A report in the Boston Globe about the Transportation Security Administration’s so-called Quiet Skies program has stirred significant alarm. The program requires that Federal Air Marshals keep watch over a handful of designated passengers — a very small number, some 35 of the 2 million-plus who fly every day — for such “suspicious” behaviors as “excessive fidgeting,” “strong body odor,” “cold penetrating stares,” and using the lavatory. There are currently around 2,000 to 3,000 marshals flying on about 5 percent of flights.

The revelation is significant, but not all that unusual. Police at all levels have long issued Suspicious Activity Reports, or SARs, on any public behavior that they consider suspect in the effort to track terrorists, which they then send to the FBI or Fusion Centers — clusters of local police, FBI, and intelligence that focus on terrorism (and only rarely find anything to do). The Quiet Skies program mainly seems to be an extension of that and of another program in which air marshals keep tabs on airline passengers designated as potential dangers by the FBI.

Air marshals skeptical of the program told the Globe that they felt that nonthreatening people were being followed, including “a businesswoman who happened to have traveled through a Mideast hot spot, in one case; a Southwest Airlines flight attendant, in another; a fellow federal law enforcement officer, in a third.”

We are academic researchers who have spent years studying TSA security measures and evaluating their role in averting terrorism. In several books and in dozens of academic articles, we’ve studied each layer of security from policing, intelligence, and checkpoint passenger screening to armed pilots on the flight deck. We are interested in constructing the best model of a security system by asking the question: Does the tactic reduce risk enough to justify its cost? Some security measures do much better on this than others.

Based on our work, we doubt that the Quiet Skies program is worth the cost and resources devoted to it. Indeed, the same could be said for the entire air marshal service.

The Federal Air Marshal Service is likely not worth the cost

In general, the model we’ve used is biased to favor the terrorist chances of success. For example, we do not include potential amateurism and incompetence of the terrorist group as a security layer. But even with that bias in place, a terrorist group’s chance of pulling off an attack under current security conditions has got to be pretty dispiriting for them: one in 50 for an onboard bombing attempt or one in 150 for a hijacking.

The Federal Air Marshal Service is a prime target for cutting. The program is very expensive, costing more than $1 billion per year, including losses borne by airlines forced to provide free seats for their uninvited guests. In general, applying standard cost-benefit and risk-analytic procedures, we find that spending one dollar on the service generates less than 10 cents in benefit.

The air marshals insisted to the Government Accountability Office (GAO), which, along with the National Academy of the Sciences, has recommended an overhaul of the TSA system, that one of their “primary security contributions is to deter attacks.” However, they had, as the GAO pointed out, no evidence to support the claim that they had averted even a single attack; it seems likely to be invalid.

To begin with, although the air marshals are there primarily to deal with attacks like 9/11 in which terrorists seek to commandeer an airliner, there have been no such attempts anywhere in the world since 2001 — not even in the many countries that do not employ air marshals.

Moreover, a 2015 CNN investigation found that air marshals were often medicated to help them sleep and, because of their hectic schedule, were also often sleep-deprived. The Quiet Skies program is unlikely to help with this issue.

However, reducing the air marshal budget by 75 percent (still leaving hundreds of them around for special assignments should any arise, such as following up on actual valid tips), and spending part of the savings on less expensive security measures such as training pilots on how to resist forced cabin entry, would lead to better aviation security at a savings of hundreds of millions of dollars each year for both the taxpayers and the airlines.

The real risk of an airplane terrorist attack

But missing from the discussion has been a broader issue.

Since 9/11, there have been no terrorist attacks or attempts whatsoever on airliners leaving American airports. Indeed, for that period, the chance that an airline passenger would be killed by a terrorist anywhere in the world is one in 110 million.

Is this phenomenon influenced in part by the intensified TSA security measures put in place since 9/11? We think so. But it’s also important to consider whether there are actually many terrorists out there thinking about attacking airlines — a primary element in the rationale for the air marshals.

As both the GAO and the TSA recognize, terrorists discouraged from attacking a hard target like an airliner can only too readily transfer their attention to any one of a nearly infinite number of other potential targets that are anything but secure: congregations of people in restaurants, in offices, at sporting events, or standing in security lines at the airport.

Yet terrorism, however tragic and newsworthy, remains a remarkably rare phenomenon in the United States and in the rest of the developed world — Islamist terrorists have killed a total of six people a year since 9/11 in the US. If security measures like the air marshal service were deterring large numbers of people from attacking airliners, we would expect far more mayhem in other places.

There is no way to attain perfect aviation security from terrorism except by grounding all airliners. If that remedy is deemed to be unacceptable, we will have to live with a degree of risk. The questions that need to be asked, then, are not “do some passengers smell or fidget or stare penetratingly?” but “Are we safe enough?” and “How much should we be willing to spend for a small reduction in a risk that is already extremely low?” and “Can we modify security measures in a way that keeps the risk acceptable while reducing costs significantly?”

Perhaps the skies are already quiet enough.

John Mueller is a political scientist at Ohio State University and a senior fellow at the Cato Institute. Mark Stewart is a civil engineer and risk analyst at the University of Newcastle in Australia. Their most recent books are Are We Safe Enough? Measuring and Assessing Aviation Security and Chasing Ghosts: The Policing of Terrorism.

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