But the criminologists and psychologists who study mass killings aren't so baffled. While news reports often define mass shootings solely by body count, researchers instead look at qualitative traits like the psychology of the perpetrator, his relationship to the victims and how he carries out the crime.
Building on Dr. Dietz's seminal 1986 article on mass murder in the Bulletin of the New York Academy of Medicine, researchers have used these characteristics to develop a taxonomy of mass killing outside of warfare. The major types include serial, cult, gang, family and spree killings.
But it is another kind that dominates the headlines: the massacre or rampage shooting. Whereas the other types of mass murder usually occur in multiple incidents or in a concealed manner, massacres occur as a single, typically very public event.
In 2004, Paul E. Mullen, then the director of the Victorian Institute of Forensic Mental Health, wrote an illuminating study based in part on his personal interviews with rampage shooters who survived their acts. He notes that rampage shootings tend to follow a definite pattern, what he called a "program for murder and suicide."
The shooter, almost always a young man, enters an area filled with many people. He is heavily armed. He may begin by targeting a few specific victims, but he soon moves on to "indiscriminate killings where just killing people is the prime aim." He typically has no plan for escape and kills himself or is killed by police.
Among the more pervasive myths about massacre killers is that they simply snap. In fact, Dr. Mullen and others have found that rampage shooters usually plan their actions meticulously, even ritualistically, for months in advance. Like serial killers, massacre killers usually don't have impulsive personalities; they tend to be obsessive and highly organized.
Survivors typically report that the shooters appear to be not enraged but cold and calculating.
Central to the massacre pattern is the killer's self-styling.
James L. Knoll IV, the director of forensic psychiatry at the State University of New York's Upstate Medical University, describes in a 2010 article how perpetrators often model themselves after commandos, wearing military dress or black clothing. Investigators usually find they had a lifelong fascination with weaponry, warfare, and military and survivalist culture.
Their methodical comportment during the act is part of this styling.
Contrary to the common assumption, writes author Michael D. Kelleher in his 1997 book "Flash Point," mass killers are "rarely insane, in either the legal or ethical senses of the term," and they don't typically have the "debilitating delusions and insidious psychotic fantasies of the paranoid schizophrenic."
Dr. Knoll affirms that "the literature does not reflect a strong link with serious mental illness."
Instead, massacre killers are typically marked by what are considered personality disorders: grandiosity, resentment, self-righteousness, a sense of entitlement. They become, says Dr. Knoll, " 'collectors of injustice' who nurture their wounded narcissism." To preserve their egos, they exaggerate past humiliations and externalize their anger, blaming others for their frustrations. They develop violent fantasies of heroic revenge against an uncaring world.
Whereas serial killers are driven by long-standing sadistic and sexual pleasure in inflicting pain, massacre killers usually have no prior history of violence.
Instead, writes Eric W. Hickey, dean of the California School of Forensic Studies, in his 2009 book "Serial Murderers and Their Victims," massacre killers commit a single and final act in which violence becomes a "medium" to make a " 'final statement' in or about life."
Fantasy, public expression and messaging are central to what motivates and defines massacre killings.
Mass shooters aim to tell a story through their actions. They create a narrative about how the world has forced them to act, and then must persuade themselves to believe it. The final step is crafting the story for others and telling it through spoken warnings beforehand, taunting words to victims or manifestos created for public airing.