Bookmakers and Keynesian Beauty Contests

For any number of reasons, I spend a decent amount of time thinking about how lines are set at a sportsbook.1 I think there are a couple common misconceptions about how a point spread is created. An analogy to the stock market is useful.

When talking about how the stock market works, John Maynard Keynes referred to the idea of a ‘beauty contest’ where the goal isn’t to pick the most beautiful person out of a set of contestants, but instead to choose the one you expect to be the most popular choice. At first thought, you might just go with your own preference. A more sophisticated person thinking a bit deeper might instead pick the one they expect most other people to choose. Somebody even MORE sophisticated might instead pick the one they expect other people to expect other people to choose. And so on, and so on, and so on.  

Keynes’s point was to apply this to the stock market – think about a company’s stock price and how you expect it to move. Should it be based on how a company will perform? Or based on investors’ best guess as to how a company will perform? Or investors’ best guess about investors’ best guess about how a company to perform?2

Back to gambling. Imagine the Bulls are favored by three and a half points against the Lakers. At the most basic level, there will be people who assume that bookmakers expect the Bulls to win by 3-4 points (or, put another way – that the median outcome of a game between the two teams is for the Bulls to win by 3 or 4 points). This is… not entirely accurate. Why? Because bookmakers don’t make money by betting on games or accurately predicting outcomes; they make money by having roughly similar amounts of wagering on both sides of a market, matching buyers and sellers and pocketing their vig. In this way, oddsmaking is a Keynesian beauty contest. From an oddsmaker’s perspective, you really don’t care about the outcome of a game – what you care about is inducing betting in relatively even amounts on both sides. 

Except hang on. That’s not right either. There’s more than one bookmaker in the world, and there’s no reason every gambler has to come to you. Imagine you have a spectacular model and feel very confident about three things: (1) the Bulls should be favored by three points, (2) that the right line to get a 50-50 wagering split would be Bulls by six points, and (3) you have three competitors who are not as good at predicting the split and will probably set their line around Bulls by three points. If you actually post the line you think is correct (#2) but stick out meaningfully compared to other market markets, then any ‘sharp’ bettors will quickly swarm you with bets on the Lakers, and you will have a very conclusively uneven set of wagers.3 

That is not a recipe for success. Instead, you have to actually take this beauty contest a step further – and have your line determined not just by your view on the game, or your view on the public’s view on the game, but your view of bookmaker’s view of the public’s view of the game. This is not the most intuitive thing in the world! And it goes against what a lot of pseudo-sophisticated bettors like to throw out when someone mentions ‘how good Vegas is’ at predicting games. But if you take a step back to think about it, it makes sense (and at least one bookmaker agrees it’s how it works). In the long run, prices will likely adjust to be closer to that 50-50 split you were accurately considering (#2), but in the short run you need to start more in line with other books (#3) or find yourself hopelessly lopsided.  

Another reasonable question – does this actually matter? Or put another way, does setting lines based on a third level Keynesian beauty contest really make a difference versus setting lines based on what you think will happen in a game? In truth, not really. Imagine the opposite were true – that somehow bookmakers were systematically biased in some way compared to the actual outcome of a game. A bettor could clean up just by betting against that bias – and if their wagers were large enough, the sportsbook would end up losing money.4 The only way for that to not happen all the time is for the market to be reasonably efficient enough that spreads are a pretty good predictor of the outcome of the game. But it’s still a fun5 thought experiment on how the lines are set, even if you end up in the same place at the end.

If any of this is interesting, I really do recommend The Logic of Sports Betting. I’m not getting paid for that plug, I just found the book to be a pretty great overview of how to think about sportsbooks and the mechanics behind how lines are set, rather than a gimmicky ‘here’s how to beat Vegas’ that one may expect.