And yet the public’s reaction wasn’t that dramatic. In a Sept. 22-24 YouGov poll, a plurality, 39 percent, said that Romney’s comments were a “serious mistake” — but the vast majority of these people (85 percent) were Democrats and therefore not likely to vote for Romney anyway. The rest said that Romney’s comments were either a minor mistake (19 percent) or “not a mistake” (38 percent), with the latter category populated mainly by Republicans. Political independents were more likely to say that Romney’s comments were “not a mistake” (44 percent) than a “serious mistake” (26 percent).

Given this mixed reaction, it’s not surprising that there was no consistent movement in the horse race. For example, in the Gallup polls conducted the week prior to the video’s release, Obama had a 3-point lead (48-45 percent). The week after the release, Obama had a 2-point lead (48-46 percent) and the week following a 4-point lead (49-45 percent). The Pollster averages show almost no change in the race around the video’s release.

The best-case scenario for those who believed the video mattered comes from the YouGov polls. In those polls, Romney’s numbers did drop: Obama had a 49-44 percent lead in the Sept. 15-17 poll, with the rest undecided or supporting another candidate; two weeks later, in the Sept. 29-Oct. 1 poll, his lead was 49-41 percent. Respondents in these polls had also been interviewed in December 2011, so we are able to track trends among voters who originally supported Obama or Romney or were undecided in a then-hypothetical Obama-Romney race. We found that most of this September drop in support for Romney was among his previous supporters: He lost 5 points among those who actually favored him when first interviewed in December 2011. These losses did not mean voters were leaving Romney for Obama. Instead they were becoming undecided—suggesting that they could be won back over to Romney’s side, especially if they had been Romney supporters until that point.

And this is exactly what happened after the first debate. These temporarily undecided Republicans came back to Romney. Indeed, the immediate improvement in Romney’s personal image in the wake of the debate — which we documented here — belies the idea that the 47 percent video had a lasting impact. It was more a stiff jab than a knockout blow to his campaign.

But what about the video’s impact on something more specific: voters’ perceptions of Romney’s “empathy,” or his ability to understand the problems of ordinary Americans? After all, the Obama campaign had been attacking him on precisely this front, focusing on Romney’s time at Bain Capital, and some of Romney’s earlier remarks — about his friendships with NASCAR team owners, about Ann Romney’s two Cadillacs — only seemed to further the Obama campaign’s portrait of him as an out-of-touch plutocrat. Did the video add fuel to the fire?

We tracked perceptions of the candidates’ empathy throughout the campaign, specifically how well voters thought that phrases like “cares about people like me” and “cares about the middle class” described the candidates. Once again, we found no changes in perceptions after the video’s release, just as Washington Post polls found no change in perceptions of which candidate “better understands the economic problems people in this country are having.” Here is a figure with the most relevant “cares about” trends:

Voters perceived Obama more favorably on this dimension, but this was true even in January 2012. Ultimately, Romney’s “empathy problem” may have been less his problem and more the Republican Party’s problem. In every presidential election between 1984 and 2008, the Democratic candidate has been perceived as more likely to “care about people like me” than the Republican.

Are these national polls obscuring the real effects of the video, which may have been magnified in battleground states because of Democratic ads? In our book, we analyze the effects of both sides’ advertising throughout the summer and fall. Consistent with previous studies, we find that ads had only small and short-lived effects on people’s vote intentions. Neither candidate could get a large and durable enough advantage in advertising to win many votes. As a result, it is unlikely that battleground state advertising magnified the video’s effects.

Of course, there is always the hypothetical: What would have happened if the video had never been released? Could Romney have bounced back after Obama’s post-convention bump in the polls? It is certainly true that, had the 47 percent video never come to light, the conversation during the last two weeks of September would have been different. But how beneficial would that conversation have been to Romney? Would other events in September, like Romney’s reaction to the Benghazi attacks and Obama’s lead in the polls, have continued to cast a shadow? We cannot know, but it is not obvious that, without the video’s release, the weeks after the Democratic National Convention would have been so much more favorable to Romney as to change the dynamics of the race.

It is always tempting for those following a presidential election closely — pundits, reporters and political scientists alike — to assume that every new twist is the proverbial game-changer. But in retrospect, the 47 percent video did not live up to the hype.