How do you solve a problem like mass shootings? The answer is one that, understandably, few people want to hear: You probably can’t.

That’s the logical, if grim, conclusion to be drawn from a new Congressional Research Service Report on “Public Mass Shootings in the United States.” CRS strives to be studiously neutral, so they’re not going to put it quite like that.

Instead, the report’s authors say things like “the utility of widely employed preventive measures in these areas [law enforcement and public health] to fight public mass shootings is far from clear.”

As the Daily Beast’s Megan McCardle observed in December, “it is beyond horrible to suggest that even a small number of attacks are largely unavoidable. I don’t like saying it. Unfortunately, I think it’s true.” The tragic fact is, there’s not a great deal that public policy can do to avert spree shootings.

Still, it’s worth asking, as CRS does, “what are the parameters of this threat?” The report defines “public mass shootings” as incidents involving four or more deaths and “gunmen who select victims somewhat indiscriminately,” excluding drug trafficking, gang activity and terrorism.

By that measure, there have been 78 such incidents in the U.S. since 1983, claiming a total of 547 lives. Horrifying as that toll is, it represents a substantially lower risk than lightning strikes, which have killed 54 Americans a year on average over the last 30 years.

The fact that spree shootings occur so rarely makes the problem extraordinarily difficult to solve, and the solutions aren’t costless.

CRS notes the Obama administration’s support for using the Community Oriented Policing Services program to put more armed officers in schools. Still, they observe, “schools continue to be among the safest places for children,” and only eight of the 78 mass shootings they’ve identified over the last three decades occurred in primary or secondary schools.

Moreover, “there are those who question the impact of such officers on the learning environment.” Indeed, the New York Times recently reported the main effect of the policy so far has been “a surge in arrests or misdemeanor charges for essentially nonviolent behavior,” feeding the “school-to-prison pipeline.”

CRS isn’t dramatically more optimistic about the likelihood that enhanced mental health services in the schools will avert school shootings. Only four of the 78 incidents they identified since 1983 involved high schoolers or middle schoolers as assailants. They quote a National Institute of Justice report noting “[t]here is no accurate or useful profile of ‘the school shooter.’ ”

The CRS report doesn’t look at gun control, focusing instead on federal health and safety policy with regard to mass shootings. But, as my colleague Bob Levy pointed out recently, “the two most exhaustive studies on gun control were conducted by the National Academy of Sciences and the Centers for Disease Control,” in 2004 and 2003, respectively.

Neither NAS nor CDC could identify any regulation that meaningfully reduced gun violence. Levy notes that “random multi-victim killings are a fraction of 1 percent of all murders in the U.S.” If it’s difficult to show that gun control positively affects that larger class, it’s well-nigh impossible to conclude it will impact the much smaller one.

In the CRS report’s conclusion, the authors underscore the “overarching difficulty confronting experts interested in crafting policy to address mass shootings. Essentially, baseline metrics gauging the effectiveness of policies to thwart public mass shootings are often unclear or unavailable.”

H.L. Mencken put it more starkly: “The fact that I have no remedy,” the libertarian gadfly and journalist wrote in 1956, “is no reason for my accepting yours. It simply supports the strong probability that yours is a fake.”