How bookies can outwit smart bettors

A solution to a fundamental problem for market makers in dynamic conditions

Credit: Associated Press

Michael Maiello | Jun 10, 2019

Sections Economics

Sports-betting markets are based entirely on predictions. A bettor has to pick a winning contestant, and a market maker―a bookie―bets on the opponent. The predictions rely on available information about both sides as well as conditions that might affect the outcome. As bookies have to take the other side of every bet, they have to know what they’re doing. But a bookie can be manipulated by a skillful bettor.

Chicago Booth’s John R. Birge, Booth PhD candidate Yifan Feng, Duke’s N. Bora Keskin, and Uber’s Adam Schultz explore the dynamics of how a bookie can keep from being manipulated. Because the sports-betting market shares features with financial markets that rely on spreads―including credit default swaps and options―the implications of the research could apply far beyond the $4.9 billion-a-year Nevada sports-betting industry. The findings may interest sports bettors and hedge-fund managers alike.

The researchers identify a key problem for bookies and financial market makers: they are vulnerable to being bluffed by knowledgeable bettors or bettors with inside information, such as whether a star is able to play. The bets being placed are the bookie’s best source of information—by analyzing betting patterns, a bookie can effectively crowdsource information about the expected outcome of an event. However, a clever bettor might place some phony bets to throw the bookie off. Through the application of a theoretical model, the researchers identify a set of policies, which they call inertial policies, that enable bookies to strike a balance between learning from market participants and bluff proofing their business.

Say you want to place a bet on the Chicago Bulls, a National Basketball Association team. A sports bookie might take the bet on the condition that the Bulls would have to win by, say, six points, or else you lose the bet. If the bookie sets the spread right, you’ll still place the bet, the Bulls can still win, and the bookie can still make money. As the bettor, you can’t be happy with this because a bookie who never gets the spread wrong never loses. This dynamic is also at play in other predictions markets, including options markets, where investors pay a premium for the right to buy or sell stocks or commodities at a certain price, or the CDS market, where investors pay to bet on whether an event such as a corporate bankruptcy will happen.

Birge, Feng, Keskin, and Schultz imagine a bettor who knows more than the bookie, creating an interesting dilemma for both sides. The betting market is a prime source of information for the bookie. If everybody wants to bet on the Bulls, the bookie takes note and factors that into the calculation of the spread. If the bookie notices that particularly smart bettors are bullish on the Bulls, the bookie sets the spread even wider. 

If a bettor has perfect knowledge of the statistical distribution of outcomes for the event he’s betting on, and always bets according to this knowledge, he can make no money, the researchers reason, because the bookie will never bet with him on terms that allow him to win.

In the researchers’ model, when a market maker accepts a transaction—whether it’s a sports bet, an options contract, or a CDS contract—she has to estimate the likelihood of being forced to pay out and build in compensation for taking that risk: commission. For the bettor, the payoff can be summarized as betting $1 to win $1 minus the commission. If the bettor loses, he loses only the money he put up. If the bettor wins, the market maker is left with only the commission. 

If a bettor has perfect knowledge of the statistical distribution of outcomes for the event he’s betting on, and always bets according to this knowledge, he can make no money, the researchers reason, because the bookie will never bet with him on terms that allow him to win. This bettor’s very act of placing a bet tips off the bookie, whose goal is to place the point spread in the median of the distribution of outcomes. The bettor may try to lie (or bluff) and take the losing side of a few smaller bets to trick the bookie into setting spreads too tightly later on, creating opportunities to exploit mispricing. If the bookie uses the standard rational economic model for setting point spreads (known as a Bayesian policy) without considering the possibility of such a clever bettor, the skillful bettor can fool the bookie into setting a spread that leads to big payouts to the bettor and losses for the bookie. 

This is where the researchers’ inertial policies come in. A key variable in those policies is the difference between “positive” and “negative” bets—that is, the difference between how many bets have been made in favor of a particular event (i.e., the Bulls winning by at least the current point spread) versus the number of bets against that event. Using this information, the bookie can set the spread close enough to the median of the outcome distribution that the informed bettor has no incentive to bluff, given the cost of commission.

“We propose a solution to the market maker’s problem by constructing a dynamic learning policy that collects information at a judiciously selected rate,” they write. “The spread converges in an ‘inertial’ way to make it too costly for the informed bettor to bluff, which resolves the tradeoff between learning and bluff-proofing.”