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It is 15 below zero – using what US meteorologists call RealFeel temperature – in Brooklyn’s notorious Marcy Projects. The cold has driven the drug dealers off the streets; police, who have taken to patrolling in fours since two officers were gunned down in a police car last December, are scarce; and at the Ponce Funeral Home the trade is all of the natural-causes kind.

Although there was an attempted murder in Queens on Friday that left a man on life-support, New York has enjoyed an almost unprecedented 12-day streak without a homicide. While many pointed to the weather, the embattled New York mayor, Bill de Blasio, sought to improve his strained relationship with the police department, attributing the lull to its hard work.

After months dominated by allegations that US law enforcement is reckless in the use of deadly force, especially when it comes to African-American men, there’s a new criminal-justice narrative: US crime rates are falling, often dramatically, even as incarceration rates begin to level off.

The changes are apparent even in Marcy Projects, the neighborhood made famous by homeboy Shawn Carter, aka Jay-Z, who used to describe it in songs such as Murda Marcyville.

“Thirty-some odd years ago I’d find dead people on my corner when I came to work,” recalls a community guard who gave her name only as Deborah. In 1990 there were 71 murders here; in 2012 there was just one. “It’s calmed down a lot. Mostly that’s ’cause of the police. They’re more present now.”

The fall in crime in this part of the Bedford-Stuyvesant district is mirrored across the metropolis. In 2014 there were 333 murders in New York City, half the number committed in 2000 and a quarter of the 1,384 recorded in 1985.

While crime statistics are difficult to interpret – violent crimes such as rape and assault have not reduced so markedly – the trend overall is repeated across the US. From its peak in 1991, violent crime is down 51%; property crime 4% lower; and murder down 54%.

During that same time, incarceration nearly doubled. The US prison population now stands at 2.4 million – up 800% since 1980 – or roughly a quarter of the world’s total. The cost? About $80bn a year. The overall cost of the US criminal justice system is placed at $240bn, or about half of the federal deficit.

But according to What Caused the Crime Decline?, a study published last week by the Brennan centre for justice at New York University school of law, there is no definitive link between falling crime and mass incarceration.

The finding runs counter to previous studies claiming that incarceration accounts for as much as a third of the fall in crime. Once violent criminals were taken off the streets in the 1990s, the study claims, an additional 1.1 million low-level or non-violent offenders were jailed without any further benefit.

“The rate of incarceration has passed even the point of diminishing returns and now makes no effective difference,” said Oliver Roeder, one of the study’s three authors.

The Brennan research looked closely at theories to explain the decline, from the legalisation of abortion to the introduction of unleaded petrol, the growth in income and employment, to changes in alcohol consumption and an ageing population. Of 14 factors that might explain some of the drop, “even adding all of them together fails to explain the majority of the decrease”, the authors concluded.

Perhaps significantly, the study comes at a moment of increasing political will in Washington to reform the criminal justice system.

Last year the US Sentencing Commission agreed that nearly 50,000 federal drug offenders would be made eligible for reduced sentences, while low-level, non-violent drug offenders would no longer be charged with offences that carried severe mandatory sentences.

Even in tough-on-crime Texas, where one in every 10 US prisoners is held, incarceration levels have started to decline from a peak prison population approaching 200,000.

The US attorney general, Eric Holder, who has described the criminal justice system as “in many ways broken”, recently highlighted a small decline in the federal prison population as a breakthrough for advocates of reform.

“High incarceration rates and longer-than-necessary prison terms have not played a significant role in materially improving public safety, reducing crime or strengthening communities,” Holder said. And in his state of the union address last month, Barack Obama added his voice, saying the fall in crime and incarceration should be the “starting point” for reform.

At the same time the FBI director, James Comey, described US law enforcement as being “at a crossroads” after the shooting by police of Michael Brown in Ferguson, Missouri, and the choking to death of Eric Garner in New York that sparked nationwide protests last year. Comey acknowledged “hard truths” about racial bias in policing. He called for an “open and honest discussion about what our relationship is today – what it should be, what it could be, and what it needs to be”.

But trying to draw conclusions about the relationship between crime and crime prevention was fraught with uncertainty, warned Daniel Nagin, professor of public policy at Carnegie Mellon University in Pittsburgh.

“If I told you medicine cures disease, you’d say what medicine and what disease. Crime is the same. Trying to lump dozens of different policies together doesn’t make sense. It’s a precarious exercise, almost a form of cocktail-party conversation.” If there was an agreed strategy, he said, it was to focus police attention on crime hotspots, or even “hot people”, a technique developed for the New York subway system by Jack Maple, a bowtie and homburg-wearing traffic policeman who tracked the pattern of crimes on 55ft of maps pinned to a wall – “charts of the future” – and assigned officers accordingly.

Maple, who died in 2001, modelled what is now known as CompStat on the methods developed by Fighter Command to deploy resources against German bombers during the Battle of Britain. “Treat every case as if your mother was the victim,” Maple would advise the officers under him.

The Brennan study singled out CompStat, finding that data-driven analysis is used by 41 of the 50 largest cities in America and attributing it to a drop of between 5% and 15% in violent crime, property crime and murder wherever it is deployed.

Nagin believes CompStat is only a first step. Without the support of the community, even the most efficient policing can be ineffective. “Once you focus on a hotspot or hot person, the question is: what do you do, how you go about doing it, and what is the impact on the community?”

But the broad policy shift against further jailings must stand as a significant course correction in the odyssey of US criminal justice.

Near the spot where the two police officers, Rafael Ramos and Wenjian Liu, were shot by a man on a suicide mission to avenge Eric Garner and Michael Brown, a group of young African-American men milled around in the cold. Falling incarceration levels were news to them, but increased policing was not. “They got this place locked down,” said one of their number, Louis G. “They even put the lights up. Now nobody can do anything.”