To me, the debate Tuesday night was a very solid “win” for President Obama, more so than most of the instant analysis or early polling suggested.

Gov. Mitt Romney continued to refuse to explain his policy proposals – especially his magical tax plan. But this time, Obama rather sternly pointed out this problem. As in this from Obama:

Now, Governor Romney was a very successful investor. If somebody came to you, governor, with a plan that said, here, I want to spend $7 or $8 trillion, and then we’re going to pay for it, but we can’t tell you until maybe after the election how we’re going to do it, you wouldn’t take such a sketchy deal, and neither should you, the American people, because the math doesn’t add up.

By the debased standards of probative value we bring to such things, it was a lively, substantive and informative debate, but only by those debased standards. It’s hard to believe that anyone who has been paying attention to the campaign or to the news would have actually learned many new facts. There were countless examples of the two men exchanging self-serving half-truths that, when assembled, never added up to anywhere near a whole truth but will provide plenty of work for the fact-checkers.

Emotional highlight

The emotional peak of the evening (and also one of the best examples of what I mean about probative value) may have occurred at the end, over the tragedy at the U.S. consulate in Benghazi, Libya, in which the U.S ambassador and three other U.S. officials were killed.

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The regular guy from the audience (one Kerry Ladka) asked Obama rather bluntly and succinctly: “Who was it that denied enhanced security and why?”

“Well, let me first of all talk about our diplomats, because they serve all around the world and do an incredible job in a very dangerous situation,” Obama began his reply.

According to the transcript I’m using, Obama spoke for eight paragraphs (and clearly would have gone longer if moderator Candy Crowley hadn’t stopped him) but the president never commented on either who denied enhanced security, nor why, although he did say that he would “investigate fully, regardless of where the facts lead us.”

He segued into a general review of his foreign policy accomplishments – promises made, promises kept. And frankly, the list was impressive, including, as it did, the winding down of two wars and the killing of Osama bin Laden.

But Romney smelled some home cooking, and when his turn came (he kept it to just seven paragraphs), he turned back to Libya and asserted that it had taken two weeks for Obama to acknowledge that the attack had been conducted by terrorists.

To me, this “fact” would be not much more than a gotcha. I’m more impressed with winding down those wars, (although that part of Obama’s answer was not responsive to the question) and view Romney’s effort to capitalize on the Benghazi incident as crassly political. But, it turns out, Romney’s “fact” was also flawed because, unbeknownst to Romney (and I’ll admit I was also unaware of this) Obama referred (somewhat indirectly) to “an act of terror” on the very first day after the attack. So Romney is going to get dinged by the fact-checkers.

Two wars

But really, if we are going to decide whether to reelect Obama, and if his handling of foreign policy is one of the factors on which we are going to decide, isn’t the winding down of the two wars actually a lot more relevant? Romney has occasionally expressed some quibbles about those policies, but the chink-du-jour in Obama’s foreign policy armor is all about Benghazi. This is what I mean about probative value.

Anyway, there were plenty of moments like these. Romney did a pretty good job of indicting the state of the economy, but a much worse job of convincing anyone other than the already-convinced that he has a plan that will get better results.

The instant polling gave Obama the edge. A CNN poll of registered voters who viewed the debate found that 46 percent said Obama won; 39 percent said Romney did. A poll using an online panel of uncommitted voters and conducted by CBS News found 37 percent said Obama won, 30 percent said Romney did and 33 percent said the debate was a tie.

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The instant analysis, other than on Fox (where both Sean Hannity and Karl Rove opined that Romney had torn Obama apart), was that Obama had either won big or won small or at least halted the Romney surge in the polls that started with the first debate (although we’ll really need some more polls to confirm that).