Ninety-five percent of students from Battery Park City & TriBeCa (colored blue, above) graduate on time, compared to 61 percent in the Bronx district colored pink. (Courtesy Measure of America)

A child’s access to a decent education shouldn’t be limited by his Zip code. That mantra has helped drive the school choice movement during the past two decades, pushing a growing number of cities to embrace policies that allow children from poor families to escape troubled neighborhood schools and enroll elsewhere.

But has it worked? Has school choice been able to interrupt the strong link between home environments and academic success?

Not yet, according to a new analysis of New York City high school graduation rates. Researchers found that — a decade after the city adopted a universal school choice policy for high school students — a child’s likelihood of graduating on time remains tightly linked to the poverty rate, household income and adult educational attainment in that child’s neighborhood.

“On this measure, the well-known link between a student’s neighborhood conditions and educational outcomes is as strong as ever,” said Sarah Burd-Sharps of Measure of America, which conducted the analysis and is a project of the nonprofit Social Science Research Council.

New York City offers a real-life laboratory for questions of school choice: In 2004, the city did away with assigned neighborhood high schools. Instead, all eighth-graders choose 12 schools they’d like to attend, and they are accepted either on the basis of merit (in the case of selective schools) or luck in a citywide lottery.

The city’s overall graduation rate has climbed significantly and surpassed 70 percent for the first time in 2015. There were marked gaps between racial groups: 85 percent of Asian students and 82 percent of whites graduated on time, compared to just 65 percent of black students and 64 percent of Latinos.

Schools and states have been publicly reporting such racial achievement gaps for more than a decade. But neighborhood gaps are rarely studied or reported, and they cannot be understood using publicly available data.

Researchers at Measure of America — whose mission is to capture and publicize metrics of the nation’s well-being — requested student-level data to map graduation rates against New York City’s 59 community districts. They found an enormous range, from a 60.9 percent graduation rate in Bronx District 5 to a 95.1 graduation rate in Manhattan Districts 1 and 2, which includes Battery Park City, Greenwich Village and Soho.

That 34-point neighborhood gap was substantially larger than the racial achievement gaps.

The analysis doesn’t attempt to study the change in the neighborhood gap over time, so it’s possible that there have been improvements during the past decade as New York’s school choice policy has taken hold.

Burd-Sharps said that even if the gap is smaller than it used to be, it is still way too large. “And the cost to families is high,” she said.

The cost comes in the form of time and resources to visit open houses and navigate each school’s application requirements, not to mention the time and resources it takes for students to travel to schools far from their homes. Burd-Sharps said that the city needs to ask whether families have access to “real choice … or just choice theater.”

“They do literally have a choice from among every high school in New York City, but if they don’t have the time or the contacts or the understanding of how to work within the system, they don’t have real choice,” she said.

The analysis calls on New York City to reassess its approach to trying to change the lives of its neediest students, arguing that these students need more than a system of choice to overcome their difficult home circumstances.

“We often hear about smart, motivated teens from poor pockets of the city who have benefited from leaving underperforming schools behind. But what about those who have not benefited?” the authors wrote. “For them, the link between neighborhood conditions and school quality remains as strong as ever, even if the school they now attend is farther from home.”

The analysis was performed with Data2Go.NYC, a mapping and data website that Measure of America developed with funding from the Leona M. and Harry B. Helmsley Charitable Trust. Measure of America’s other funders are listed here.