Sunday, December 18, 2011

The Favorite/Long Shot Bias – Analysis of Superbowl Futures

by Michael Beuoy

In the week14 post, I outlined an approach to test the validity of the rankings by looking at Superbowl futures. At the time, I thought that Chris Cox’s NFL Forecast tool allowed for customization at the team strength level. Unfortunately, it doesn’t, but Chris was nice enough to run a one-off of his model, using the GWP’s from the Week 15 Betting Market Rankings.

Here are the results of the analysis. I took Superbowl futures from (thanks Ed) as of December 14. I then removed the “vig” from the odds under the assumption that each bet had the same (negative) expected value. In this case, the vig turned out to be a whopping 28%.

Futures Odds – The actual odds from
Futures Odds w/o Vig – Those same odds with the vig removed
NFL Forecast Odds – The odds of winning the Superbowl according to Chris Cox’s NFL Forecast simulation, using the week 15 Betting Market GWP’s
Futures Prob – The same as “Futures Odds w/o Vig” but expressed as a probability
NFL Forecast Prob - The same as “NFL Forecast Odds” but expressed as a probability
Exp Val / $ Bet – For you inveterate gamblers, the expected value of a $1 bet, using the “Futures Odds” column as the payout and the “NFL Forecast Prob” column for the probabilities

At 4.5 to 1, the Patriots are the only positive expected value bet, according to the NFL Forecast probabilities. Unfortunately for me, it’s against my religion to side with the Patriots on anything.

   Team   Future OddsFutures Odds w/o VigNFL Fcst OddsFutures ProbNFL Fcst ProbExp Val / $ Bet

My hope going into this was that the probabilities would align fairly closely. As can be seen from the table above, that was not the case. However, the results did follow a pattern that was familiar to me; one very similar to what is found in thoroughbred racing betting markets. The pattern becomes more apparent if you graph the NFL Forecast Odds against the No Vig Odds (shown on a log scale):

The straight line indicates perfect agreement between the two approaches. As the NFL Forecast odds get higher, the actual odds drop further below the line. If we take the NFL Forecast odds as the “real” odds, this means that the bigger the longshot a team is, the worse the value of the bet. Here’s one more view of the same data:

In horse racing, there is what’s known as the Favorite-Long Shot Bias. It’s a remarkably persistent phenomenon in which favorites are consistently underbet and longshots are consistently overbet (see Fig. 1 from the link). There are many theories behind what causes this. I’m partial to the most prevalent explanation, which is that gamblers are willing to pay a higher price for a low probability / high payoff bet than they are for high probability / low payoff bet. If you’re at the track, are you really going to be hi-fiving your friends after making a $5 profit on your $10 bet on a 3 to 2 horse? Similarly, laying down money on the Packers to win the Superbowl, at this point in the season, is not going to impress many people if the Packers happen to win.

This can also explain why lotteries are so popular, despite being one of the worst expected value bets you can make. Or why slots pay out worse than blackjack (jackpots are sexier than the slow and steady progression of blackjack). And, it appears to explain the payout odds of a team winning the Superbowl. That being said, there are alternative explanations:

• My conversion from GPF to GWP could be off. I use the formula GWP = 1/(1+exp(-GPF/7)). If the GWPs should be more “compressed” than what I have them as, then the odds should line up more closely. However, I just did a more thorough check, using NFL games back to 1998, and “GPF/7” generates the lowest mean squared error in terms of predicting win percentage at a given spread (I may share that in a separate post)
• Injuries. The GWPs are calibrated to match the market’s near - term predictions. An injury to a key player can cause a strong team’s performance to regress to the mean. It’s possible that the Superbowl futures have factored that uncertainty into the payouts.

I don’t think these alternatives could explain the magnitude of the discrepancy I’m seeing between the two sets of odds, so I’m sticking by the Favorite-Long Shot bias explanation.

A HUGE thanks to Chris Cox at for running a custom version his model for me and sending the results.

1 comment:

j holz said...

I made my living betting on sports futures for five years and I can tell you the longshot bias is definitely alive and well. You should have seen how many people bet the giants at 40-1 to win the super bowl four years ago, then bragged about their payday. The real odds against a giants win were six times that, and bettors could have gotten paid six times as much by simply betting on each game and letting it ride, instead of taking the future.

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