alleged offenders—or, as the GAO calls them, “criminal aliens”—for an average of about 7 arrests per offender.

Sounds like a bad lot, and it probably is. But wait. The “incarcerated alien population” doesn’t include just Mexicans. Neither does it say anything about the behavior of undocumented Mexican immigrants in general. We need more “facts and sober analysis.”

As it turns out, data on Mexican criminal aliens are hard to come by, but we can make some educated guesses. Start by assuming, just for the moment, that all 249,000 alleged offenders in the above paragraph are undocumented Mexicans. The Pew Research Center estimates that 6.2 million undocumented Mexicans lived in the U.S. during 2011. That would put the number of all “criminal aliens” at 4% of all undocumented Mexicans in the U.S. If Mexicans make up half of all undocumented immigrants, and we apply that to our percentage, we’re down to 2%.

By comparison the total number of U.S. residents arrested in 2011, according to the FBI, was about 9.5 million—or 1% of the U.S. population. Not exactly a significant difference.

The Lessons We Might Draw from This

Everyone would agree that keeping criminals from other countries out of the U.S. is a good thing. But in terms of crime, at least, Trump’s solution sounds like massive overkill.

More troubling is this: Trump hangs essentially his whole case on this statistic—and it clearly doesn’t say what he says it does. Worse, the fallacy of his “shocking 3 million” claim, together with his wild profusion of other claims, lend weight to the charge that Trump just makes it up as he goes along, pulling statistics out of the air, without heed for accuracy.

Yes, I know. Candidates have used isolated statistics to prove dubious points since…well, probably since there have been candidates and statistics. But Trump has raised this game to another level, apparently citing random statistics as support for extreme, even dangerous, positions. That means he deserves special scrutiny.

Put another way, we have to find out to what extent the emperor has no clothes. Do all his positions rest on erroneous or obsolete facts? We’ll see.