As much as mental health experts and criminologists may point to all these "warning signs" in the behavior of mass killers after a tragedy such as the Newtown shootings, the reality is that there are hundreds of thousands of people who fit that profile, Levin said. It's very hard to predict who will commit such a crime.
Planning for a crime
Carrying out planning rules out a diagnosis of psychosis, which is associated with a disconnect from reality, Garbarino said.
"The overwhelming majority of mass killers are not psychotic, and they're quite methodical in the way they commit an execution of the people they feel are responsible for their problems," Levin said.
Many shooters do appear to plan their attack over time, Ash said. From a passing thought, they become obsessed with revenge fantasies. They will read about previous shootings online; the websites they read may hint at what they're planning. From there, they move toward scoping out a location and deciding what they will wear.
That assassinations occur after a planning process like this is an insight from the U.S. Secret Service, Ash said. If agents come across someone who has been tracking the president's movements for six months, that's a much higher-risk situation than someone who just has an idea about attacking.
In the April 20, 1999, Columbine High School shootings, Harris and Klebold had clearly done significant planning. Officials found a piece of notebook paper "showing a diagram of the Columbine High School cafeteria with two X's next to the pillars," and a list of how many people were there before and after the first lunch period, the sheriff's department said. Both boys had written an itinerary for the day of the shooting.
The largest single school shooting in U.S. history, which occurred at Virginia Tech in 2007, was perpetrated by Seung-Hui Cho. Cho had been declared mentally ill and "an imminent danger" to himself by a Virginia special justice, CNN reported in 2007.
The massacre, in which Cho killed 32 people before turning the gun on himself, was not spur-of-the-moment, either. During the two hours between the two shootings he committed at different dormitories on April 16, 2007, Cho mailed a package with 27 videotaped messages and an 1,800-word statement to NBC News. "You forced me into a corner and gave me only one option," he said in one of the videos.
Schizophrenia is a diagnosis that has come up in some instances of mass killings -- for instance, Jared Loughner, who killed six people and wounded former U.S. Rep. Gabrielle Giffords outside an Arizona supermarket in 2011.
Ted Kaczynski, the "Unabomber," received a diagnosis of schizophrenia from court-appointed psychiatrists. This is an especially likely diagnosis in cases when the shooter is in his late teens or early 20s, because symptoms often do not develop until that age, Levin said.
But in other cases, the shooters' "pathology" is more clearly tied to their situations, Levin said. They have given up hope for the future, and they seek revenge. They believe they are the victims, and the people they are shooting are villains.
School shooters specifically tend to come from middle- or upper-class families, Garbarino said. In poorer areas already rife with violence, kids with the same vulnerabilities may drop out of school or end up in the criminal justice system much earlier than in a resource-rich community, so school itself might hold less meaning for them.
"For school shooters, they're sort of emotionally living and dying in high school," Garbarino said.
Kipland P. Kinkel, a freshman at Thurston High School in Springfield, Oregon, killed his parents and two students in his school's cafeteria in 1998. His parents were both teachers. His family had taken him to therapy, concerned about his obsession with guns and explosives.
"They got every possible resource, and it still didn't work," Garbarino said.
Garbarino interviewed a young man who had brought guns and bombs to school on Valentine's Day of his senior year of high school. The boy had studied the Columbine shooting and contemplated killing himself or his tormenters, who had been bullying him. Before he acted, a couple of girls saw him and found his behavior odd; one of them went to get a police officer. He surrendered and went to jail. He said in retrospect that he didn't want the girls to get hit if he started shooting.
School shootings by students dropped significantly after Columbine because schools took action to encourage everyone in their communities to bring threats to school officials' attention, Ash said.
"We've averted a number of mass killings at schools around the country in recent years because young people are beginning to inform when they hear one of their peers threatened in the hallway," Levin said. "They may inform a resource officer, a parent, a teacher, a school psychologist."