Today’s Big Match-Up

February 3, 2019
Posted by Jay Livingston

It’s Superbowl Sunday, and this year we’re about to see a contest between two rivals that have met several times previously on this blog. No, not the Rams and the Patriots, not exactly. It’s The Wisdom of Crowds versus The Smart Money.

The theory of the wisdom of crowds says that the average guess of all the interested participants is better than the guesses of the experts. The full title of James Surowiecki’s 2004 book on the topic is The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations. He begins with the famous anecdote of Galton at the fair. Here’s a summary from an earlier blog post on the topic.

Plymouth, England, 1906. On display is an ox, slaughtered and dressed. How much does it weigh? Fairgoers submitted their guesses. A statistician, Francis Galton, happened to be there and recorded the data. Galton was also a eugenicist, so he was certain that the guesses of the masses would be less accurate than those of the experts. But it turned out that the crowd, as a group, was far more accurate. The average of all the guesses (n=787) was within one pound of the actual weight (1,198 lbs). No individual guess came that close.

Surowiecki doesn’t say much about sports betting, unless you consider ox-weight estimation to be a sport. But my immediate reaction was that if Surowiecki is right, then bookmakers should be an endangered species, constantly paying out on many bets and collecting few. Not a good way to run a business.

Sports books are experts. They set a line that they think will bring in an equal amount on both sides.* They often assume that the public will share their views on the abilities of the teams, and often they are right. But sometimes, the public thinks that the bookmakers are wrong and bet so much on one team that the books have to adjust the point spread to bring in more action on the other side.

This year, bookmakers judged the Rams and Patriots as evenly matched. The opening line on the Superbowl was pick-’em. Neither team was favored. (A small number of books had the Rams as a 1-point favorite, a few others had the Patriots by one.) The crowd roared in on the Patriots, and the books quickly raised the line to New England minus 2½. Bet the Rams, and you start the game ahead by that many points. Or bet them without points and get $120 for a $100.

Even that couldn’t attract enough money on LA.  Bookies are holding three times as much money on the Pats as on the Rams. On Thursday, a high roller bet $2 million on the Rams at the MGM, and that still didn’t offset the New England money. If the Rams win and MGM has to pay out that $2M, it will still finish well in the black.

It’s not just the oddsmakers who think the crowd is wrong. The “sharps,” professional gamblers who make a living from sports betting,** are also hitting the Rams — just not in large enough amounts to balance the millions of dollars coming in on the Pats.

I am posting this four hours before kickoff, and perhaps the crowd will move in with lots of money on the Rams, but I doubt it. If things stay as they are, today’s game is a good example of The Wisdom of Crowds vs. The Smart Money. (Of course, it is only  a single data point and by itself will prove nothing.)
UPDATE: The crowd was wise. The Patriots won 13 - 3. The crowd was also wise on the over/under which started at about 58, but the crowd, betting heavily on the under, brought it down a couple of points.

* Most point-spread bets are 11-10 — the bettor wagers $110 to win $100. If the action is evenly divided, the book makes money no matter who wins, paying out $100 to each winner and collecting $110 from each loser.

** The guy who made the $2M bet is not considered a sharp, even though he won a very large bet last year when he took the Eagles over the Patriots in last year’s Superbowl.


Andrew Gelman said...


The bookies get the vig, so they don't have to beat the wisdom of crowds, they just don't have to lose to it by too much.

Jay Livingston said...

Andrew, The standard 110-100 odds keep the bookies in the black in the long run. But there are still games, and this year’s Superbowl was one, where the betting is so lopsided that even with the vig, the bookies lose a lot of money if the wrong side wins.

Even so, the Superbowl line held at 2½. This year, 16% of NFL were decided by three points. So if you move the line to 3, you risk having a push on all the new money coming in at +3 and still losing the old bets at 2½. (When books set when the original line at 3, they’re even more reluctant to move it, for the same reason, except now, they lose all those new bets. Of course, now that betting is online rather than by telephone, they also adjust the vig the same way they adjust the money line. One side might be 120-100 while the other is even money.)