Active shooter incidents are becoming more common, according to an FBI report released Wednesday.

The study defines "active shooter incident" as one involving "an individual or individuals actively engaged in killing or attempting to kill people in a populated area." An active shooter incident isn't exactly the same thing as a mass killing, which according to a new federal definition involves at least three fatalities. Only 40 percent of the incidents in the FBI report would qualify as mass killings. (Sidebar: How sad is it that our official vocabulary of killing has grown so complex and precise in recent years?)

Over the past seven years, we've averaged 16.4 active shooter incidents per year -- that's roughly one every three weeks. The study underscores just how fast these things typically happen: Among shootings whose duration could be ascertained, 69 percent were over in five minutes or less, and 36 percent were over in two minutes or less.

The majority of the incidents in the report -- 60 percent -- were over before police could arrive on the scene.

"Even when law enforcement was present or able to respond within minutes, civilians often had to make life and death decisions, and, therefore, should be engaged in training and discussions on decisions they may face," the report's authors write.

More than half of the incidents ended on the shooter's initiative, when the shooter either committed suicide, stopped shooting or fled the scene. Unarmed citizens were able to successfully restrain the shooters in 13 percent of the incidents, while armed citizens (not police offers) played a role in only 4 percent of incidents.

The NRA line that "the only thing that stops a bad guy with a gun is a good guy with a gun" did not prove accurate in this report. Unarmed citizens are three times more likely to stop an active shooter than armed citizens, the study shows. Most of those armed citizens, in turn, were actually armed private security guards.

The study also breaks down where active shooter incidents occur. Nearly half of the incidents happened at businesses or malls. Nearly a quarter happened at schools and universities, while another 10 percent took place on government properties. Only 4.4 percent happened at home.

Some researchers debate whether incidents like these are truly on the rise. Northeastern University criminologist James Alan Fox has long criticized what he sees as the overuse of the term "active shooter." In an e-mail, he said that "it is not clear whether the increase in active shooter events is completely related to the actual case count or to the availability and accessibility of news reports to identify such events, particularly those where few if any victims died."

Regardless of the overall trend, these events are still relatively rare. The overall rate of gun homicides is down sharply over the past 20 years, according to a Pew Research Center analysis. Active shooter incidents account for roughly three-tenths of one percent of all gun homicides in the United States.

But the FBI report is noteworthy for the detailed statistics it provides on the nature of these incidents. Perhaps the most disturbing finding is the nexus with domestic violence: