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In short, what would happen if the rest of the country followed New York City's example?

As the American prison population has doubled in the past two decades, the city has been a remarkable exception to the trend: the number of its residents in prison has shrunk. Its incarceration rate, once high by national standards, has plunged well below the United States average and has hit another new low, as Mayor Michael R. Bloomberg announced recently. And crime in the city has fallen by more than 75 percent, almost twice as much as in the rest of the country.

Whatever has made New York the safest big city in America, that feat has certainly not been accomplished by locking up more criminals.

"The precise causes of New York's crime decline will be debated by social scientists until the Sun hits the Earth," said Michael Jacobson, a criminologist who ran the city's Correction and Probation Departments during the 1990s and is now the president of the Vera Institute of Justice, a criminal justice research group. "But the 50,000-foot story from New York is that you can drive down crime while decreasing your jail and prison population — and save a huge amount of money in the process."

New York's singular success has attracted attention across the country from public officials whose budgets have been strained by the prison boom. The 2.3 million people behind bars in America, a fifth of the world's prisoners, cost taxpayers more than $75 billion a year. The strict penal policies were intended to reduce crime, but they have led to a historic, if largely unrecognized, shift in priorities away from policing.

"The United States today is the only country I know of that spends more on prisons than police," said Lawrence W. Sherman, an American criminologist on the faculties of the University of Maryland and Cambridge University in Britain. "In England and Wales, the spending on police is twice as high as on corrections. In Australia it's more than three times higher. In Japan it's seven times higher. Only in the United States is it lower, and only in our recent history."

Before the era of mass incarceration began in the 1980s, local policing accounted for more than 40 percent of spending for criminal justice, while 25 percent went to prisons and parole programs. But since 1990, nearly 35 percent has gone to the prison system, while the portion of criminal justice spending for local policing has fallen to slightly more than 30 percent.

New York, while now an exception to the mass-incarceration trend, also happens to be the place that inspired it. When New York State four decades ago commissioned an evaluation of programs to rehabilitate criminals, the conclusions were so discouraging that the researchers were initially forbidden to publish them.

Eventually one of the criminologists, Robert Martinson, summarized the results in 1974 in the journal Public Interest. His article, "What Works? Questions and Answers About Prison Reform," was soon known as the "nothing works" thesis. Dr. Martinson concluded that rehabilitation strategies "cannot overcome, or even appreciably reduce, the powerful tendencies of offenders to continue in criminal behavior."

An outgrowth of the study was a consensus to eliminate parole for many offenders and to mandate long sentences determined by formulas rather than rely on the discretion of judges and parole boards.

Dr. Martinson wrote an article in 1979 recanting his "nothing works" conclusion, but by then it was too late. The trend toward tougher sentences continued, causing prison populations to grow rapidly in the 1980s throughout the country, including in New York. When crime kept rising anyway, sentences often were further lengthened.

But New York diverged from the national trend in the early 1990s, when it began expanding its police force and introduced a computerized system to track crimes and complaints. Officers also aggressively enforced laws against guns, illegal drugs and petty crimes like turnstile jumping in the subways. Arrests for misdemeanors increased sharply.

Yet serious crime went down. So though more people were being locked up for brief periods — including many who were unable to make bail and were awaiting trial — the local jail population was shrinking and fewer city residents were serving time in state prisons.

"Even with more people coming into the system, the overall bed count was declining because people weren't staying as long," Dr. Jacobson, who was correction commissioner from 1995 to 1998, recalled.

"It was a nightmare to administer because there was so much churning and turnover, but it was good news for the city."

Saving $1.5 Billion a Year

Even as the city grew by nearly a million people in the last two decades, the number of New Yorkers behind bars fell by a third, to below 40,000 today.

If the city had followed the national trend, nearly 60,000 additional New Yorkers would be behind bars today, and the number of city and state correction officers would have more than doubled since 1990, said Franklin E. Zimring, a criminologist at the University of California, Berkeley.

By not expanding the jail and prison populations, he calculates in his 2011 book, "The City That Became Safe," the city and the state have been saving $1.5 billion a year, more than twice as much as it cost to finance the additional police officers in the 1990s.

The crime decline, which has lasted for two decades, has been so striking that some critics wonder if the police stopped reporting some offenses. The police vehemently deny that, and numbers have continued dropping even for crimes that are difficult to hide — homicides, most notably.

Policing, of course, is not the only possible explanation for the safer streets. A shift in demographics, the arrival of new immigrants, the waning of the crack epidemic, and other economic and social changes had an impact on neighborhoods in New York — and in the rest of the country, where crime also declined in the 1990s.

But the drop was much steeper and more prolonged in New York than elsewhere. And while researchers attributed about a quarter of the decline in the rest of America to the stricter penal policies, that explanation did not apply to a city that was locking up fewer people. Something else was responsible, and criminologists have been trying to figure out how to repeat it.

"The intellectual tragedy of the New York crime miracle is that it had no experiments to identify just what worked," Dr. Sherman said.

His frustration is shared by David Weisburd, a criminologist at George Mason University in Virginia and Hebrew University in Jerusalem.

"As long as crime is going down, New York's police don't seem to want to know which strategies are working and which aren't," Dr. Weisburd said. "When I proposed an experiment to one police official in the last administration, he replied, 'You could only bring me bad news.' "

Elsewhere, studies have shown that crime drops when more police officers are hired, so it is not surprising that the expansion of New York's police force in the 1990s by more than a third was accompanied by a drop in crime. But during the past decade, the force has shrunk by 15 percent, and yet crime has mostly continued falling.

When Dr. Zimring and other criminologists look at this trend, and compare it with the fluctuating crime rates in other cities, they conclude that the retreat in crime in New York is not just a matter of the number of police officers. Those officers must be doing something right, but what exactly?

The most likely answer is a shift in strategy called hot-spot policing.

In the 1970s, research had shown that a small percentage of criminals committed a large share of crimes, so it had seemed logical to concentrate on catching repeat offenders and locking them up.

But after computerized crime mapping was introduced, it turned out that crime was even more concentrated by place than by person.

In city after city, researchers found that half of crimes occur within about 5 percent of an urban area — a few buildings, intersections and blocks, often near transit stops and businesses like convenience stores, bars and nightclubs.

The criminal population keeps changing as men in their 30s drop out and are replaced by teenagers, but crimes keep occurring at the same places.

A Focus on Hot Spots

Researchers suggested: Perhaps the authorities should pay less attention to individual criminals and more attention to the hot spots where they operate.

Dr. Sherman, Dr. Weisburd and colleagues have tested the idea in randomized experiments in Jersey City; Houston; Kansas City, Mo.; Minneapolis; Philadelphia; Sacramento; and cities in Britain and Australia.

Typically, a list of hot spots was identified, and then half were randomly chosen to receive extra police attention, like more frequent patrols. Other strategies were also used, like improving street lighting, fencing vacant lots or arresting people for minor violations.

As hoped, there were fewer crimes and complaints at the hot spots chosen for extra attention than at those that were not. And once police officers started to show up often and at unpredictable intervals, they did not need to stay more than 15 minutes to have a lasting impact.

Nonetheless, the hot-spot strategy was initially met with skepticism by police veterans.

"We assumed that if we hit one area hard, the crime would just move somewhere else," said Frank Gajewski, a former police chief of Jersey City, who worked with Dr. Weisburd on the experiments there.

But Dr. Weisburd won over Mr. Gajewski and other skeptics — and also won the 2010 Stockholm Prize, criminology's version of the Nobel — by showing that crime was not simply being displaced. Moreover, he and his colleagues reported a "spatial diffusion of crime prevention benefits" because crime also declined in adjoining areas, as the police in Jersey City had observed.

"Crime doesn't move as easily we thought it did," Mr. Gajewski said. "If I'm a robber, I want to be in a familiar, easily accessible place with certain characteristics. I need targets to rob, but I don't want people in the neighborhood watching me or challenging me. Maybe I work near a bus stop where there are vacant buildings or empty lots. If the police start focusing there, I can't just move to the next block and find the same conditions."

After more than two dozen experiments around the world, criminologists generally agree that hot-spot policing is "an effective crime prevention strategy," in the words of Anthony Braga, a criminologist at Harvard and Rutgers who led a review of the research literature last year.

Many experts also see it as the best explanation for the crime drop in New York. Although the city's police did not participate in randomized experiments, they did use computerized crime mapping to focus on hot spots in the 1990s. This strategy was intensified with a program called Operation Impact, which was started in 2003 by Raymond W. Kelly, then and now the police commissioner.

Commissioner Kelly gives the strategy credit for the continued decline of crime despite the reduced police force.

There is supporting evidence from Dennis C. Smith, a political scientist at New York University who led an analysis of trends in the dozens of precincts where the city's police focus on "impact zones," as the hot spots are called. Rates of murder, rape, grand larceny, robbery and assault declined significantly faster in precincts with hot-spot policing than in those without it.

The Stop-and-Frisk Debate

One part of the hot-spot strategy in New York has been highly controversial: the stopping and frisking of hundreds of thousands of people each year, ostensibly to search for weapons or other contraband.

Some critics say that the tactic has been used so often and so brusquely in New York that it has undermined policing by arousing disrespect for the law, especially among young black and Latino men, who are disproportionately stopped and searched. Research shows that people who feel treated unfairly by the police can become more likely to commit crimes in the future.

"The million-dollar question in policing right now is whether there are ways to get the benefits of stop-and-frisk without the collateral costs," said Jens Ludwig, an economist who directs the University of Chicago Crime Lab. He found benefits from the tactic — a decline in gunshot injuries — in an experiment with the Pittsburgh police.

"Getting the police to stop people more often and search them for illegal guns does help keep guns off the street and reduce gun violence," Dr. Ludwig said. "That's not to say whether or not stop-and-frisk is worth the costs that the practice imposes on society. But there's a complicated trade-off here that needs to be acknowledged."

Defenders of stop-and-frisk, including Mayor Bloomberg, argue that when it is done properly and politely, the practice prevents crimes that disproportionately hurt the city's minorities.

"If New York went back to the policing of the 1980s," Dr. Smith said, "there would be hundreds of thousands more victims of serious crimes every year, and the great majority of them would be African-American and Hispanic."

Police officials note that if the homicide rate of the 1980s persisted, 1,200 additional New Yorkers, most of them black or Latino men, would have been killed last year — when the police recorded 417 murders. Further, if the city's incarceration rate had followed the national trend, an additional 100,000 black and Hispanic men would have been sent to prison in the past decade, Dr. Zimring calculates.

Whether or not other cities adopt New York's specific stop-and-frisk tactics, social scientists say the rest of the country could benefit by adding police officers and concentrating on hot spots.

Dr. Ludwig and Philip J. Cook, a Duke University economist, calculate that nationwide, money diverted from prison to policing would buy at least four times as much reduction in crime. They suggest shrinking the prison population by a quarter and using the savings to hire another 100,000 police officers.

Diverting that money to the police would be tricky politically, because corrections budgets are zealously defended in state capitals by prison administrators, unions and legislators.

But there is at least one prison administrator, Dr. Jacobson, the former correction commissioner in New York, who would send the money elsewhere.

"If you had a dollar to spend on reducing crime, and you looked at the science instead of the politics, you would never spend it on the prison system," Dr. Jacobson said. "There is no better example of big government run amok."

That is the same lesson that William J. Bratton draws from his experience as New York's police commissioner in the 1990s. "We showed in New York that the future of policing is not in handcuffs," Mr. Bratton said. "The United States has locked up so many people that it has the highest incarceration rate in the world, but we can't arrest and incarcerate our way out of crime. We need to focus on preventing crime instead of responding to it."