But mass killings are very rare events, and because people with mental illness contribute so little to overall violence, these measures would have little impact on everyday firearm-related killings. Consider that between 2001 and 2010, there were nearly 120,000 gun-related homicides, according to the National Center for Health Statistics. Few were perpetrated by people with mental illness.

Perhaps more significant, we are not very good at predicting who is likely to be dangerous in the future. According to Dr. Michael Stone, professor of clinical psychiatry at Columbia and an expert on mass murderers, “Most of these killers are young men who are not floridly psychotic. They tend to be paranoid loners who hold a grudge and are full of rage.”

Even though we know from large-scale epidemiologic studies like the E.C.A. study that a young psychotic male who is intoxicated with alcohol and has a history of involuntary commitment is at a high risk of violence, most individuals who fit this profile are harmless.

Jeffrey Swanson, a professor of psychiatry at Duke University and a leading expert in the epidemiology of violence, said in an e-mail, “Can we reliably predict violence? ‘No’ is the short answer. Psychiatrists, using clinical judgment, are not much better than chance at predicting which individual patients will do something violent and which will not.”

It would be even harder to predict a mass shooting, Dr. Swanson said, “You can profile the perpetrators after the fact and you’ll get a description of troubled young men, which also matches the description of thousands of other troubled young men who would never do something like this.”

Even if clinicians could predict violence perfectly, keeping guns from people with mental illness is easier said than done. Nearly five years after Congress enacted the National Instant Criminal Background Check System, only about half of the states have submitted more than a tiny proportion of their mental health records.