During the second presidential debate Tuesday night, the round red-carpeted floor at Hofstra University in Hempstead, N.Y., resembled a boxing ring more than a stage. And frequently, substance took some unexpected blows.

Who won? Who knows? The rematch of Obama vs. Romney was a great night for physical theater. Rhetoric was sidelined by spectacle. At times, the thinly veiled aggression grew so hot — with President Obama and Mitt Romney closing in on each other like streetfighters — that you wondered if the two would come to fisticuffs.

Action was expected with the town-hall format, and the candidates in chairs, not protected behind lecterns, and the audience seated in a close semicircle around them. But it’s like theater in the round, hellish for any actor to negotiate, even with rehearsal. Risks abound: How do you look confident while you’re wheeling around the space? When do you turn, when do you walk, how far do you go? How far can you go?

In the days leading up to the debate, there was talk about this freer format revealing the candidates’ ability to show empathy. They’d have a chance to show their softer sides, in intimate proximity with members of the audience.

We didn’t see their softer sides.

The evening began awkwardly, as soon as the president and Romney took the floor. With the audience applauding them, Obama turned to sit. Romney stood, beaming. Obama rose to half-standing. Romney held his ground. As the camera drew back, here was our first view of the two candidates: Romney solidly on two feet, the president stooped and uncertain, with one foot hooked around his chair leg.

He was so eager to swap out this image for one of firm assuredness that he caused one of the questioners to fumble his microphone, by striding over to him a bit too quickly. But interaction with the audience was quickly swept to the corners. The real showdown was between the two men.

“In the last four years you’ve cut permits and licenses on federal lands and federal waters in half,” Romney charged, turning to his opponent and hacking at the air.

“Not true,” Obama called out, eyes blazing. Then he looked away.

“How much did you cut the licenses by?” Romney continued, stepping closer to Obama. His finger jabbed the air. Obama tried to cut him off. Romney kept coming at him, and Obama got out of his chair, his head high and tilted back a bit, which felt like a silent taunt. (Say it again — I dare ya.)

Romney stepped forward, staring at Obama. The two men locked eyes.

You held your breath.

Obama looked away, and you let it out.

Time and again, as the tension built, Obama defused it with his eyes. It was a successful technique. He seemed to have decided that he would match Romney move for move, going so far at one point as to step toward moderator Candy Crowley’s desk so he was exactly the same distance away from it as his opponent. They could be sharing the free-throw line.

Obama had learned from his opening misstep, and he made sure he stood when Romney stood, took a step when Romney took a step, chopped up empty space with his hand just as crisply as the Republican.

But he didn’t match his opponent’s chilling gaze. Romney wanted a staring contest, but Obama didn’t take that bait. He shunted it aside, cutting his eyes to the audience. Or he’d diminish the threat with a joke.

“Mr. President, have you looked at your pension? Have you looked at your pension?” Romney asked in a breathless staccato.

Obama made a show of avoiding his opponent. He looked to Crowley with a grin, widened it to show his teeth, let out a chuckle. Finally, in a smooth legato, he delivered a crippling zinger: “You know, I — I don’t look at my pension.” He shot Romney a look, and just as quickly glanced away. He addressed the punch line to the audience:

“It’s not as big as yours, so it doesn’t take as long.”

In the laughs that followed, you heard the pressure being equalized.

In a figurative fight, every nuance matters. The smiles — if Romney’s were too tight, Obama’s were too broad. The strolling around — too much, too little? They navigated the space uneasily more often than not.

But Obama knew, perhaps intuitively, perhaps by virtue of a lifetime of guardedness, how to avoid escalation.

He simply looked away.

In the battle for style, this wasn’t a knockout. It was a victory on points, to the man who knew how to back off — without backing down.