How profitable is the account difference betting market? We will consider this issue in the context of discussions about whether bookmaker companies choose “their” side by placing quotes on this market.

Betting on the difference in the account is quite popular among both beginners and experienced players. Like the handicap betting market, the odds of opposing teams or athletes are evened in some way. However, can a bookmaker artificially create a situation in which this market becomes not as “fair” as it seems? But this may well happen if the bookmaker, as they say, “takes the side” of one of the rivals. But can such a situation happen in principle?

A few years ago, renowned economist Stephen Levitt published a research paper in which he questioned the currently accepted view of the efficiency of betting markets, the collective wisdom of bettors, and the profitability of betting companies only through commissioning fees.

According to Levitt, everything is exactly the opposite: bookmakers most often occupy positions with high risk (if we bear in mind the expected outcomes of sporting events), which means that the odds set by them after deducting the margin significantly deviate from the “fair” ones. They do this to achieve higher profit margins by playing on the bias of bettors who are less competent in predicting game outcomes.

Most likely, the author of the article made such conclusions thanks to two important observations. First, during 21 seasons of the National Football League (NFL) from 1980 to 2001, only 48.2% of favorites managed to cover the difference in the score (as we know, to balance the odds of both teams in betting, the favorites were negative handicap). Second, in an NFL betting contest in one of the covered seasons, 285 participants placed 19,770 bets on the outcomes of 242 different matches: of those bets, 60.6% were on favorites. If such an obvious bias in favor of betting on the favorite actually existed in the market, then these two conclusions would directly contradict each other.

Here are a few more factors. The sample of players studied by Levitt was still quite small, while the players regarded what was happening as a competition, and not as trading in the real market. In addition, we do not have information about the ratio of the amount of money placed in the form of bets – bookmaker companies never disclose such data. In other words, the value of 60.6% refers to the number of bets, and not to their share in the total amount, and it is far from the fact that these two values even approximately coincide. Let’s not forget that the author of this article analyzed only one market.

Here we will try to expand Levitt’s analysis to include the National Basketball Association (NBA) score difference market and see if the bookmakers are actually choosing their side. If such a state of affairs does take place, then it entails far-reaching consequences that make us doubt the reliability of the coefficients as a reflection of the real probability of the event outcome. We will then look at the observed NBA score difference bets in the context of whether they are in line with Levitt’s findings. Let’s start with how it would actually look like a state of affairs in which the bookmaker company would choose one of the parties.

** Bookmaker balancing **

Let’s imagine a simple competition with two opponents (team A and team B), where the probability of each of them winning is 50%. Thus, the fair odds for any of them are 2.00. Now let’s assume that the bookmaker applies a 2.5% evenly distributed margin, reducing the odds per entrant to 1.95. For each of these contests, we find one hundred players, each of whom places 100 rubles on team A or team B. Also, suppose that there are 100 such contests in total, which makes the total turnover equal to 10,000 rubles. What profit can the bookmaker expect depending on the change in the proportion of bets on teams A and B or the frequency of wins of these teams?

Let’s start with the simplest case: a passive bookmaker tries to balance the money for both teams (A and B). If both teams win 50% of the time, then the bookmaker will receive 125 rubles for bets placed on team A and 125 rubles for bets placed on team B. The total profit will be 250 rubles, which corresponds to 2.5% of the players’ turnover of all funds , which fully reflects the margin included in the odds.

But what if Team A wins on fewer or more occasions than Team B? let’s imagine an extreme case in which team A never wins. The bookmaker will receive all 5,000 rubles for the bets placed on this team, and he will not have to pay anything to the players who bet on team A. On the other hand, all bets on team B will turn out to be winning. With odds of 1.95, the bookmaker will have to pay 4,750 rubles in winnings for the betters who placed these bets. But the total remaining profit of the bookmaker will still be 250 rubles.

This amount will remain unchanged regardless of how often Team A or Team B wins. If Team A wins, for example, 70% of the time, then the bookmaker will need to pay 3325 and 1425 rubles for winning bets for teams A and B respectively. At the same time, however, the bookmaker will receive 1,500 and 3,500 rubles for losing bets. The total profit of the bookmaker’s office, as we can see, is again equal to 250 rubles.

If the exact distribution of income and expenses for the bookmaker, depending on the bets placed on teams A and B, will differ, then the total profit for offering balanced bets will still always correspond to the bookmaker’s margin. This is why the theory of the balancing action taken by bookmakers is so popular among bettors.

** How does betting bias affect? **

Now let’s assume that the bettors do not bet equally on teams A and B. What happens to the bookmaker’s income in this case? If teams A and B each win 50% of the time, the bookmaker’s profit will still be 250 rubles (the same 2.5%).

Let’s say that there are no bets on team A at all. In this scenario, if team B continues to win 50% of the time, the losing bets will bring the bookmaker an earnings of 5,000 rubles, and he will have to pay 4,750 rubles at the winning rates. The total profit of the bookmaker is still the same. Suppose 80% of players bet on team A. Then the bookmaker will have to pay 3800 and 950 rubles to those who bet on teams A and B, respectively, but at the same time he will receive 4000 and 1000 rubles in the form of earnings. The total profit of the bookmaker will remain the same again.

** Side selection **

Now consider a situation in which both win percentages and betting ratios begin to deviate from the 50% equilibrium position. Given Levitt’s findings, let’s say that 60% of players place bets on Team A, but that Team A will win only 48% of the time.

In this case, the bookmaker will have to pay 2736 and 1976 rubles for winning bets on teams A and B, respectively, earning 3120 and 1920 rubles on losing bets. Let the total return on bets on team B give losses of 56 rubles, but this is more than offset by the difference between income and expenses on bets on team A (384 rubles). Thus, the total profit of the bookmaker is 328 rubles, or 3.28% of the turnover for all bets.

In this scenario, based on the unreasonably high number of bets on team A, the bookmaker can increase its profit if team A wins less than 50% of the time. In this thought experiment, our bookmaker was lucky, because we made the value of the true probability of such an outcome equal to 50%.

When it comes to the real betting market, according to Levitt’s assumption, if the bookmaker sets the odds for different outcomes as if they are equally probable, but at the same time knows that the participant in the competition on which the players prefer to place their bets will win less than 50% of the time, he will increase his refund to a level that will significantly exceed the declared profit margin.

Despite the fact that such behavior is associated with the risk of demonstrating dishonesty to players, the bookmaker will be happy to use this opportunity, being confident that he is more accurate in assessing the true probabilities of outcomes than his clients, and is more likely to conduct yourself rationally.

The Table below shows how the ratio of actual bookmaker earnings to total betting player turnover will change depending on the percentage of bets on Team A and the frequency with which Team A wins. The ratio of the bookmaker’s profit to the total turnover of bets placed by players is shown as a percentage.

We can see that with a balanced supply, when team A wins 50% of the time, the turnover profit corresponds to the theoretical profit margin. Conversely, the bookmaker could have achieved better results in cases where players are more likely to bet on team A, but it wins less often. The same is true for Team B: you just need to flip the Spreadsheet diagonally from the top left to the bottom right.

** Bias effect **

Returning to Levitt’s observations, let us ask the question: why do players prefer to bet on the favorite in the market for the difference in the score, despite the fact that a handicap in the form of points deduction is applied to this participant in the competition? Levitt never provided an explanation, but other betting experts have suggested a psychological rationale for the bias: the so-called intuitive confidence phenomenon.

They found that nearly two-thirds of the gamblers who placed difference bets with online bookmakers during the 2003 and 2004 NFL seasons preferred favorites. For college football matches, the share of such rates has reached 70%. In addition, the more intuitive bettors became more confident that one side would win, the more confident they were that that side would be able to cover that margin.

Such an intuitive bias arises from the fact that the peculiarities of cognitive processes force us to replace the more expensive judgment attempt to predict the difference in the score between teams with simplified predictions of which team will win. Conversely, when teams of roughly equal forces face off in the same match, the intuitive confidence in the winner becomes weaker, and the bias that one side can cover the score difference also diminishes.

As already mentioned, Levitt’s research did not take into account the volume of bets placed by players, only their percentage. We tried to fill this gap by analyzing the judgments of 178 participants, who were asked to predict the outcome of 226 Sunday NFL matches in the 2007 season by placing hypothetical bets on the winner.

Our observations have confirmed the previous result. Even more intrigue was added by the conclusion that even in cases where participants were explicitly informed that the proposed difference in the score was rigged not in favor of the favorite, the number of players who believed that the favorite would still be able to cover this difference remained practically unchanged.

If a bookmaker can increase its stake from 2.5% to 3.3% thanks to a slight manipulation of the difference in the score, will it be able to subtly increase this percentage by a large amount? If 60% of the players who placed bets on the difference in the account give their preference to the favorite, who wins 45% of the time, the bookmaker’s profit will increase to 4.5%, and if the favorite’s performance drops to 40%, then the profit indicator will increase to 6 , 4%.

However, in the end, the players will still pay attention to these manipulations, so the bookmaker must use common sense in choosing the correct values. Intuitive bias can have a strong enough effect that the difference between 48 and 50% goes unnoticed, but further manipulation of the score difference can cause the behavioral reactions of the players to force them to find a new balance point, and the number of people who are confident in the ability of the favorite to cover the difference will be significantly reduced.

In the table above, you can see that if the stake falls below 50%, then the bookmaker earns less than his theoretical margin suggests. Under realistic conditions, he will only earn the money that he manages to get before the players notice the fraud. If we talk about the effect of bias in evaluating outsiders and favorites, which often affects the markets for placing bets with fixed odds, it should be noted that such cognitive biases exist here, but they are very weak.

** Impact on market efficiency **

From the conclusions of Levitt, who believes that bookmakers are not just engaged in passive earnings on margin, but are actively performing some rather risky manipulations, taking into account the preferences of the players and, accordingly, manipulating offers on the market for difference bets in the account to increase their profits, it follows that the odds of such bookmakers cannot be effective in fair reflection of the true probabilities of event outcomes. Actually, what could you expect if the odds for bets on the difference in the account, suggesting a 50% chance of success, allow the bookmaker to achieve the desired result only in 48% of cases?

Let’s not forget that Levitt’s data has been outdated for twenty years. In the world of sports betting, a lot has changed since then. The number of bookmaker companies, gamblers has increased, and there are also more predictive models, markets, and finally, money. In turn, a higher level of competition should usually imply a move towards greater efficiency and more accurate ratios.

In fact, Levitt’s conclusion that sports betting is not like the financial market is not far from the truth: Action coordinators prefer to become part of these actions to increase their profits, and analysis of more recent data also supports this assumption.