The Wisdom of Crowds Redux —Bookies and Bettors

February 5, 2017
Posted by Jay Livingston

Several posts in the early years of this blog (e.g., here ) looked at the “wisdom of crowds” – the idea that the collective wisdom of large numbers of interested people is usually more accurate than the guesses of a few experts. Each post focused on a single event, usually a football game, where the public favored one side while the “smart money” (a small number of professional gamblers) favored the other. 

My thesis was that at least in sports gambling, the crowd was not so wise. If it were, it would have put a lot of bookmakers out of business.

The only data I had, unfortunately, was anecdotal – a few games, like the 2010 Superbowl, where the public heavily favored one side and lost. But this season, I’ve compiled a more complete data set – all NFL games. My indicator of the crowd’s opinion is the change in the point spread late in the week – from Friday to kickoff.*  If the spread goes up, it’s probably because the public is betting the favorite. The bookies are raising the line to attract more money on the underdog and thus balance their books. (On most bets the bettor puts up $110 to win $100. The book with equal amounts on both sides – say $1100 on the favorite, $1100 on the underdog –  is guaranteed a net of $100 no matter who wins.)

I looked at games this season where the line moved by at least one point.** Here are the results.

If you had bed against the wisdom of crowds, you’d have won 54 bets and lost 32. Putting up $110 to win $100 on each of the 86 games, you’d have come out $1880 to the good on a total investment of $9460 – about a 20% return. And except for the first week – 1 Win, 3 Losses – the whole season you’d have been in the black, playing with house money.

As for today’s Superbowl, there has been no movement in the line. It opened at 3 two weeks ago and has stayed there.*** Small bettors are tending towards the Patriots, larger bettors towards the Falcons, so the money is about evenly distributed. Of course the deluge of bets in the next few hours could change that balance.

My own hunch is that the Falcons will win it on the field.

* Line changes early in the week are usually caused by large bets from “sharps.”

** The change in the point spread is not a perfect variable. For one thing, different books put out different lines. I used the consensus number. For another, bookmakers now respond to betting imbalances by changing the odds rather than the point spread. For example, in today’s Superbowl, the point spread is 3. If a book is getting too much action on the Patriots and needs more Falcons money, rather than raising the line to 3½, they will adjust the “vig.” Bettors usually think of the vig as a tax on losing bets. If you win, you get $100. If you lose, you pay $100 plus the tax – usually 10%. But to balance the bets, a book might raise the vig on the Patriots to 15% or 20% and lower the Falcon bettors’ rate to 5% or even 0%.  In this case, the unchanged point spread would be misleading. The public would be betting on the Patriots, but the line remains at 3.

*** Books are very reluctant to change a point spread of 3. It’s the most common outcome – out 10% of games are decided by three points. If a book raises the line to 3½ and gets a lot of action on the underdog, and if the final score is 20-17, the book loses all those 3½-point bets while not collecting on the 3-point bets. That’s one reason that when the line is 3, books are much more likely to adjust the vig rather than the points.

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