By any reasonable measure, Marco Rubio struggled, mightily, during parts of the G.O.P. debate on Saturday night. Chris Christie savaged the Florida Senator for his inexperience and his reliance on canned talking points. Rubio responded, to a degree, with canned talking points, thereby demonstrating Christie’s basic critique that Rubio is an empty suit, similar to Barack Obama in 2008.* The conventional wisdom is that Rubio’s performance arrested his Iowa momentum and will blunt his support in the New Hampshire primary. At the same time, Christie’s performance, along with those of Jeb Bush and John Kasich, positioned the more moderate governors to excel in Tuesday’s contest.

All of this assumes that debates significantly affect electoral outcomes. Do they? The question is simple, but answering it is enormously complex. There are several issues to untangle.

The relationship between public opinion, political behavior, and persuasive information, like a debate, depends on the nature of the information and the consumer. In brief, highly informed citizens are the most likely to consume things like debates, but they are also the least likely to change their minds when presented with the information. Their attitudes and behaviors tend to be durable. Less informed citizens are indeed the most likely to be persuaded by new information, like debates, but they are also the least likely to consume that information. They are also less likely to vote, so even if persuasion occurs, it may not be linked to behavioral outcomes. The middle group, where the bulk of Americans are, know something and do consume some persuasive material, but they have to see it repetitively. Even given exposure, the information has to directly conflict with their conceptions and be persuasive enough to change actions.

So, for firm supporters of Rubio, Cruz, or Trump (or Christie, Bush, Kasich, or Carson), there is little chance Saturday mattered. For undecideds to be swayed, they would have to not only watch the debate, but interpret it in a way that is similar to the conventional wisdom stated above. The critique, to grasp it, required a particular impression of Rubio, some knowledge of his past, and the ability to contextualize Christie’s attack as it related to President Obama. That is not difficult for those who pay close attention to politics, but it may be beyond those for whom politics is only an occasional diversion.

Also, there are rival interpretations of what we saw. It is possible voters were turned off by Christie’s aggression, tone, and mockery. Rubio is also more telegenic than the New Jersey governor, and that positive disposition may have offset how voters weighed the information. After all, for many, images not only matter, but they are more critical than words. Was Christie able to scramble Rubio’s image with that exchange? And maybe more directly, did he help his own in the process?

The same is true for the other candidates on the stage. Yes, Govs. Kasich and Bush had solid performances, but will they be able to overcome perceptions that already exist? They are viewed, largely, as “establishment” moderates. Will a debate be able to make that an appealing pitch to an electorate that appears to be angry and tired of the system?

There is also the issue of media coverage of the debate. Debates may matter most when they create a uniform elite narrative that is then reported to consumers collectively. This sort of media coverage is critical because it extends the information beyond the actual event and if elite opinion is not fragmented, voters are more likely to be exposed to that narrative, incorporate it, and act upon it. Given the near universal agreement that Rubio suffered from the debate, there is a real chance the media’s portrayal of his performance will cost him more support than the debate.

Finally, when we think about debates and their possible influence, we have to remember some methodological concerns. If one wants to argue a debate (A) has a causal influence on an electoral outcome (B), there is much heavy lifting that must take place before that claim is respected. First, there is a temporal issue. Did A take place before B? Yes. Second, if A did not occur, would B still happen? In other words, if B exists without A, A cannot be the cause of B. Would the vote totals exist without the debate? This is a difficult counterfactual to measure outside of an experimental setting. Such research designs, as they relate to debates, indicate the information surrounding the debate (both pre and post) is more important than the debate (see above). Third, and this one is most difficult, are we sure A is the sole cause of B? Or, is it possible that variables C, D, and E also play a role in B? Perhaps demographics, advertising, retail politics, economic indicators, religion, or a host of other variables influenced the vote (either at the individual or aggregate level) as much or more than a debate performance.

My educated guess is that Rubio’s performance will indeed hurt him in New Hampshire. Why? There are large numbers of undecided voters in New Hampshire, so the potential for persuasion exists. Also, the particular attack actually worked to define and undermine Rubio’s particular image of youth and vigor. Christie’s salvo turned Rubio’s primary positives into negatives. Fairly or not, it seems like the kind of argument that could shift some outcomes. Additionally, the media coverage has been fairly uniform and negative, which suggests the debate’s impact lasted much longer than the debate itself, and that is bad for Rubio.

Even given that, it is difficult to determine how much the New Hampshire results will shape the rest of the campaign. Trump will win, it seems, and while there may be some short-term benefit to Christie, Kasich, or Bush, they are not well-positioned to turn South and compete in states that are more traditionally conservative. Rubio could be damaged. If his results bottom-out on Tuesday (and he finishes behind one or more of the governors), it may be difficult to overcome. If anything, the G.O.P. debate may have extended the contest, which actually strengthens Donald Trump. As long as his opponents are fragmented, which will continue as long as several of them are viable, he is more likely to turn his plurality support into electoral victories, which will give him momentum and a whiff of inevitability.

*I honestly think Rubio was right in the exchange, but his execution made Christie appear to be correct. To see President Obama as a failure due to inexperience is simply poor judgment on Christie’s part. It is a false association. Rubio should have explicitly attacked the premise of the question, instead he assumed he had made his thinking explicit, but he did not.