Studies show that even people who have been diagnosed with a serious disability — like schizophrenia—are only slightly more prone to violent behavior than the general population. Under the influence of drugs and alcohol, the mentally ill are more likely to turn violent, but then again, so is the average person.

“You could come up with a descriptive profile of all the people who have perpetrated mass shootings like this. And you’d get a description of troubled young men that matches the description of thousands of other troubled young men that never do this,” said Jeffrey Swanson, professor in Psychiatry and Behavioral Sciences at Duke University.

Troubled young people certainly need more help than many get now, and improving the mental-health care system is an important first step. Federal, state, and local officials can always do more to fund mental-health care programs in their communities, promote screening for mental illness in high schools, and encourage parents to be on the alert for violent tendencies in their children.

But even psychiatrists struggle to pinpoint who could turn violent.