As with last week’s vice presidential debate, the public and pundits alike registered snap judgments about the first presidential debate. It’s conventional wisdom that the best way to see who’s winning a debate is to watch with the sound off. Below, we do the opposite: TV off, and transcript in hand.

With the sound off, you can focus on body language, physical comfort and the intangibles that supposedly decide who triumphed. We went back and watched a bit of the first presidential debate with the sound off. And the conventional wisdom is right: Mitt Romney came off much better than President Barack Obama.

But to understand what was essentially a weedy tax argument that no normal human being could possibly follow, it’s best to read the debate transcript. Reading the debate doesn’t necessarily change the impression of who won, but it does show how specific each candidate was in what he said.

A few notes:

Romney’s $8 trillion plan

We all remember the endless argument over Romney’s $5 trillion tax plan. But the argument Obama was trying to make — and that he did make over and again — was that $5 trillion is an underestimate.

Obama: “Romney’s central economic plan calls for a $5 trillion tax cut — on top of the extension of the Bush tax cuts — that’s another trillion dollars — and $2 trillion in additional military spending that the military hasn’t asked for. That’s $8 trillion. How we pay for that, reduce the deficit, and make the investments that we need to make, without dumping those costs onto middle-class Americans, I think is one of the central questions of this campaign.”

Let’s run through that math a bit more slowly. Romney’s tax cuts cost $5 trillion over 10 years before his (unnamed) offsets. Extending the Bush tax cuts on income over $250,000 adds another $1 trillion. Then there’s the $2 trillion in new defense spending. So before Romney can cut the deficit by a dime, he has to come up with $8 trillion in offsets and savings for these plans.

It probably wasn’t wise for Obama to keep hammering at this point. You need to understand the budget pretty well to understand what he’s saying. But it’s clear that this is what really offends him about Romney’s policy proposals. As someone who has had to sit in budget negotiations trying to make much smaller numbers work, he knows there’s no way that Romney can do what he’s saying he’ll do, and the fact that Romney hasn’t given us any details proves it.

Romney’s tax priorities

Romney was more explicit than he’s previously been on how he’s thinking about taxes. For instance:

Romney: “My number one principle is that there will be no tax cut that adds to the deficit. I want to underline that: no tax cut that adds to the deficit.”

He’s always said he won’t permit his tax cuts to add to the deficit. But he also says he won’t cut taxes on the rich, and he will cut rates by 20 percent across the board, and he won’t eliminate tax breaks for savings and investment, and when you add up all these promises, you find the math doesn’t work.

One way of reading Romney’s comments is that if the math doesn’t work, he’ll sacrifice his tax cuts before he adds to the deficit. But that’s undercut by this:

Romney: “For us not to lose revenue, have the government run out of money, I also lower deductions and credits and exemptions, so that we keep taking in the same money when you also account for growth.”

Romney is saying, clearly, that he intends to assume faster growth will help pay for his tax cuts. How much faster growth is he expecting? What will he do if it doesn’t happen? He hasn’t said.

Where’s Obama’s plan?

It’s striking, while reading the transcript, to see how much of the debate focused on what Romney wants to do and whether it will work. The impression you come away with is that Romney has a bunch of big ideas that may not add up, but that Obama doesn’t have any big ideas at all. That isn’t entirely true to his policy agenda. The American Jobs Act, for instance, is a big idea. But Obama’s not running on it.

As one commentator wrote after the debate, “to a remarkable extent for an incumbent, Obama and his team have redirected this campaign into a referendum on the challenger.” Before the debate, the conventional wisdom was that this has been an accomplishment for the Obama campaign. In the debate, it hurt them badly.

Obama on Social Security

Obama: “You know, I suspect that, on Social Security, we’ve got a somewhat similar position. Social Security is structurally sound. It’s going to have to be tweaked the way it was by Ronald Reagan and Speaker — Democratic Speaker Tip O’Neill. But it is — the basic structure is sound.”

Both Obama and the Republicans have simply refused to name major Social Security cuts, taxes or reforms in their budgets. But insofar as that hides a consensus, it’s a procedural consensus: Both sides believe that changes to Social Security are too dangerous to attempt without bipartisan cover. Whether a bipartisan process would lead to agreement on how to change Social Security remains an open question. But this answer does get at one truth: Obama is a lot more open to cutting Social Security as part of a “grand bargain” than many liberals would like.

Romney on Medicare

The structure of the Medicare conversation is interesting. Romney emphasizes that his plan won’t touch anyone over age 55, and then he spends some time attacking Obama for the Medicare cuts in the Affordable Care Act. It falls on Obama to introduce Romney’s premium-support plan into the conversation.

The way Romney approaches the whole discussion suggests he thinks it’s a political loser, and the way he repeatedly emphasizes that it won’t touch current seniors signals to non-seniors that this is an awful plan that they will hate.

Romney on Dodd-Frank

Romney eloquently attacks Dodd-Frank for essentially designating some financial institutions as too big to fail. The idea, of course, is that these actors are subject to much more stringent regulations and oversight so that they don’t fail. He says he disagrees with this approach, and that he’ll repeal and replace it. But neither moderator Jim Lehrer nor Obama ever force him to say what he would replace it with.

The bipartisanship two-step

We should look at this comment by Romney to Obama as the culmination of the GOP’s plan over the past four years:

Romney: “I like the way we did it in Massachusetts. I like the fact that in my state, we had Republicans and Democrats come together and work together. What you did instead was to push through a plan without a single Republican vote.”

Got that? Republicans refused to work with you, Mr. President, and that makes you a harsh partisan. Democrats were willing to work with me, and that makes me a bipartisan uniter.

Toward the end, Romney talks about how he “had the great experience … of being elected in a state where my legislature was 87 percent Democrat.” It’s a somewhat irrelevant argument, given that there’s no way Democrats will hold a substantial majority in the House or Senate at the beginning of a Romney presidency, but it was a very smart one for Romney to make. This leads to one of Obama’s better riffs:

Obama: “What’s important is occasionally you’ve got to say no … to folks both in your own party and in the other party. And, you know, yes, have we had some fights between me and the Republicans when they fought back against us reining in the excesses of Wall Street? Absolutely, because that was a fight that needed to be had. … And so part of leadership and governing is both saying what it is that you are for, but also being willing to say no to some things. And I’ve got to tell you, Governor Romney, when it comes to his own party during the course of this campaign, has not displayed that willingness to say no to some of the more extreme parts of his party.”

It’s interesting how little effort Obama expended tying Romney to House Republicans or the Ryan budget or really anything except for a particular price tag for his tax cuts.

Which isn’t to say Romney was particularly thematic in his strategy, either. More so than Obama, he actually stuck pretty tightly to the questions asked of him and focused on delivering clear, appealing answers. He didn’t win through a superior overarching strategy so much as he won by simply doing a better job.

But did he win by lying? This is a meme that cropped up after the debate, and while Romney did tell a few whoppers — that his health plan covers pre-existing conditions and that half of the green-energy investments made in the stimulus have failed — he mostly danced around the ambiguities in his policies in a way that appeared to confound Obama.

Indeed, while Obama’s policies are much more specific than Romney’s, Romney’s performance was much more specific than Obama’s. You saw this in the closing statements, where Obama ended with gauzy generalities and Romney closed by ticking off concrete policy promises.

On to Round 2

Top surrogates for both candidates predict that a more aggressive Obama will show up for their second debate, on Tuesday. So stay tuned.