An analysis of sportsbook behavior and how to profit

This is actually not my text, it’s from Chris Ludwiczak’s honor thesis, published in 2014. A Reddit post reminded me about it, therefore I’m publishing it here so that our readers may see it as well:

If a sportsbook can attract the same amount of betting dollars on each team, it will earn a risk-free return of about 4.5% or 1/22 on the total money bet due to the ‘bet 11 to win 10’ principle. While this is the most rational expectation of how a sportsbook operates, Steven Levitt was not convinced. He saw three possibilities for how sportsbooks set prices.

  1. The first was the traditional model described above, where sportsbooks set prices in an attempt to equalize the volume of betting on each side.
  2. The second possibility assumed that bookmakers could perfectly predict the expected outcome if the game were played a large number of times and by setting the ‘correct’ price, the sportsbook will still earn the riskfree rate. Since both of these possibilities assume the bookmaker is perfect at predicting unknown variables, Levitt decided the actual strategy is likely somewhere in the middle.
  3. The third possibility assumed the sportsbook was better than the average bettor (but not necessarily perfect) at both predicting the outcome of a game and predicting public sentiment for each team. If this is true, sportsbooks would then be able to skew lines slightly against the team the public will favor. This will introduce risk for a sportsbook, but it will also increase expected returns if done correctly.

Levitt Hypothesis: His hypothesis claims that since sportsbooks are the best at predicting the outcome of games and public sentiment, they are able to shade lines against public favorites, especially on the road, in order to increase profits above the risk free return of 4.5% (Levitt, 2004). This hypothesis makes several important claims that go directly against the traditional model. His findings also include a graph about the win rates of all the competitors to show that win rates are normally distributed with a mean of 42/85, or just under 50%. Although the number of bets on any particular game was often far from equal, no one was able to find real success, and the average bettor was as good as the flip of a coin. Over the long term, a bettor (betting an equal amount on each game) with a win rate of 50% will lose at the 4.5% rate that the sportsbook wins.

A much larger percentage of dollars are bet, and accepted, on road favorites. In addition, the higher the pointspread on the game, the higher the percentage of dollars that is bet, and accepted, on the favorite. Specifically, being a road favorite increases the percentage of bets on that team by more than 16%. Also, with each additional point that a favorite is favored by, the percentage of dollars bet on that team rises by 1.31%. Seven-point favorites, for example, have a higher percentage of bets on them than a three-point favorite. Put simply, fans over bet the best teams in the league which leads to sportsbooks accepting a much higher percentage of the wagering dollars on big favorites and road favorites. This leads to a closing pointspread in this market which maximizes profits as the sportsbook does not strictly attempt to set a market clearing price – Paul & Weinbach, 2007.

This supports the idea that sportsbooks are not pricing to simply clear the market and take the risk free return, but rather they are trying to encourage as much action as possible while keeping more of the action on the favorite (after skewing the line against the favorite).

It makes sense then that if a sportsbook makes a deliberate effort to stray from this range, there is value on one side or the other depending on which way the sportsbook strays. This situation should be decidedly profitable and, more importantly, it should always be profitable (as long as the sportsbook is winning). When the sportsbook strays from normal behavior, there must be a reason and that reason should tell us the sportsbook knows something that the betting public doesn’t. Interestingly, the reason itself doesn’t actually matter to us. The only thing that matters is that if we see a sportsbook make a deliberate effort to stray from the normal betting percentage, we can ride the coattails of the experts and beat them at their own game. The key word to remember is deliberate.

So how exactly do we identify when the sportsbook is making a deliberate effort? There are two main cases which make sense theoretically and which should be relatively easy to spot with some experience.

  1. The first situation is reverse line movement, which is when the line (point spread) moves in the opposite direction from what would increase efficiency. This is not a new idea and many online handicapping sites have tried to use this strategy. If a home favorite has 74% of public bets and the line is currently at -4, it would make sense that the bookmaker increases the line, maybe up to -5 or -6, in order to bring the bet percentage down closer to the regression model. Thus, if a sportsbook lowers the line to -3, this is very likely a deliberate effort to have more than the usual amount of action on the home favorite. In this case, we should be very confident that the sportsbook is shading against the road favorite and there is great value in betting on the underdog. The reason we can be so confident that this reverse line movement is a signal of value is because there is no logical reason a sportsbook would do this in an efficient market. The only viable reason for this reverse movement is that the sportsbook wants to have more than the normal amount of action on a particular team, thereby taking a position on the other team since they stand to lose money if the public favorite covers. If we believe this to be true, it would be ludicrous not to take advantage of the information.
  2. The second situation that may arise in a betting week to signal value is what we can call a lack of line movement in order to increase efficiency. Let’s assume that on Monday, the bet percentage is hovering around 70% for a 5 point home favorite. By Friday, the bet percentage has slowly risen to 80% and the sportsbook has chosen not to move the line. This would be an example of a lack of line movement. With a 5 point spread on a home favorite, the bet percentage implied by efficiency would be in the ballpark of 58-59% (with some small variance). If a sportsbook appears to be happy with a bet percentage over 70% for the majority of the betting week, it would be reasonable to assume the casino wants more than the normal amount of action on the home favorite. However, this situation is where we must be very careful about our observations. If the bet percentage was 80% on Monday and decreases to 70% by Friday, this may not be a deliberate effort to stray from the norm. Rather, it would be reasonable for the sportsbook to assume the bet percentage will continue to drop in the next two days and wind up close to the level implied by efficiency. We need to remember that the regression model has some unknown variance in the data which we may be able to estimate through experience.

TL;DR: This study talks about combining the art of understanding sportsbook behavior with the science of following sportsbook predictions to gain an advantage on the betting public. The science is easy to explain; it is the art that requires experience to master.

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