Broncos? Seahawks? Put Your Money on Volatility
Sports fans watch the point spread of an upcoming game to see how the "market" -- the bookmaking process -- judges the likely outcome, but many don't know that the same market also tells us how exciting game is likely to be. The information in the market suggests that Sunday's Super Bowl could be very exciting.
Most sports fans (and all sports bettors) are familiar with the idea of the point spread. For example, as we write the point spread for the Super Bowl has the Seattle Seahawks as two-point underdogs, meaning that the market expects the Denver Broncos to win by two. That's pretty tight, and it suggests (a little deceptively, as we explain below) a close game. Less well known to sports fans (but well known to sports bettors) is the idea of money-line odds. The money-line on a Seattle Seahawks victory is currently 115. That means that if you bet $100 on the Seahawks and they win, you would receive $115. We can turn that into a probability. The market is pricing the bet so that $100 (what you put up to make the bet) is the expected value of what you get back in total after the bet, which is $215, since you get your $100 back and $115 in winnings. That is, $100 = probability of Seahawks victory times $215, which means that the probability of a Seahawks victory is $100/$215 = .465, or 46.5 percent.
But there is other information lurking behind those numbers that suggests a much wilder game. With a few assumptions that use the same thinking behind the Black-Scholes option-pricing model, we can infer how uncertain the market is about the outcome of the game. A market that was completely certain of the outcome would have no doubt that the Broncos would beat the Seahawks by two points, and the probability of a Seahawks victory would be zero. A market that was very uncertain might still expect a two point victory, but would allow a large chance of a Seahawks upset.
Not surprisingly, the relatively high probability of a Seahawks victory (46.5 percent) tells us that while the Broncos are favored, there's considerable uncertainty among bettors about who will win this game. Using a little math, we can express that uncertainty in terms of the "implied volatility" of the difference in the final scores. The implied volatility is the point spread divided by a function (the standard normal quantile function) of the probability, that is, -2 divided by a function of 0.465. When you solve this equation, you get 22.7, which is more than a three touchdown volatility! This tells us that while the market expects a Broncos victory, that does not mean that the market expects the game to be a close one for four quarters. And the potentially large swings in the score are consistent with the pretty high probability of a Seahawks victory, notwithstanding that the Seahawks are underdogs. Broncos fans should not expect to ride a small lead from start to finish and focus mainly on the commercials, and Seahawks fans shouldn't fret at the first Peyton Manning touchdown. In others words, the market is telling us to hold tight for a possibly wild ride.
(J.B. Heaton is a partner at the law firm Bartlit Beck Herman Palenchar & Scott LLP in Chicago. Nicholas G. Polson is professor of econometrics and statistics at the University of Chicago Booth School of Business.)
If you want to see all the math, here is an academic paper co-written by one of us: "The Implied Volatility of a Sports Game."
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James B Heaton at firstname.lastname@example.org
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