With the memory of the conventions fading and initial signs pointing toward an Obama bounce, attention is already turning to Romney’s ability to mount a comeback. In the minds of many, Team Romney’s financial advantage tops the list of reasons for Republican optimism. Indeed, the Romney campaign and its allied super PACs are poised to spend millions on a historic advertising campaign that some argue could bury Obama and swing undecided voters toward Romney. And yet ...

There are good reasons to doubt whether Romney will get his money’s worth. Most of Romney’s ads are geared toward attacking the president’s performance, but Obama has been president for four years and voters have a settled impression of his character and record. The stability of Obama’s approval ratings are highly consistent with an electorate that has largely made up its mind about the President. A recent poll even shows that the public knows it’s made up its mind: According to Pew Research, 90 percent of registered voters say they already know what they need to know about Obama.

The stability of the race over the last three months confirms that advertisements are unlikely to make a difference. Voters in the battleground states have already weathered a full presidential campaign’s worth of advertisements—hundreds of millions of dollars in the battleground states—but there was little evidence of a substantial shift in either direction. To the extent that there was any shift, it came in June and early July when Obama made gains after switching to an overwhelmingly negative advertising strategy, even though Team Romney has outspent Team Obama by two-to-one over the last two months. Unless the Romney campaign has a fundamentally new pitch, it’s hard to see why voters that have already heard these advertisements will now suddenly find them persuasive.

The fact that Team Romney is poised to spend even more money doesn’t undermine this analysis. GOP-aligned Super PACs aired uncontested advertisements in Michigan, eastern Pennsylvania, Wisconsin, Minnesota, and New Mexico, but only Wisconsin moved into the toss-up column after Paul Ryan was selected as Romney’s running mate. The Republican National Convention could be reinterpreted as a three hour, nationally televised infomercial, and yet Romney didn’t receive any bounce at all. And while the science of ad spending is somewhat unscientific, there is probably a point of diminishing returns, even if the exact slope of the diminishing curve is uncertain. Team Romney has already been airing advertisements at or above saturation levels for months. The rule-of-thumb is that 1,000 gross-rating-points (GRP) of advertisements are enough to get your message out to voters, but Team Romney has routinely exceeded 2,500 GRP in critical markets in August. For comparison, Palm Beach received 3,200 GRP from Bush’s campaign in the final week of the 2000 presidential campaign.

Even if Romney can leverage his resources effectively, research by political scientists seems to confirm that a large advantage in ad spending only produces minor gains in a presidential election contest, probably because voters will learn quite a bit about the candidates independent from the airwaves. On average, Michael Franz and Travis Ridout found that 1,000 additional advertisements by Obama produced a statistically significant but minor (.5 percent) improvement in Obama's performance. Similarly, Darren Shaw found that a 1000 GRP shift resulted in an additional .2 points in a given media market in 2004. That's not much, but it could have flipped a few states in an election as close as 2000. And in some areas with large numbers of persuadable voters, the influence of uncontested ads could be even greater than the national average. That said, Obama could backload ad spending, which would probably minimize the consequences of getting outspent, since Sasha Issenberg has reported that "eggheads" researching on behalf of Rick Perry--of all people--found that the effects of campaign advertisements tend to fade relatively quickly (if you've enjoyed this article, just go ahead and buy The Victory Lab).