In the past, we've looked at post-debate polling in general to get a sense for how the fortunes of candidates fared. This is also imprecise, since polls measure any number of factors during discrete periods of time. The extent to which a debate is what moves a candidate up or down is very hard to determine.
But, it's probably the best tool we've got. And, contra Mr. Trump above, no candidate has done worse in the 7- and 14-day periods after debates than him.
After the first four Republican debates, Trump has seen a decline of 2.8 points over the ensuing week, on average, and a drop of 2.2 points after another week has passed. That's skewed a bit thanks to the boost he got in the wake of the Paris attacks, which helped put him into positive territory after the most recent Republican debate.
But you can see the pattern below.
Trump saw his biggest drops after the second debate, which, not coincidentally, was the one where Carly Fiorina joined the big kid's table and proceeded to smack Trump for comments he'd made about her appearance.
You can see that Fiorina spiked in the polls afterward.
Thanks largely to that second debate, Fiorina's seen the largest 7- and 14-day average gains of any candidate.
Marco Rubio comes close. Rubio has consistently improved in the polls after his generally strong debate performances. The one exception was the most recent debate.
Ted Cruz's best debate moment came in the CNBC debate, when he railed against the news media (instead of answering a question). That performance showed up in the polls.
Ben Carson has been hit or miss. He spiked two weeks after the first debate, had a bad second one -- and then fell apart after the terror attacks in Paris. That's almost certainly not because of the debate, but because his foreign policy skills were viewed as lacking.
Jeb Bush has also been in debates.
Happily for Bush, debates don't seem to doom candidates, Scott Walker notwithstanding.
The candidate that's seen the biggest drops in the polls has been Trump, who, of course, had more support to lose. Debates don't seem to be Trump's strong suit, and it doesn't seem to matter.