Mitt Romney’s campaign has begun to push back against the notion that President Obama’s critiques on his tenure at Bain Capital have damaged him. A memo released by Mr. Romney’s pollster, Neil Newhouse, suggests that the margin between Mr. Romney and Mr. Obama has been narrowing rather than widening in the polls despite the attacks.

I would take issue with the notion that the race has been tightening. Instead, once you remove the statistical noise from the polls, the trajectory looks roughly flat based on our analysis. Mr. Obama has maintained a narrow, but fairly consistent, lead of about 2 points over perhaps the last six to eight weeks.

But Mr. Obama’s lead has also not been widening — and I think Mr. Newhouse is correct that the evidence for the impact of the Bain attacks is rather thin, or at least has been up to this point.

At the same time, Mr. Romney’s campaign has begun to behave as though the attacks are a fairly big deal. And it has backed into a more defensive posture that could change the nature of how they are perceived by the public going forward.

Mr. Obama’s position over Mr. Romney is somewhat stronger than you might expect based on Mr. Obama’s approval ratings — but not necessarily as compared to his favorability ratings, which have usually shown that more Americans than not take a favorable view of him personally.

Is Mr. Obama’s position stronger than it “should” be based on the tepid economic recovery — another sign that Mr. Romney might be a below-average candidate? That is a more debatable case, because it is hard to know exactly how the public perceives the economy and assigns credit or blame to Mr. Obama for its performance. Various models published by economists and political scientists claim that Mr. Obama should be anything from a clear underdog to a clear favorite based on the country’s economic performance.

Our economic model, which looks at a wider array of economic indicators than the other ones do, is a bit more equivocal. Essentially, it suggests that Mr. Obama’s narrow lead in the polls is broadly consistent with the economy’s lukewarm performance.

There are two things to keep in mind when interpreting this evidence. First, Mr. Obama’s lead in the polls — about 2 points — would reflect a below-average performance for an incumbent. Since World War II, elected incumbent presidents have won by an average of 7.5 points when seeking a second term.

Second, the historical evidence seems quite definitive that the public reacts more to the change in economic performance — that is, the rate of growth in crucial economic indicators in the year or so leading up to the election — than to how strong the economy is in an absolute sense. Over the last 100 years, there has been literally no relationship between the unemployment rate on Election Day — a measure of how completely the economy is fulfilling its productive potential — and the election result.

But there have been positive and statistically significant relationships between the growth rate in the economy — as measured by G.D.P., jobs, income and other indicators — and the election result.

The recent rate of growth — about 2 percent across an average of indicators, which is below average but not recessionary — points to a below-average but not necessarily losing position for Mr. Obama. Mr. Obama may also be helped somewhat by the fairly low rate of inflation, which receives some weight in our model — and, we think, also, in voters’ perceptions about how the economy is performing. It’s a little easier to adjust to a new but mediocre “normal” if grocery prices aren’t rising every time you go to the supermarket.

In short, there is no perfect way to measure the economy, let alone how voters react to it — but the horse-race polls, at least, are not manifestly inconsistent with how voters have reacted to similar circumstances in the past. The notion that Mr. Romney is an underachieving candidate may be plausible, but there is not much proof of it.

Some polls have also asked voters directly what they think about Mr. Romney’s business experience. The results vary depending on question wording, but some polls suggest that voters see it as being a roughly neutral factor overall.

A recent Washington Post / ABC News poll, for instance, found that about a quarter of voters thought that Mr. Romney’s work in “buying and restructuring companies” was a major reason to support him, another quarter said it was a major reason to oppose him, and half said that it didn’t make much difference.

It does not necessarily follow that Mr. Obama’s Bain attacks have been fruitless. They may have succeeded in turning a positive attribute for Mr. Romney — his business experience — into a neutral one. And it may be that voters do view Bain Capital as something of a negative factor, but this is counterbalanced by other strengths they perceive in Mr. Romney.

Still, the case that they are a “game changer” has been pretty tenuous — and it is hard to move the numbers in the first place in a partisan environment like this one. The vast majority of voters will make a decision based on their party affiliation, and many of those that don’t will decide based on their views of the economy. Campaign strategies and personal attacks might shift the numbers by a point or so in either direction — and in a close election like this one, that might make the difference. But they have an awful lot of partisan and economic gravity to escape.

In recent days, however, Mr. Romney’s campaign has begun to behave like Bain Capital is more of a negative factor than a positive or even neutral one. Instead of pointing to successes like Staples — and pointing out that some of Mr. Obama’s claims about the outsourcing that has allegedly occurred at some other Bain investments is factually dubious — they have instead begun to behave as though Bain Capital’s track record is nothing to be proud of.

In going on all five major news networks in a set of interviews on Friday night, Mr. Romney claimed that he was not responsible for decisions that Bain Capital made from 1999 — when he began to run the Salt Lake City Olympics — to 2002, when he began to run for governor of Massachusetts.

But voters may read between the lines in ways that Mr. Romney does not intend. If Mr. Romney is striving to avoid responsibility for whatever Bain Capital did from 1999 to 2002, it may suggest to them that some of the investments that Bain Capital made during this period were dubious.

Meanwhile, Mr. Romney may find it harder to claim the moral high ground when the details of what Bain did are murky — and Mr. Romney does not seem inclined to shed light on them, like by releasing more years of his tax returns.

In other words, Mr. Romney has in some ways begun to ignore his pollsters’ advice. Instead of being more forthright in his defense of Bain’s activities — a strategy that seemed to be roughly achieving a draw in the public’s eyes — he has been in damage-control mode, and has not necessarily been adroit at it.

That means it’s at least worth watching the polls over the next couple of weeks to see whether the attacks become more damaging going forward.

For the reasons I cited before — relatively few members of the public are “persuadable,” and they have many other matters to evaluate along with Bain Capital — it would be an upset if there were a huge swing in the polls. There may well not be any measurable change at all.

But if Mr. Romney does begin to run 4 or 5 points behind Mr. Obama in the polls — rather than zero to 3 points behind, as he has in recent weeks — that would be a sign that his strategy has backfired.