“The only way to stop a bad guy with a gun is with a good guy with a gun,” National Rifle Association (NRA) executive vice president Wayne LaPierre infamously declared following the Newtown, Connecticut school shootings in 2012. The vision of armed heroes killing armed villains and preventing loss of life is a staple of the NRA narrative, as well as of Hollywood films. In Dallas, though, it didn’t work that way. Following a peaceful Black Lives Matter protest, at least one sniper opened fire on police. Despite the presence of armed law enforcement, the shooter did great harm before he could be stopped. As of reports this morning, five officers have been killed, seven more were injured, and two civilians were also injured.

Gun proponents often point to a handful of incidents in which bystanders with firearms have managed to stop mass shooters. In 2007, for example, a gunman killed four people at a church in Colorado Springs, Colorado and was then shot and disabled by church member Jeanne Assam, who is a security guard and former police officer. In 1997, a high school shooter in Pearl, Mississippi was subdued at gunpoint by an assistant principal who was a member of the Army Reserve.

Sometimes armed bystanders are able to capture a shooter. This is the exception rather than the rule.

It’s true that sometimes, in some situations, armed bystanders (often with some training) are able to wound or capture a shooter. This is the exception rather than the rule, however, according to an FBI study of active shooter incidents between 2000 and 2013 in the United States. As defined by the FBI, active shooter incidents are those in which a shooting is in progress, and in which police or civilians have a chance to affect the outcome.

According to the FBI, active shooter scenarios mostly end because the shooter decides to end them. Of the 160 recorded cases, 90 incidents (56.3%) ended with the shooter committing suicide, ceasing to shoot, or fleeing the scene. Another 21 incidents (13.1%) ended when unarmed civilians stopped or restrained the shooter. There were 5 incidents (3.1%) in which civilians with firearms shot at the shooter, and 2 incidents (1.3%) in which off-duty police officers killed the shooter.

That leaves 45 incidents (28.1%) in which law enforcement arrived on the scene with an active shooter and exchanged gunfire. The shooter was killed or wounded in 34 of these incidents, committed suicide in 9, and surrendered in 2.

It’s clear from the FBI’s active shooter report that most bad guys with guns are not stopped by good guys with guns.

It’s clear from the FBI’s active shooter report that, contra LaPierre, most bad guys with guns are not stopped by good guys with guns. Still, around 30% of active shooter incidents between 2000 and 2013 did involve police or—much less often—civilians exchanging fire with the shooter.

No doubt, LaPierre would argue that if more civilians had guns, more active shooter incidents would end more quickly, and therefore fewer people would be killed. This position isn’t supported by the data either. In the first place, even when civilians or police use firearms against a mass shooter, it’s not always clear that “good guy” shooting reduces loss of life. For example, friendly fire from SWAT teams may have been responsible for some of the deaths in the Orlando nightclub shooting.

In Dallas, though police exchanged gunfire with the suspect, the standoff wasn’t even ended with conventional firearms, but instead came to a conclusion when authorities detonated a robot-controlled bomb. This presents another slippery slope argument in terms of the use of force. Presumably, the NRA doesn’t believe that civilians should be provided with automated bombs as a way to deter mass shootings. But if guns aren’t enough to stop attackers, where do we draw the line in order to save lives?

Moreover, most studies find that more guns make people less safe.

Moreover, most studies find that more guns make people less safe. A 2014 study of gun restrictions found that loosening gun laws, and making firearms more available, did not reduce gun fatalities. Instead, tighter restrictions reduced deaths. In line with those findings, studies have found that high rates of gun ownership are correlated with high rates of firearm fatalities: In a 2013 study looking at firearm fatalities in 27 countries, the United States was found to have the most guns, and the most gun deaths. Within the US itself, states with the highest gun ownership rates also have the highest rates of gun deaths. Similarly, guns in the home don’t make people safer; instead they increase the likelihood that someone in the family will suffer a firearm fatality.

According to Liza Gold, professor of psychiatry at Georgetown University, there is no scientific evidence that guns prevent harm, “only occasional anecdotal reports of someone preventing a crime because a person had his or her own gun,” she says. “In contrast, there is overwhelming evidence that owning a gun increases risk of homicide and suicide for the gun owner and anyone else in the home, including partners and children.”

Between 2000 and 2013, the FBI calculated 486 deaths from active shooter incidents in the United States. That’s a heartbreaking number, but it’s dwarfed by the approximately 33,000 people killed by guns in 2013, according to the Centers for Disease Control. Most of those deaths (around 60%) are suicides. Accidents account for about another 5%. Homicides make up about 35% of gun deaths—but only a tiny percentage of those are mass shootings.

All the evidence suggests that, in most cases, guns do not defuse violent situations, but exacerbate them. It’s very likely that Alton Sterling and Philando Castille would both still be alive today if the police officers who stopped them had not been armed. Guns make it easier for everyone to kill, whether they are “bad guys” or “good guys,” whether deliberately or by accident, or whether they are aiming the gun at themselves or at others. There are far, far fewer gun-toting heroes than there are gun victims.

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Correction: A previous version of this post incorrectly stated the number of deaths attributed to gun violence in the US. There were approximately 33,000 people killed by gun violence in 2013.