The connection between mental illness and mass shootings is weak, at best, because while mentally ill people can sometimes be a danger to themselves or others, very little violence is actually caused by mentally ill people. When the assailants are mentally ill, the anecdotes tend to overshadow the statistics. Both Jared Loughner, who shot and severely injured Representative Gabrielle Giffords, and the Aurora, Colorado, shooter James Holmes, for example, had histories of mood disorders. But a study of convicted murderers in Indiana found that just 18 percent had a serious mental-illness diagnosis. Killers with severe mental illnesses, in that study, were actually less likely to target strangers or use guns as their weapon, and they were no more likely than the mentally healthy to have killed multiple people.

“If we were able to magically cure schizophrenia, bipolar disorder, and major depression, that would be wonderful,” Jeffrey Swanson, a professor of psychiatry and behavioral sciences at the Duke University School of Medicine, told ProPublica. “But overall violence would go down by only about 4 percent.”

One review paper published in 2014 found that though “a history of childhood abuse, binge drinking, and male gender” are all linked to serious violence, mental illness was not, unless the person was also a drug addict. According to the National Center for Health Statistics, fewer than 5 percent of the 120,000 gun-related killings in the United States between 2001 and 2010 were perpetrated by people diagnosed with a mental illness. A 2001 study of teen mass murders found that only one out of four was mentally ill.

As Northeastern University criminologist James Alan Fox has written, in a database of indiscriminate mass shootings—defined as those with four or more victims—compiled by the Stanford Geospatial Center, just 15 percent of the assailants had a psychotic disorder, and 11 percent had paranoid schizophrenia. (Other studies have come to a higher estimate, suggesting about 23 percent of mass killers are mentally ill.)

Certainly, getting those 15 or 23 percent into treatment might chip away at their pathological thinking—and thus their potential future acts of violence. But as Fox argues, linking psychopathic killers with the mental-health system is no easy task. After studying mass shooters for decades, he’s concluded that the killers have more mundane motivations: revenge, money, power, a sense of loyalty, and a desire to foment terror.

He explained further in a 2013 paper in the journal Homicide Studies:

Revenge motivation is, by far, the most commonplace. Mass murderers often see themselves as victims—victims of injustice. They seek payback for what they perceive to be unfair treatment by targeting those they hold responsible for their misfortunes. Most often, the ones to be punished are family members (e.g., an unfaithful wife and all her children) or coworkers (e.g., an overbearing boss and all his employees).

“The thing about mass killers is that they externalize blame,” Fox told me. “All the disappointments, all the failures, the broken relationships, are because other people treated them wrong. They don’t see themselves as being inadequate and flawed.” Indeed, a recent paper similarly concluded, “very few of persons [sic] in the risky category of having anger traits combined with gun access had ever been hospitalized for a mental-health problem.” That could be because they didn’t think they needed help.