When my grandfather learned I was going to college in New York City, he knew what to give me for a high-school graduation present: a hunting knife. If I was going to make it to class, he explained, I would probably have to defend myself. Never mind that this was 2002, and crime in New York City had plummeted since its high in the early 1990s. You could never be too careful.

His concern highlights the bizarre way we think about crime. Even as crime rates have gone down around the country over the last 20 years, our fear of crime hasn’t changed much at all. Between 1990 and 2009, the national violent-crime rate was halved, while property crime dropped to 60 percent of its previous rate, according to the National Archive of Criminal Justice Data. But almost every year since 1989, most Americans have told pollsters they believe crime is getting worse.

The disparity has been especially clear in New York City. That city saw the most dramatic crime decline of all: Since 1990, the homicide rate has dropped 82 percent, robbery by 84 percent, rape by 77 percent, and auto theft a stunning 94 percent, according to the New York Police Department. These numbers have now been confirmed in an independent study by Frank Zimring of the University of California, Berkeley, who confirms that the drop in crime is “real.”

But New Yorkers don’t feel correspondingly safer. “If you walk these streets, especially at night, you know crime is definitely not down,” a cab driver who lives in Harlem told the New York Daily News in 2009. “It’s not safe. I don’t know where they get these statistics.” Same with Baltimore, where a statistical decline in crime is no match for the occasional sensational murder that reinforces the city’s reputation as a dangerous town.

Zimring says it’s typical for people to ignore drops in crime. “[T]he recent public reaction to New York’s epidemic of public safety is rather complacent,” he writes in a summary of his new study. “In one sense, this is understandable—crime statistics only command attention when citizens are worried about crime just as people only think about dentists when their teeth hurt.”

Part of the reason is that most people can’t measure the crime rate accurately based on their own experience. While you may be twice as safe statistically speaking, the odds of getting assaulted at any given moment have merely gone from very small to extraordinarily small. Perception of crime has less to do with overall trends than those in your immediate vicinity, says Daniel Lewis, a professor of social policy at Northwestern University. The places with the most crime feel crime drops most dramatically. “Most of the bad stuff happens to people in poor neighborhoods,” says Lewis. “It doesn’t happen on Fifth Avenue or the Gold Coast in Chicago. But if you’re living in Harlem today, it’s a really different place than it was in 1990.”

It also matters who you are. Old people are typically more scared of crime than young people—even though they’re the demographic least likely to be victimized. Women are generally more worried about crime than men. Fear of rape in particular has little relationship with the statistical risk, says Lewis. Personal experience is a big factor, too. Even if the crime rate drops by half, you’re more likely to feel scared if your best friend gets assaulted.

One possible reason fear of crime remains high is that powerful people have an incentive to ring the alarms anyway. Politicians score points by promising to get “tough on crime,” even after those efforts pay off and crime levels hit historic lows. Media play up only the most horrifying deeds. The result is a skewed perception of how dangerous the world is. It’s telling, though, that most people believe the danger is not on their doorstep, but beyond it. Fewer people say crime is up when asked about their area than when asked about the whole country.

Another reason for the perception gap is the constant sense that things are getting worse. Only during one short period in the last 20 years have Americans thought there was less crime than in the past. That was in the two years after Sept. 11, 2001. “People were so positive about America that I think the enemy was perceived to be much more outside the country than inside the country,” a Gallup pollster told the Boston Globe.

Keep in mind, too, that perceptions of crime lag behind crime itself. Crime went down for several years starting in 1991, but fear remained high. “That was the nastiest and most fearful period in history,” says Zimring. Congress passed a federal “truth in sentencing” law in 1994. About half of the states passed “three strikes” laws to punish habitual offenders. All this, even though crime was already on the decline.

Some criminologists think the causal relationship between fear of crime and actual crime is actually the reverse—that fear of crime itself leads to more actual crime. The “broken windows” theory of criminology, made famous by Rudy Giuliani in the 1990s, posits that police can deter serious crimes by enforcing less serious ones. If someone jumps the subway turnstile and the police chase him down, that contributes to the sense that crime is punished and the social order is preserved—which might make a would-be murderer think twice. This notion that when society feels more safe, it is more safe, is a win-win for politicians: They can take credit for reducing crime and reap the benefit of a safer-feeling city. But the fact that crime has dropped while fear of crime remains high shows once again that the relationship is more complicated than the theory suggests.

Fear of crime isn’t entirely bad, from a risk-management perspective. Someone who’s scared of being assaulted is less likely to leave the house, thus lessening the likelihood of assault. Or maybe they just avoid the street corners that make them most nervous. No matter how far the crime rate falls, these perceptions could still reduce personal risk on the margins. The problem is, shrinking from crime doesn’t make it go away. It merely deflects the danger onto someone else. Fear might work as a personal strategy; it doesn’t work as a societal one.

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