The consensus appears to be that Obama won the debate last night. CBS News put the victory margin at 30 percent, while CNN put it at 8 percent. But does that even matter?

Maybe. After the first debate, Nate Silver compared CNN instant-reaction polls and post-debate bumps from 1988 to 2008 and found an overall positive relationship between the margin in the instant-reaction poll and the post-debate bump in polls. That said, the relationship wasn't statistically significant.

I added the first two 2012 debates to Silver's database and found similar results. While Romney's 38-point margin of victory in the first debate was followed by a 3-point bump in the polls, Obama's 7-point win in the second was followed by a 2-point bump for Romney. That said, there's still a relationship, though as with Silver's data, the relationship isn't statistically significant:

The slope is positive but the intercept is negative. That means that a tie on the snap polls leads to a bounce for the challenger — in this case Romney. Obama would have needed to win by 28.15 points for Romney to not see a bounce — anything less helps Romney.

If the above relationship holds, Obama is estimated to actually lose about 0.71 points in the polls in the next week. All of which is to say that debates tend to help the challenger more than the incumbent, and instant reactions matter a great deal less than cable news would have you believe.