Dylan Matthews shakes his head:
In short, the effects on debates on eventual votes are likely mild, and, in most cases, effectively nil. Moreover, what effects do exist are often caused by factors wholly beyond the candidates’ control, like media coverage, attractiveness, and whether voters are watching a Nats game in the other panel of their TV.
Sam Wang argues that the debates do matter, but not in the way you’d expect:
The Presidential outcome is only one measure of the debates’ effectiveness. As I have shown, downticket Senate races this year have tracked Presidential preference closely. The same is likely to be true of House races. These linkages are driven in part by partisan voter intensity. If one side’s intensity fades or surges, it will affect races at all levels on the ticket. The Obama-Romney debate may well influence the shape of the Congress that the President will face in January.