The bookies loved Obama's second debate. Richard Milnes via Flickr Reading around this morning, everyone's got a theory about who won last night's Big American Chat between Barack Obama and Mitt Romney. "Obama regains the initiative to win second presidential debate", claims The Guardian, pointing to "gaffes" over Benghazi and something about "binders full of women", which sounds positively Silence of the Lambsian. Our own Tim Stanley thinks that Obama "won on points" but that he may suffer under fact-checking. "It wasn't enough," fretted Liberal Conspiracy's Sunny Hundal. The Washington Post's Greg Sargent thinks Obama "turned it around".

Who's right? Well, we could look at the instant reaction polls. FiveThirtyEight found an unusual level of agreement in them, that Obama did slightly better,in state and national polls, though not as well as Romney in the first. But, and here's the key, "The relationship between the quick-reaction polls and their eventual effect on the horse-race polls has historically been very modest, and has sometimes even run in the opposite direction of what the initial polls suggested." So Obama's slight apparent victory in the debate tells us nothing whatsoever about who's actually going to win the thing.

I'd like to return to Nicholas Nassim Taleb, the author of Fooled by Randomness whom I mentioned in yesterday's post on this subject. He suggests that, rather than listening to the views of people like me, who have to say something entertaining every day but won't lose our jobs or money if we're wrong, we should listen to people who have to be right more often than they're wrong or they will go broke. The obvious people would be bookmakers. Bookmakers who regularly get the odds wrong would have to find new jobs fairly quickly.

Luckily, I wrote down a few of the odds on offer yesterday:

Betfair: Obama 40/85, Romney 80/45

Ladbrokes: Obama 4/9, Romney 7/4

William Hill: Obama 4/9, Romney 7/4

Intrade (not technically a bookmaker but): Obama 62 per cent, Romney 38 per cent

And today:

Betfair : Obama 40/85, Romney 11/5

Ladbrokes: Obama 4/11, Romney 2/1

William Hill: Obama 2/5, Romney 2/1

Intrade: Obama 63.5 per cent, Romney 36.5 per cent

(FiveThirtyEight puts the probabilities about the same, by the way: Obama 64.8 per cent, Romney 35.2 per cent.)

So who won the debate? Well, you could look at the very slight shift in the odds towards Obama, and say "Obama". Or you could say "wait, didn't you tell us yesterday not to look frantically at every tiny change in the data? And given that Romney got such a big bump off the last one, shouldn't we expect a reversion to the mean anyway, so it would be frankly implausible for Romney not to lose a few points this time?"

And you'd be right. Did Romney win? Did Obama win? Who knows? Jonathan Bernstein, who writes "A Plain Blog About Politics", points out that if you use the "less smoothing" tool on Pollster's poll-tracker ("call it the Andrew Sullivan option"), the polls sometimes move as much as five points overnight: implausible. Moderate smoothing shows that Romney got a big bump after the first debate. And "more smoothing" shows Obama with "the same 2.5 point lead he's had all year".

Maybe a significant number of people changed their minds after last night, maybe they didn't. We don't know. The only piece of even vaguely reliable information we have is that the bookies, the poll-tracking odds-of-victory and the trading-exchange website all think Obama has about a two-thirds chance of winning. That's pretty much the same post-debate as it was pre-debate. I think XKCD's point about sports commentary applies almost perfectly here: