Original title: The profit-bias identity in sports betting: bookmaker profit as the public's prediction error
Jacek P. Dmochowski · September 2026
Sports betting steadily transfers cash from everyday bettors to bookmakers. An older model argued that bookmakers intentionally shift their prices to exploit public biases, but it assumed that the share of money bet on a team does not depend on game outcomes. The researchers revisited this idea by relaxing that assumption. They built an exact identity showing that bookmaker profit breaks down into three channels: the standard house commission, the combination of price shifting and the crowd's bias, and the direct link between bet shares and game results. They found that a public lean produces zero extra profit unless the book shifts prices to match it. When testing this on 1,139 Major League Baseball games, the researchers found that people bet heavily on favorites. However, bookmakers did not shift prices to exploit this lean, meaning their actual profits simply matched their standard commission.
Imagine a group of friends guessing the weight of a cake at a fair. The baker charges a small fee per guess. If most friends guess too high, the baker keeps the cake and the fees. The baker's profit is basically the fraction of friends who guessed wrong, minus the fee. In this paper, the bookmaker's profit is the fraction of bets placed on the losing team, minus the hold. The public's systematic error—betting on the favorite too often—drives the profit.
If you've ever placed a sports bet, you've wondered why the house always wins. This paper shows that profit isn't just about setting unfair odds—it's about the public systematically betting on the wrong side. Understanding this could help you see why your bets lose, and it reveals a surprising scenario where both the book and the bettor can profit at the same time.
The abstract does not specify whether the findings generalize beyond MLB or to other sports. It also notes that the apparent dependence between bet share and outcome is a Simpson's paradox, meaning the pooled result may be misleading. The paper does not establish whether the lack of detected shading is due to data limitations or actual bookmaker behavior.
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The profit-bias identity in sports betting: bookmaker profit as the public's prediction error — Jacek P. Dmochowski
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.