If people made better decisions, fewer people would keep guns in their homes.

Imagine that you are hospitalized, reading consent forms, and trying to choose between two operations. Operation A works 99.999967% of the time. Yet in very rare cases the surgeon’s hand slips, leading your right eyeball to squirt free of its socket and to slide down the side of your face, leaving a brown oozing trail down your cheek before your eyeball falls to the floor. Operation B works 99.994% of the time. Yet in the remaining random and rare cases, Operation B aggravates existing macular degeneration leading to blindness in the right eye.

Does your gut lead you to prefer Operation B over Operation A? Mine does. But my gut is wrong.

I fell prey to a mental mistake explored by the great cognitive psychologists Amos Tversky and Daniel Kahneman. That mistake is called the availability heuristic. We tend to regard especially vivid or scary outcomes as more likely than they actually are. We are especially horrible at evaluating or comparing rare probabilities of scary, psychologically freighted risks. Operation B is roughly 180 times as risky as Operation A. But boy, it sure doesn’t seem like it.

Which brings me to the subject of keeping a gun in your home. Having a gun at hand might sometimes avert a tragedy. It sometimes increases the risk of tragedy, too. We saw the worst possibility in Newtown, Ct. Early speculation includes the possibility that Nancy Lanza bought a deadly arsenal for protection, with utterly horrible results.

Home protection provides a common, all-too-understandable motive to buy a gun. Few things are scarier than the possibility that some violent intruder will break in when you and your loved-ones are home. This risk happens to be especially vivid for me. My gentle disabled cousin was beaten to death by two teenage burglars in his New York apartment thirty years ago.

Yet having guns around bring risks, too. Practically speaking, it’s not the incredibly rare risk of mass homicide, but the everyday risks of injury, accident, domestic altercations, and suicide. The relative risks matter. And the fact is: lethal home invasions and burglaries are incredibly rare.  You might not think so, since dramatic cases stick in your mind and tend to receive disproportionate press coverage. These cases are rare nonetheless.

How rare? I asked researchers at the Chicago Police Department and my colleague Daniel Rosenbaum at the University of Chicago Crime Lab to track down some numbers. In 2011, Chicago experienced 433 murders. Precisely one Chicago homicide that year was listed under the motive of “burglary.” Another seventeen were listed as domestic altercations. Some of these might have involved a nonresident partner entering someone’s home.  You get the point. These are really unusual crimes, even in a pretty tough city.

The Bureau of Justice Statistics reports about 100 homicides per year across America that happen in the course of household burglaries. That’s less than 1 percent of U.S. homicides. Yeah, that’s about one-180^th of the 18,735 gun suicides that occurred in America in 2009. Many people who attempt suicide can be helped—unless they have immediate access to the most efficient and lethal method of self-harm.  Then of course there are gun accidents and crimes committed by legal gun owners or by others who gain access to those same guns.

We are so afraid of each of each other, more afraid than we actually need to be. These fears are especially tragic because they so lead us astray. Because we fear the wrong things, we make the wrong decisions. In guarding ourselves against remote and vivid dangers, we make ourselves more vulnerable to other dangers, closer to home, that are so much more likely to leave us dead.