A "value added" Super Bowl study
Economists love gambling markets data almost as much as sabermetricians love Retrosheet data. And so it's not that suprising that less than VII days after Super Bowl XLI, an academic economist has run an analysis of the betting market during the big game.
It's by Keith Jacks Gamble, and it's called "An Analysis of the Super Bowl Using Price Changes on an Online Prediction Exchange." It's funny that he calls it "online prediction" instead of "online gambling," especially considering his name.
Anyway, I don't want to sound like I'm making fun of it, because it's a really nice paper. Gamble followed the tradesports.com market's estimate of the teams' winning probabilities during the game, and checked how those changed after specific big plays. For instance, the Bears' touchdown on the opening kickoff reduced the Colts' chances of winning – according to the market -- from 68% to 57.25%. And after the Colts threw an interception on their first drive, the Colts' chances dropped even farther, down to 49.25%.
(One thing I wish is that Gamble had told us more about the bid-ask spread. Gamble took the market's probability estimate as the mean of the spread; this is probably decent enough if the spread is narrow, but not so much if the spread is wide. That's because market efficiency puts the "correct" probability somewhere between the bid and ask, but not necessarily the middle. That is, in an efficient market, you don't see a 20-dollar-bill to have a bid-ask of $18/$19 – because that would enable easy profits to be made buying them up at $19. But $15/$20 is possible in a rational market, as are $20/$25 and $19.99/$20.01. And only in that last case does averaging the spread lead to the "right" estimate.
So if Gamble got his 68% from a bid/ask of, say, 65%-71%, there's more reason to doubt it than if it came from 67.5%/68.5%.)
There's no guarantee, of course, that the market is correctly calculating the probabilities – but economic conventional wisdom says it should be close. And it does seem pretty reasonable. The Colts were favored by 7 points over 60 minutes. After the Bears' touchdown, the seven points were erased – but the Colts now would expect one extra possession over the rest of the game. That extra possession is worth something – maybe two or three points? – so a probability of 57.25% seems about right.
After the subsequent interception that gave possession back to the Bears, they were up by 7. If the Colts normally would outscore the Bears by 7 in 60 minutes, their advantage might be down to only 6.5 with the time remaining in the game – giving a half-point advantage to the Bears. And now the number of possessions should be about even (since the Bears had the ball now, but the Colts would receive the kickoff in the second half). So you'd expect the Colts to be at about a half-point disadvantage now, which is reasonably consistent with the observed 49.25%.
(It isn't enough to consider possessions and time alone – there's still the issue of field position. It's possible that if you take field position into account (discussed a bit here), you might come up with 49.25% exactly.)
Gamble then computes the game's MVP by adding up all the probability changes of the plays he was involved in – similar to the "value added" method for baseball. I'm not absolutely thrilled by this method, because of the difficulty of assigning the individual plays to the individual players, and because using the specific probabilities tends to reward "clutchness," which is sensitive to the time and situation.
But, in any case, Kelvin Hayden was the most valuable player by this method, adding 18 percent of a win on the strength of his one interception/touchdown return; the top Bear was Muhsin Muhammad, at 12.25. (But illustrating one of the weaknesses of the method – the Hayden interception was on a pass meant for Muhammad. If you attribute any of that interception's impact to Muhammad, he becomes much less valuable.)
Rex Grossman was the biggest negative impacter on both teams, with –36.5. Peyton Manning was a quite-respectable 9.75.
(Hat tip: Marginal Revolution.)