Almost none of this proved to be true. In fact, as Mr. Cullen notes, Columbine was less a successful school shooting than it was a failed school bombing. Harris, later deemed a psychopath by some psychologists, and Klebold, a suicidal depressive, did not seek out specific groups or individuals. They wanted to blow up the entire place and kill hundreds indiscriminately with a homemade propane bomb. But their device failed to detonate. Only then did they begin using the guns that had unlawfully been supplied to them by others.

Yet the “loner versus bullies” vengeance template came to be widely accepted and applied to later shootings. It can be the sort of facile notion that appeals to those eager for a rational theory to explain an action that is utterly irrational. It can also be unnerving. What high school does not have its share of student bullies and oddballs? Not surprisingly, some parents live in fear that their own children could become tomorrow’s victims.

How severe is the threat of school shootings? Certitudes are elusive. Some analyses show an increase over the years, others a decline. One complication is a dearth of research drawing on universally accepted data. Some studies include stabbings in the tally of shootings, or events that occur not on school grounds but nearby, or suicides, or accidental discharges of weapons, or gang fights bearing no resemblance to the Columbine-style massacres that people tend to think of when they hear of school shootings.