Mitt Romney won decisively last night. Here’s a partial list of things to watch in order to gauge whether Romney is successfully reshaping the race in a fundamental way, which he needs to do.

1) Ohio. Obama leads by 5.5 points in the state in the Real Clear Politics average. No matter how good Romney was last night, that’s a steep hill to climb. If Romney doesn’t win Ohio, his path to electoral college victory is extremely daunting. Check out James Downie’s piece on how bad the electoral math currently looks for Romney and how hard it will be for him to overcome it.

Romney’s pedigree and profile are a terrible fit for Ohio. The state’s unemployment rate is lower than the national average; Romney opposed the auto bailout that seems to be partly responsible for that. One recent poll found that only 38 percent of voters there say he cares about the needs and problems of people like them. If Romney starts to make real gains in the state, that will be a sign that he changed voter perceptions of himself and his policies and priorities in a meaningful way that could turn this into a genuinely close contest.

2) Romney’s national “middle class”and “empathy” numbers. The fundamental problem Romney has, in poll after poll, is that people believe that Romney’s policies are skewed towards the rich, and that he doesn’t understand people’s problems. Last night Romney did manage, I think, to project an earnestness and passion about public policy (even if his plans are full of evasions and contradictions) that will go some way towards diluting his plutocratic image.

As I said yesterday, Romney “skillfully played the part of the technocratic centrist he used to be and whose balanced approach to policy and government he has completely abandoned.” Jonathan Chait has similar thoughts: “He was obsessive about portraying himself as a moderate, using every possible opening or ambiguity — and, when necessary, making them up — to shove his way to the center.”

Romney almost certainly made gains in persuading people that he has the knowledge and competence to handle the office of the presidency. But it still remains to be seen whether he has altered fundamental perceptions about his policies and the priorities that drive them. Nate Cohn points out that if he didn’t succeed at that, the debate might not have changed the race to the degree he needed. So watch those national “middle class” and “empathy” numbers.

3) More fight from Obama. It is mystifying that Obama allowed Romney to come across as the one on the stage who was really fighting. Yes, Obama did do well in some exchanges that pundits are not giving him credit for — over Medicare, Romney’s tax plan, and the contrast between the Bush and Clinton approaches — but he missed key opportunities to pin down Romney on his policy evasions. Jonathan Cohn has a good piece that lays out all of the holes Romney exposed in his plans, noting Obama’s botched chances to pin down Romney on his tax and Medicare proposals:

I wish Obama had pressed him on this inconsistency even more directly than he did: “OK, governor, you say you can offset the $5 trillion cost of your tax plan. Tell us how, with real numbers. Are you getting rid of the home mortgage deduction? The exclusion for health insurance? Be straight with the American people about what you are proposing.” Obama didn’t do that, but it’s a question Romney has never been willing to answer....

The real shame of the exchange was that Romney’s own [Medicare] plan got so little attention. Again, I wish Obama could have pressed Romney harder, or explained more clearly, why the voucher scheme he proposes would likely end the guarantee Medicare now makes to seniors — and why current retirees, as well as future ones, would feel the impact.

The Obama camp seems to have calculated that he just had to appear thoughtful and substantive, and not spark any fireworks, to preserve a dynamic in the race that currently favors him. But the result was that Romney came across as feistier and more energetic than Obama did. Obama repeatedly failed to seize opportunities to expose Romney in a powerful and compelling enough way on the stark ideological differences between the two men. As Steve Benen notes, Romney had great success obscuring the true nature of his policies to recast his ideas as more palatable to the American mainstream. Obama was way too complicit in allowing that to happen.

Romney took command. Obama didn’t fight. Beyond the noise of the policy back and forth, voters sense this kind of thing on a basic level. More of this from Obama will demoralize supporters and feed a bad developing press narrative about Romney as the hungry challenger on offense, gaining momentum daily. It has to change.