It would be foolish, however, to come to any conclusions based on this evidence, since we're still talking about only five data points, most of which are not very relevant. Most incumbent elections are not very close -- the incumbent either cruises to victory or gets crushed -- and so there just aren't that many instructive cases in the range that we care about, which practically speaking means when the President's approval rating is somewhere in the 40s.
A better approach might be to look at Obama's polling against Sarah Palin. There have been 11 Palin versus Obama polls that have come out this year -- 8 by Public Policy Polling and one each from Rasmussen, Clarus, and Marist. Those polls showed Obama approval ranging from 49 percent to 55 percent -- not far from Dowd's sweet spot -- but Obama defeating Palin by margins ranging from 6 points to 23.
(More numbers after the jump...)
If we make a scatterplot of these polls, we can extrapolate backward to get an estimate of where Obama's approval rating would need to be in order to bring Palin into a tie with him; the answer is about 43 percent.So, really, Obama would need to be a good 8-10 points down from where he is now (40% or below) for Palin to have a decent chance. That's just going on the raw numbers and not the "Oh my God, are we really going to be electing this woman President?" factor that I think would give Obama an even larger cushion than just the 40%.
If we do the same thing with Mitt Romney's numbers, on the other hand, we get a breakeven point of 46 percent:
So, one way to look at this is that Palin gives Obama an approval rating bonus of about 3 points: if Obama can defeat a Generic Republican with an approval rating of X, he can defeat Palin with an approval rating of X-3.
Caveats abound, of course -- this conclusion too is based on some fairly limited evidence. But if you told me that Obama's Gallup approval rating was 45 percent on Election Eve 2012 and that his opponent was Sarah Palin, I'd put my money on Obama and feel pretty good about it. And if Obama's approval ratings were instead in the 47-51 range that Dowd specifies, I'd give Palin very long odds of defeating the incumbent.
Still, it's an interesting exercise.