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Anomalies: Super Bowl Coin Toss Betting

2008 February 4
by Brad Humphreys

In terms of betting, the Super Bowl is one of the most popular events in the world. Sports books, as well as trading markets like TradeSports that operate like betting markets, offer a wide variety of bets/contracts on the Super Bowl. I like to follow the trading of contracts on TradeSports in real time for large handle events like the Super Bowl to see how markets interpret the information that is revealed on the field. While surfing around the TradeSports web site before the game, I noticed among the “proposition” contracts offered was a contract on the Super Bowl coin toss coming up heads. Based on the volume of trades, this was the most popular Super Bowl proposition bet on TradeSports, and based on other web sites, proposition bets on the Super Bowl coin toss are one of the most popular Super Bowl prop bets.

For those unfamiliar with TradeSports, and other prediction markets, this site allows members to buy and sell contracts on specific events occurring. Each contract is worth $10 if the event happens and zero if it does not. So if you purchase a contract on the event “heads on the Super Bowl coin toss,” you get $10 if the toss is heads and zero if the toss is tails. Up until the coin toss takes place, these contracts can be bought and sold on a market at whatever the prevailing price is at that moment. By convention, TradeSport prices are normalized to the 0-100 interval, so that the price can be interpreted as an estimate of the buyer or seller’s subjective probability of the event taking place.

As anyone who has taken a statistics class knows, the expected value of the toss of a fair coin is 50/50 – a 50% chance of heads and a 50% chance of tails. So the expected value of a $10 contract on “heads on the Super Bowl coin toss” is 0.50*$10+0.50*0=$5, or 50 when expressed in the TradeSports price metric. TradeSports also makes price-volume data available for all contracts. There were 86 transactions, involving 275 contracts, in this particular market. The graph below shows the frequency distributions for the prices paid in these transactions.

This distribution is interesting, to say the least. The mean price was 50.33 and the median 50.35. Why would anyone pay more than 50 for a contract with an expected value of 50? Of the 85 transactions, 52 of them took place at a price greater than 50. Those two trades at 52, which are the equivalent of betting $5.20 for a 50% chance of winning $10, both came minutes before the coin toss.

There are several possible explanations for why we would observe prices not equal to 50 in this market. Risk seeking in the Friedman-Savage sense, consumption benefits from gambling, and a number of Kahneman-Tversky type heuristic decision rules immediately come to mind. FYI, in 42 Super Bowl coin tosses heads has come up 20 times and tails has come up 22 times. I was unable to locate a year-by-year list of outcomes, so we can’t determine if there is a “hot hand” in Super Bowl coin tosses.

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