MASS killers like Elliot Rodger teach society all the wrong lessons about the connection between violence, mental illness and guns — and what we should do about it. One of the biggest misconceptions, pushed by our commentators and politicians, is that we can prevent these tragedies if we improve our mental health care system. It is a comforting notion, but nothing could be further from the truth.

And although the intense media attention might suggest otherwise, mass killings — when four or more people are killed at once — are very rare events. In 2012, they accounted for only about 0.15 percent of all homicides in the United States. Because of their horrific nature, however, they receive lurid media attention that distorts the public’s perception about the real risk posed by the mentally ill.

Anyone who watched Elliot Rodger’s chilling YouTube video, detailing his plan for murderous vengeance before he killed six people last week near Santa Barbara, Calif., would understandably conflate madness with violence. While it is true that most mass killers have a psychiatric illness, the vast majority of violent people are not mentally ill and most mentally ill people are not violent. Indeed, only about 4 percent of overall violence in the United States can be attributed to those with mental illness. Most homicides in the United States are committed by people without mental illness who use guns.

Mass killers are almost always young men who tend to be angry loners. They are often psychotic, seething with resentment and planning revenge for perceived slights and injuries. As a group, they tend to avoid contact with the mental health care system, so it’s tough to identify and help them. Even when they have received psychiatric evaluation and treatment, as in the case of Mr. Rodger and Adam Lanza, who killed 20 children and seven adults, including his mother, in Connecticut in 2012, we have to acknowledge that our current ability to predict who is likely to be violent is no better than chance.