Even before the death toll in last Friday’s school massacre in Newtown, Conn., was determined, politicians, pundits, and professors of varied disciplines were all over the news, pushing their proposals for change. Some talked about the role of guns, others about mental-health services, and still more about the need for better security in schools and other public places. Whatever their agenda and the passion behind it, those advocates made certain explicit or implied assumptions about patterns in mass murder and the profile of the assailants. Unfortunately, those assumptions do not always align with the facts.

Myth: Mass shootings are on the rise. Reality: Over the past three decades, there has been an average of 20 mass shootings a year in the United States, each with at least four victims killed by gunfire. Occasionally, and mostly by sheer coincidence, several episodes have been clustered closely in time. Over all, however, there has not been an upward trajectory. To the contrary, the real growth has been in the style and pervasiveness of news-media coverage, thanks in large part to technological advances in reporting.

Myth: Mass murderers snap and kill indiscriminately. Reality: Mass murderers typically plan their assaults for days, weeks, or months. They are deliberate in preparing their missions and determined to follow through, no matter what impediments are placed in their path.

Myth: Enhanced background checks will keep dangerous weapons out of the hands of these madmen. Reality: Most mass murderers do not have criminal records or a history of psychiatric hospitalization. They would not be disqualified from purchasing their weapons legally. Certainly, people cannot be denied their Second Amendment rights just because they look strange or act in an odd manner. Besides, mass killers could always find an alternative way of securing the needed weaponry, even if they had to steal from family members or friends.

Myth: Restoring the federal ban on assault weapons will prevent these horrible crimes. Reality: The overwhelming majority of mass murderers use firearms that would not be restricted by an assault-weapons ban. In fact, semiautomatic handguns are far more prevalent in mass shootings. Of course, limiting the size of ammunition clips would at least force a gunman to pause to reload or switch weapons.

Myth: Greater attention and response to the telltale warning signs will allow us to identify would-be mass killers before they act. Reality: While there are some common features in the profile of a mass murderer (depression, resentment, social isolation, tendency to blame others for their misfortunes, fascination with violence, and interest in weaponry), those characteristics are all fairly prevalent in the general population. Any attempt to predict would produce many false positives. Actually, the telltale warning signs come into clear focus only after the deadly deed.

Myth: Widening the availability of mental-health services and reducing the stigma associated with mental illness will allow unstable individuals to get the treatment they need. Reality: With their tendency to externalize blame and see themselves as victims of mistreatment, mass murderers perceive the problem to be in others, not themselves. They would generally resist attempts to encourage them to seek help. And, besides, our constant references to mass murderers as “wackos” or “sickos” don’t do much to destigmatize the mentally ill.

Myth: Increasing security in schools and other places will deter mass murder. Reality: Most security measures will serve only as a minor inconvenience for those who are dead set on mass murder. If anything, excessive security and a fortress-like environment serve as a constant reminder of danger and vulnerability.

Myth: Students need to be prepared for the worst by participating in lockdown drills. Reality: Lockdown drills can be very traumatizing, especially for young children. Also, it is questionable whether they would recall those lessons amid the hysteria associated with an actual shooting. The faculty and staff need to be adequately trained, and the kids just advised to listen to instructions. Schools should take the same low-key approach to the unlikely event of a shooting as the airlines do to the unlikely event of a crash. Passengers aren’t drilled in evacuation procedures but can assume the crew is sufficiently trained.

Myth: Expanding “right to carry” provisions will deter mass killers or at least stop them in their tracks and reduce the body counts. Reality: Mass killers are often described by surviving witnesses as being relaxed and calm during their rampages, owing to their level of planning. In contrast, the rest of us are taken by surprise and respond frantically. A sudden and wild shootout involving the assailant and citizens armed with concealed weapons would potentially catch countless innocent victims in the crossfire.

Myth: We just need to enforce existing gun laws as well as increase the threat of the death penalty. Reality: Mass killers typically expect to die, usually by their own hand or else by first responders. Nothing in the way of prosecution or punishment would divert them from their missions. They are ready to leave their miserable existence, but want some payback first.

In the immediate aftermath of the Newtown school shootings, there seems to be great momentum to establish policies and procedures designed to make us all safer. Sensible gun laws, affordable mental-health care, and reasonable security measures are all worthwhile, and would enhance the well-being of millions of Americans. We shouldn’t, however, expect such efforts to take a big bite out of mass murder. Of course, a nibble or two would be reason enough.