In 2011, Gallup’s polling showed that President Obama averaged an 80 percent approval rating among Democrats and 12 percent among Republicans, making his third year in office one of the most polarizing on record. For a candidate whose campaign promised an era of post-partisan unity, it must be a disappointing reality check.

But on Friday, political scientist Keith Poole released a study that probably cheered the White House. According to Poole’s highly respected classification system, Obama is the most moderate Democratic president since World War II. Which raises a question: How can Obama simultaneously be one of the most divisive and most moderate presidents of the past century?

Poole’s study is based on a system for sorting politicians known as “DW-Nominate.” But DW-Nominate doesn’t directly measure ideology. Instead, it measures coalitions. It’s got pretty much every roll-call vote taken between 1789 and December 2011. It looks to see who votes together and how often. The assumption is that the most ideological members of both parties will do the least crossover voting. And it works. Its results line up with both common sense and alternative ways of measuring ideology, like the scorecard kept by the American Conservative Union.

Over the past century, DW-Nominate has revealed a steady increase in congressional polarization. Democrats have moved to the left, while Republicans have moved to the right. But Republicans have moved a lot farther than Democrats.

“Republicans in both chambers are polarizing more quickly than Democrats,” said Sean Theriault, a political scientist at the University of Texas at Austin. “If the Democratic senators have taken one step toward their ideological home, House Democrats have taken two steps, Senate Republicans three steps and House Republicans four steps.”

DW-Nominate rates presidents by processing Congressional Quarterly’s “Presidential Support” index, which tracks roll-call votes on which the president has expressed a clear position. The system then rates the president by looking at the coalitions that emerged in support of his legislation. In essence, it judges the president’s ideology by judging the ideology of the president’s congressional supporters. So how, in an age of incredible congressional polarization, could this system rank Obama as a moderate?

One answer, says Poole, is that Obama is very careful about taking positions on congressional legislation. In the 111th Congress, he took only 78 such positions. Compare that with George W. Bush, who took 291 positions during the 110th Congress, or Bill Clinton, who took 314 positions during the 103rd Congress. So part of the answer might be that, with the exception of high-profile bills such as health-care reform, Obama is hanging back from most of the congressional squabbling.

Another is that the system doesn’t account for preference intensity. The health-care reform law was a very polarizing vote. But it was only one vote. Or, depending on how CQ counted the law’s multiple legislative incarnations, a couple of votes.

Although the peculiarities of using DW-Nominate to rate presidents are worth pointing out, the data also tell us something else that’s important: Obama is a pretty moderate president. I doubt he’s actually more moderate than Clinton, as the system suggests. But he’s vastly more moderate than the political rhetoric surrounding his presidency — something that was also true for Clinton.

Obama’s financial rescue effort was largely a continuation of the Bush administration’s policies. He resisted calls to nationalize or break up the big banks; modeled his health-care reform bill after legislation that Republicans had proposed in Congress and Mitt Romney had passed in Massachusetts; extended the Bush tax cuts once and intends to make most of them permanent; signed legislation cutting domestic discretionary spending to its lowest level in decades; and supported the same sort of cap-and-trade plan that John McCain once introduced in the Senate. Obama’s presidency has been ambitious, and it’s been polarizing. But in terms of the policy it has produced, it’s been much closer to the market-based approach of Clinton than the forthright reliance on government of LBJ.

Republicans, however, can and should take partial credit for this. Obama is so moderate in part because the Republicans are so extreme. Politicians are ideological, of course, but they are also opportunistic. And the GOP, in closing ranks against almost every major initiative Obama has attempted, has taken away most of his opportunities to be truly liberal. The fight to get to 60 votes in the Senate has ensured, over and over, that Obama must aim his legislation at either the most conservative Democrats or the most moderate Republicans. In this, Obama has only been as liberal as Democratic Sen. Ben Nelson and Republican Sen. Scott Brown have permitted him to be. And that’s not very liberal.

That’s left Obama as a moderate president in an immoderate time. For progressives, that moderation has been repeatedly frustrating. For conservatives, it’s been obscured by a caricature of the president as a free-enterprise-hating socialist. And for the White House, it’s been a calculated strategy. We’ll know in November whether it was the right one.