Are the NFL gambling lines consistent with each other?
According to this old Boston Globe article, Daryl Morey discovered that the Pythagorean Projection for the NFL should use the exponent 2.37. That means that from the Vegas betting line and the over/under, we should be able to come up with an estimate of the probability of winning the game.
For instance, last night, the Patriots were favored by 13.5 points over the Giants. And the over/under was 46.5 points. That means that the expected score, in a sense, was Patriots 30, Giants 16.5.
Using Pythagoras on that score, we get that New England should have had a 80.5% chance of winning the game.
But the market prediction, from tradesports.com, was 88.0%. (Sorry, no link.)
So why the difference? I can think of a couple of possible reasons:
1. Pythagoras doesn't work well on such heavy favorites;
2. The distributions are not symmetrical, so even though the *median* score is 30-16.5, the *mean* score is something else;
3. The market for outright wins is less efficient than the point-spread market.
I'd bet #2 is the correct answer, that strategic differences (such as the leading team taking time off the clock instead of going for more points) make the comparison inaccurate. In any case, I doubt #3: if it were that easy to make money by betting the heavy underdog to win, someone would have noticed by now.
P.S. This NYT article says that as of last week, the Patriots were 1:8 favorites to win the Super Bowl. That can't be right – those would be the odds of winning one game against a mediocre team, not three straight against quality opponents. The betting is at about even odds at TradeSports.