At hearings of the Senate Homeland and Governmental Affairs Committee earlier this month, former congresswoman Jane Harman (D-CA), now head of the Wilson Center in Washington, made a gallant stab at coming up with, and hailing, some homeland-security functions that “execute well.”

At the top of Harman’s list was the observation that Customs and Border Protection (CBP) last year stopped more than 3,100 individuals from boarding U.S.-bound aircraft at foreign airports for national-security reasons. Since these were plucked out of more than fifteen million travelers that went through fifteen preclearance locations overseas, it was, she exclaimed enthusiastically, “like picking needles from a haystack!”

Committee chair Senator Joseph Lieberman (I-CT) waxed even more enthusiastic about the number, concluding grandly that it “took very sophisticated data systems and implementation of those systems to make that happen” and that “we’re all safer as a result of it.”

This was an exercise in serial innumeracy, of course, because the relevant statistic is not how many individuals were denied entry but how many of those denied actually presented a security threat. Neither enthusiast presented relevant data, but, judging from the fact that no one apparently was arrested (we’d tend to know if they had been), the number was likely just about zero. Nor was information presented about the problems or costly inconvenience inflicted upon the many who were likely waylaid in error.

Moreover, it is not clear where the Harman/Lieberman number even comes from. According to Homeland Security officials interviewed by Michael Schmidt for a recent article in the New York Times, only 250 people in each of the last two years were turned away or even pulled aside for questioning as potential national security risks by preclearance screeners. Maybe CBP is even more “sophisticated” at picking needles from haystacks than Harman and Lieberman give it credit for. Does that mean we’re even safer as a result? Or less so?

Schmidt also supplies information that calls into question the whole preclearance enterprise. Stimulated in considerable measure by the failed underwear-bomber attempt to blow up an airliner flying from Europe to Detroit in 2009, the program is, as Department of Homeland Security chief Janet Napolitano stresses “an expensive proposition.” Although it has been instituted so far only in airports in Canada, the Caribbean and Ireland, it already costs $115 million a year. Expansion to hundreds of other airports (including the one the underwear bomber actually took off from) is not only costly but also requires a major diplomatic effort because it involves cajoling foreign governments into granting the United States police-like powers on their own soil. The program has not foiled any major plots thus far, notes Schmidt, and he pointedly adds that it would scarcely be difficult for a would-be terrorist to avoid the few airports with preclearance screening to board at one of the many that do not enjoy that security frill.

But the main innumeracy issue in all this is that the key question, as usual when homeland security is up for consideration, is simply left out of the discussion. The place to begin is not “are we safer” with the security measure in place but how safe are we without it.

We have calculated that, for the twelve-year period from 1999 through 2010 (which includes 9/11, of course), there was one chance in twenty-two million that an airplane flight would be hijacked or otherwise attacked by terrorists.

The question that should be asked of the numerically challenged, then, is the one posed a decade ago by risk analyst Howard Kunreuther: “How much should we be willing to pay for small reductions in probabilities that are already extremely low?”