The new methodology, introduced in 2008 and based on recommendations from the National Academy of Sciences, also factored in noncash benefits such as food stamps and tax credits.

What emerged was a new landscape of hardship. Poverty dipped in places like the South Bronx and hardscrabble corners of Brooklyn, where subsidized housing and government assistance cushion the poorest of the poor. But it rose in places like Queens and Staten Island, where low-wage workers struggle to pay market-rate rents, earning too much to qualify for most benefits, but too little to get by.

“It changes, to a degree, our vision of poverty across neighborhoods,” Dr. Levitan said. “Poverty is less concentrated geographically. It is more widespread across the city.”

That kind of talk might give any mayor heartburn. But Dr. Levitan, 65, who spent a decade as an analyst at the Community Service Society, a research and advocacy group, before joining the city, said he never worried about losing Mr. Bloomberg’s support. (Nor did he fret over what the mayor might think of his son working as a spokesman for Mr. de Blasio’s campaign.)

In 2010, the Obama administration said it would adopt a version of New York’s model as a companion to the federal formula. In April, when Dr. Levitan issued his annual report, Mr. de Blasio took notice.

Mr. Bloomberg’s aides and others say the mayor deserves credit for creating the Center for Economic Opportunity, which houses Dr. Levitan’s research unit and other antipoverty initiatives focused on education and jobs, including a $130 million program to assist black and Latino men. They also point to the construction of 50,000 units of affordable housing, among other efforts.

But Mr. de Blasio and others say more needed to be done. The fact remains, according to Dr. Levitan’s measure, that poverty is higher than it was in 2008, which highlights the challenges facing the incoming mayor.