Down but not quite out, these Americans form a diverse group sometimes called “near poor” and sometimes simply overlooked — and a new count suggests they are far more numerous than previously understood.

When the Census Bureau this month released a new measure of poverty, meant to better count disposable income, it began altering the portrait of national need. Perhaps the most startling differences between the old measure and the new involves data the government has not yet published, showing 51 million people with incomes less than 50 percent above the poverty line. That number of Americans is 76 percent higher than the official account, published in September. All told, that places 100 million people — one in three Americans — either in poverty or in the fretful zone just above it…

Patched together a half-century ago, the official poverty measure has long been seen as flawed. It ignores hundreds of billions the needy receive in food stamps, tax credits and other programs, and the similarly large sums paid in taxes, medical care and work expenses. The new method, called the Supplemental Poverty Measure, counts all those factors and adjusts for differences in the cost of living, which the official measure ignores…

Of the 51 million who appear near poor under the fuller measure, nearly 20 percent were lifted up from poverty by benefits the official count overlooks. But more than half were pushed down from higher income levels: more than eight million by taxes, six million by medical expenses, and four million by work expenses like transportation and child care.