Standard & Poor’s decision to downgrade the United States has drawn a lot of criticism. The White House called its performance, which included a miscalculation of about $2 trillion, “amateur hour.” Rep. Barney Frank was even less sparing. “These are some of the people who have the worst records of incompetence and irresponsibility around,” he told Rachel Maddow. They are trying to “justify their reputation.”

All of this is true. But it doesn’t make Standard & Poor’s wrong. In fact, this downgrade is arguably serving two important functions: It’s drawing attention to the failures in the American political system, as well as the failures in Standard & Poor’s.

Let’s begin with the country. “The downgrade reflects our view that the effectiveness, stability, and predictability of American policymaking and political institutions have weakened at a time of ongoing fiscal and economic challenges,” Standard & Poor’s said in the statement accompanying Friday’s decision.

After Republicans in Congress spent three months weighing whether or not to default on our debt and Senate Minority Leader Mitch McConnell said that paying our bills would never again be a foregone conclusion, can anyone really argue with that? After every Republican presidential candidate save Jon Huntsman either remained silent on, or flatly opposed, the deal to raise the debt ceiling, can anyone really say that U.S. debt is completely riskless? That there’s no chance of a political miscalculation, and if there is such a chance, that they can perfectly predict the outcome of the ensuing chaos?

In Washington, it’s almost trite to say that the political system is broken. It’s been clear for some time that things really are different, that norms and procedures that once kept fractious congresses functioning have eroded with terrifying speed. If anything, S&P is, as usual, noticing the deterioration too late. But that doesn’t mean the deterioration is not real, or that it should be ignored.

That said, S&P’s report is a joke. The problem isn’t the agency’s $2 trillion mistake. It’s possible for the agency to have made that mistake without harming its underlying point about the weakness and unpredictability of American political institutions. But S&P hasn’t confined its argument to our political institutions. The original draft of its report included a section in the executive summary laying out the deficit math for the next decade. When that math proved wrong, S&P simply deleted the section. But that’s inconsistent with the calculations S&P left in the final report.

In both versions, Standard & Poor’s says it would upgrade our outlook from “negative” to “stable” if the Bush tax cuts for income over $250,000 expire. That would net Treasury about $900 billion over 10 years. So according to S&P, $900 billion is a big deal. And it’s a big deal because of how much it would reduce the deficit. So let’s look at that.

The original report says that $900 billion in fresh revenues would mean net public debt drops from an estimated 93 percent of gross domestic product in 2021 to 87 percent of GDP. The second version of the report — the one written after they discovered a $2 trillion mistake — revises its estimate for America’s baseline debt path down to “74 percent of GDP by the end of 2011 to 79 percent in 2015 and 85 percent by 2021.” In other words, S&P’s technical correction improved our deficit outlook by more than letting the high-end tax cuts expire, which S&P had said would raise enough money to stabilize our rating. If the numbers mattered, then by S&P’s own logic, that should have changed the agency’s opinion of our finances.

Similarly, the firm has previously explained that while a $4 trillion deal could have saved the U.S. credit rating, a $2.4 trillion deal — which is what we got — was insufficient to stabilize the debt. But because their original calculations misplaced $2 trillion, the deal and the correction should have added $2.4 trillion plus $2 trillion to our bottom line. That, again, is more than $4 trillion.

I spoke with Standard & Poor’s about these concerns. The response wasn’t particularly compelling.

“The point we were making on the numbers is that nobody we know is claiming this deal, however you do it, will halt the rise in the debt burden,” said David Beers, an analyst responsible for sovereign debt.

That’s true, but $4 trillion is $4 trillion is $4 trillion. The debt burden doesn’t care whether our fiscal picture improves because of a deal or the combination of a deal and a technical correction.

My hunch is that S&P was making a political argument and felt the need to cast it as deficit arithmetic. Then, when its arithmetic proved wrong, it was left looking foolish. As it stands, you cannot coherently merge the first and second versions of S&P’s explanation of the downgrade. That should tell you something about how rigorous its framework is, even if it doesn’t obviate the still-legitimate points it made about our political system.