officers at one end of the curve, a small number at the other end, and the bulk of the problem situated in the middle. The bell-curve assumption has become so much a part of our mental architecture that we tend to use it to organize experience automatically.

But when the LAPD was investigated by a special commission headed by Warren Christopher, a very different picture emerged. Between 1986 and 1990, allegations of excessive force or improper tactics were made against eighteen hundred of the eighty-five hundred officers in the LAPD. The broad middle had scarcely been accused of anything. Furthermore, more than fourteen hundred officers had only one or two allegations made against them—and bear in mind that these were not proven charges, that they happened in a four-year period, and that allegations of excessive force are an inevitable feature of urban police work. (The NYPD receives about three thousand such complaints a year.) A hundred and eighty-three officers, however, had four or more complaints against them, forty-four officers had six or more complaints, sixteen had eight or more, and one had sixteen complaints. If you were to graph the troubles of the LAPD, it wouldn’t look like a bell curve. It would look more like a hockey stick. It would follow what statisticians call a power law distribution—where all the activity is not in the middle but at one extreme.

The Christopher Commission’s report repeatedly comes back to what it describes as the extreme concentration of problematic officers. One officer had been the subject of thirteen allegations of excessive use of force, five other complaints, twenty-eight “use of force reports” (that is, documented internal accounts of inappropriate behavior), and one shooting. Another had six excessive-force complaints, nineteen other complaints, ten use-of-force reports, and three shootings. A third had twenty-seven use-of-force reports, and a fourth had thirty-five. Another had a file full of complaints for doing things like “striking an arrestee on the back of the neck with the butt of a shotgun for no apparent reason while the arrestee was kneeling and handcuffed,” beating up a thirteen-year-old juvenile, and throwing an arrestee from his chair and kicking him in the back and side of the head while he was handcuffed and lying on his stomach.

The report gives the strong impression that if you fired those forty-four cops, the LAPD would suddenly become a pretty well-functioning police department. But the report also suggests that the problem is tougher than it seems, because those forty-four bad cops were so bad that the institutional mechanisms in place to get rid of bad apples clearly weren’t working. If you made the mistake of assuming that the department’s troubles fell into a normal distribution, you’d propose solutions that would raise the performance of the middle—like better training or better hiring—when the middle didn’t need help. For those hard-core few who did need help, meanwhile, the medicine that helped the middle wouldn’t be nearly strong enough.

In the 1980s, when homelessness first surfaced as a national issue, the assumption was that the problem fit a normal distribution: that the vast majority of the homeless were in the same state of semipermanent distress. It was an assumption that bred despair: if there were so many homeless, with so many problems, what could be done to help them? Then, in the early 1990s, a young Boston College graduate student named Dennis Culhane lived in a shelter in Philadelphia for seven weeks as part of the research for his dissertation. A few months later he went back and was surprised to discover that he couldn’t find any of the people he had recently spent so much time with. “It made me realize that most of these people were getting on with their own lives,” he said.

Culhane then put together a database—the first of its kind—to track who was coming in and out of the shelter system. What he discovered profoundly changed the way homelessness is understood. Homelessness doesn’t have a normal distribution, it turned out. It has a power-law distribution. “We found that eighty percent of the homeless were in and out really quickly,” he said. “In Philadelphia, the most common length of time that someone is homeless is one day. And the second most common length is two days. And they never come back. Anyone who ever has to stay in a shelter involuntarily knows that all you think about is how to make sure you never come back.”

The next 10 percent were what Culhane calls episodic users. They would come for three weeks at a time, and return periodically, particularly in the winter. They were quite young, and they were often heavy drug users. It was the last 10 percent—the group at the farthest edge of the curve—that interested Culhane the most. They were the chronically homeless, who lived in the shelters, sometimes for years at a time. They were older. Many were mentally ill or physically disabled, and when we think about homelessness as a social problem—the people sleeping on the sidewalk, aggressively panhandling, lying drunk in doorways, huddled on subway grates and under bridges— it’s this group that we have in mind. In the early 1990s, Culhane’s database suggested that New York City had a quarter of a million people who were homeless at some point in the previous half decade—which was a surprisingly high number. But only about twenty-five hundred were chronically homeless.

It turns out, furthermore, that this group costs the health-care and social-services systems far more than anyone had ever anticipated. Culhane estimates that in New York at least $62 million was being spent annually to shelter just those twenty-five hundred hard-core homeless. “It costs twenty-four thousand dollars a year for one of these shelter beds,” Culhane said. “We’re talking about a cot eighteen inches away from the next cot.” Boston Health Care for the Homeless Program, a leading service group for the homeless in Boston, recently tracked the medical expenses of a hundred and nineteen chronically homeless people. In the course of five years, thirty-three people died and seven more were sent to nursing homes, and the group still accounted for 18,834 emergency-room visits—at a minimum cost of $1,000 a visit. The University of California, San Diego, Medical Center followed fifteen chronically homeless inebriates and found that over eighteen months, those fifteen people were treated at the hospital’s emergency room 417 times, and ran up bills that averaged $100,000 each. One person—San Diego’s counterpart to Murray Barr—came to the emergency room eighty-seven times.

“If it’s a medical admission, it’s likely to be the guys with the really complex pneumonia,” James Dunford, the city of San Diego’s emergency medical director and the author of the observational study, said. “They are drunk and they aspirate and get vomit in their lungs and develop a lung abscess, and they get hypothermia on top of that, because they’re out in the rain. They end up in the intensive-care unit with these very complicated medical infections. These are the guys who typically get hit by cars and buses and trucks. They often have a neurosurgical catastrophe as well. So they are very prone to just falling down and cracking their head and getting a subdural hematoma, which, if not drained, could kill them, and it’s the guy who falls down and hits his head who ends up costing you at least fifty thousand dollars. Meanwhile, they are going through alcohol withdrawal and have devastating liver disease that only adds to their inability to fight infections. There is no end to the issues. We do this huge drill. We run up big lab fees, and the nurses want to quit, because they see the same guys come in over and over, and all we’re doing is making them capable of walking down the block.”

The homelessness problem is like the LAPD’s bad-cop problem. It’s a matter of a few hard cases, and that’s good news, because when a problem is that concentrated you can wrap your arms around it and think about solving it. The bad news is that those few hard cases are hard. They are falling-down drunks with liver disease and complex infections and mental illness. They need time and attention and lots of money. But enormous sums of money are already being spent on the chronically homeless, and Culhane saw that the kind of money it would take to solve the homeless problem could well be less than the kind of money it took to ignore it. Murray Barr used more health-care dollars, after all, than almost anyone in the state of Nevada. It would probably have been cheaper to give him a full-time nurse and his own apartment.

The leading exponent for the power-law theory of homelessness is Philip Mangano, who, since he was appointed by President Bush in 2002, has been the executive director of the US Interagency Council on Homelessness, a group that oversees the programs of twenty federal agencies. Mangano is a slender man, with a mane of white hair and a magnetic presence, who got his start as an advocate for the homeless in Massachusetts. He is on the road constantly, crisscrossing the United States, educating local mayors and city councils about the real shape of the homelessness curve. Simply running soup kitchens and shelters, he argues, allows the chronically homeless to remain chronically homeless. You build a shelter and a soup kitchen if you think that homelessness is a problem with a broad and unmanageable middle. But if it’s a problem at the fringe it can be solved. So far, Mangano has convinced more than two hundred cities to radically reevaluate their policy for dealing with the homeless.

“I was in St. Louis recently,” Mangano said, back in June, when he dropped by New York on his way to Boise, Idaho. “I spoke with people doing services there. They had a very difficult group of people they couldn’t reach no matter what they offered. So I said, ‘Take some of your money and rent some apartments and go out to those people, and literally go out there with the key and say to them, “This is the key to an apartment. If you come with me right now I am going to give it to you, and you are going to have that apartment.” ’ And so they did. And one by one those people were coming in. Our intent is to take homeless policy from the old idea of funding programs that

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