The tax overhaul that New York state passed this week has been widely described in news reports as raising taxes on the rich and cutting them for the middle class — even as a win for Occupy Wall Street protesters and a possible blueprint for Congress.

But perhaps New Yorkers need to take a closer look.

Under the overhaul, which was passed on Thursday, one bracket of wealthy New Yorkers will get a bigger tax cut than the taxpayers in any other bracket. Specifically, individuals making between $500,000 and $2 million will pay 2.12 percent less in state income taxes for 2012. In contrast, individuals making between $40,000 and $150,000 are only getting a reduction of 0.4 percent, as this New York Times chart shows.

So why are the tax-code changes being cast as a win for the middle class? As is often the case when cutting through political spin, it comes down to baselines used for calculating the differences year to year.

New York Gov. Andrew Cuomo — and apparently much of the media — have been using New York’s base rate of 6.85 percent to calculate the “raised” taxes for the rich. But for the past three years, New Yorkers making more than $200,000 (or $300,000 for households) have paid the base rate along with an income-tax surcharge on top of it. It’s also known as the “millionaires’ tax,” and it expires at the end of this year.

Here’s what the tax package, known as the Fair Tax Plan, would actually do if you look at the effective tax rates and not just the base tax rate (a modified version of The Times’ chart):

Household Income 2011 2012 Difference
$40k-$150k 6.85% 6.45% -0.4%
$150k-$300k 6.85% 6.65% -0.2%
$300k-$500k 6.85+surtax=7.85% 6.85% -1%
$500k-$2M 6.85+surtax=8.97% 6.85% -2.12%
$2M+ 6.85+surtax=8.97% 8.82% -0.15%

Cuomo has said he believes the tax overhaul will help to close the state’s deficit and stimulate the economy by cutting taxes for the middle class. And it’s true; his tax plan indeed has the wealthy paying more than they would if the surtax had been allowed to expire.

But in reality, as The Times points out a few paragraphs into its story, the cuts for individuals in the lower tax brackets are modest, and the revenue to be produced by the tax-code changes — projected at about $1.9 billion — is about half of the $4 billion raised annually by the expiring surtax.