Arbitrage in the Sports Gambling Market

Everybody wants to find opportunities for arbitrage profits. Who wouldn't like money for free? The typical definition, such as the one found in the Economics Glossary defines arbitrage as "the opportunity to buy an asset at a low price then immediately selling it on a different market for a higher price." If I can buy an asset for $5, turn around and sell it for $20 and make $15 for my trouble, that is arbitrage. The $15 I gain represents an arbitrage profit.

Other Types of Arbitrage

However, there are other ways to earn arbitrage profits than buying something on one market and selling it on another. I recently saw an arbitrage opportunity when I visited a number of sports gambling sites that were offering bets on the number of games Major League Baseball's Toronto Blue Jays would win this season.

How these bets typically work is that the sportsbooks set a benchmark number of how many games the team will win that year. Then you can bet whether you think the team will win more games than the benchmark (known as "over") or less games than the benchmark (known as "under"). The benchmark number of wins are set by the sportsbooks so that the number of gamblers who bet over is roughly equal to the number who bet under.

I was recently surprised to find that these benchmark numbers varied quite a bit between different sportsbooks. Here is an example:

Sportsbook A: Number of Blue Jays Wins Over/Under: 72.5
Sportsbook B: Number of Blue Jays Wins Over/Under: 68.5

The ".5's" typical in these types of lines. In the case of Sports Book A, it allows 73 wins to be counted as "over" 72 wins to be counted as "under". That way there are no ties.

A savvy bettor could, in theory, make a series of bets that ensured they would not lose money on any outcome and in some cases, win a great deal of money. Considering the following sets of bets:

Arbitrage Bets

Bet $100 at even odds on "Under 72.5" 72.5 at Sportsbook A
Bet $100 at even odds on "Over 68.5" 68.5 at Sportsbook B

If the Blue Jays win 68 games or less then they would win A's bet and lose B's and break even. If they won 73 or more they would lose A's bet and win B's, also breaking even.

The interesting situation comes when the Blue Jays win 69, 70, 71, or 72 games. In those situations the bettor would win both bets and be up $200.

Arbitrage in Theory vs. Practice

Sounds like a great plan, though in the case of sports gambling it is unworkable in practice, due to transaction costs. Transaction costs undermine many arbitrage schemes such as this one as they turn break-even propositions into losing ones. In the case of sports gambling, the sportsbooks require that you bet $110 in order to win $100. This $10 difference, which is how the sportsbooks make money, acts a transaction cost. With transaction costs, instead of breaking even the bettor loses $10 if the Blue Jays win 73 games or more or 68 games and less. Because the bettor makes $200 if the Jays win between 69 and 72 games this still might be a good gamble, but it is no longer an arbitrage scenario as there are ways to lose money.

The sports gambling case is just one market where there is the potential for close to arbitrage profits to be had. I am quite certain that if you looked carefully, you could find many other situations where there are profits to be made through arbitrage.

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