How does the public bet?
Poorly. Part 2 of a series on the algebra of betting.
Author’s note: I had intended to follow up my previous post on oddsmaking and how bookmakers operate with a post on how the public bets. And will do that here. However, this post will also include a response or rejoinder to Zvi Moshowitz’s recent analysis of what we know about legal sports betting. The post is worth reading in full.
In the last post, we covered how professional bettors bet using the Kelly Strategy - and how oddsmakers—who are themselves professional bettors—use this, combined with knowledge about how other professional bettors bet, to create highly advantageous situations for themselves.
The key thing that makes this possible is that the difference between a professional bettor and a recreational player is massive. Not a few narrow percentage points. But rather, a massive philosophical difference in how to approach gambling.
Why do regular people bet?
Where professionals bet to win money, recreational players bet either to enhance their enjoyment of the game (entertainment bettors) or because they are gambling addicts (addict bettors). And make no mistake—unless you are placing bets using multiple algorithms to assess outcome likelihood, error, confidence of each, and bet-sizing—if you bet, you are either an entertainment bettor or a addict bettor.
Entertainment bettors bet to enhance their enjoyment of the game. They find sports more exciting to watch if they have “skin in the game”. For them, typically, watching sports is something they grew up with, but now that their youthful passion for sports fandom has worn off, they need something to sweeten the deal for themselves. Thus, they bet.
Addict bettors bet because they are gamblers. This group of people is not dissimilar from those who you can find decorating casino slot machine chairs throughout the country. When they say that Vegas wasn’t built on winners, these are the people that Vegas was built on; these people are going bankrupt because they cannot control their losses; these people are the reason that there is a national a gambling addiction hotline: 1-800-GAMBLER.
How do regular people bet?
Unlike professional bettors, whose behavior we can formalize—because it is rational and goal oriented—it is very difficult to formalize the irrational behavior of people who lose money on sports betting. And make no mistake, the public loses money on sports betting. Industry leader FanDuel makes nearly $1B / year on bets.
Entertainment Bettors
Entertainment Bettors bet for entertainment purposes. Therefore, we can imagine a theoretical inequality governing entertainment bettors decision making:
Where
a is the amount bet
p and q are the probabilities of winning and losing, respectively
ep and eq are the excitement of winning and losing, respectively
and u is the amount of money 1 unit of excitement is worth
Under this formulation, entertainment bettors are perfectly rational creatures. They’re paying for entertainment at a rate that makes sense for them.
However, there are two problems with this.
First off, we know that entertainment bettors do not know p and q. They might be able to make informed guesses about p and q, but if they were able to get accurate understandings of p and q, they would probably following professional betting patterns. In that case, the entertainment aspect would change—you are now watching to be entertained by winning money and being correct about your assessments—but the fundamental motivation stays the same.
Second, ep and eq are not constants. They are themselves variables that depend on a litany of factors, including the value of u and the value of a.
For example, we should expect that as a increases towards 100% of a persons net worth, the value of eq goes to negative infinity rather quickly. In fact, by the time a has increased to a substantial portion of your bankroll, the pain of a loss — eq —is much greater than the joy of a win. Some might call this loss aversion; most would call this sanity.
Tied up in that is one’s appetite for gambling, which is set by u. There’s a famous story about Michael Jordan gambling with an acquaintance, who asks him what the stakes are. To which Jordan replies, “whatever amount makes you uncomfortable.” Jordan’s insight here is that his desired u is much greater than his opponent’s. This gives him an advantage because as u increases, eq increases faster than ep. If he can sufficiently increase eq, then Jordan can induce bad decision making in his opponent via loss aversion.
In practical terms, however, as we make more money, have higher net worths, or build up a tolerance to gambling over time, u will increase, relative to both eq and ep. That is that the quantities u/eq and u/ep will both increase. This means that the amount an entertainment bettor bets is expected to go up over time, despite them being negative expected value gamblers.
What is most important, however, is the first point: because entertainment bettors are wrong about p and q, they are highly profitable for oddsmakers. Because entertainment bettors do not factor in expected value of their bets—rather playing for excitement—they are not sensitive to the small changes in odds that make huge differences for professional players. Remember that a shift in a line from +105 to -110 can make a bet go from a no-play to a sizable bet for a professional. For the entertainment player, these differences don’t even register as differences at all.
Addict Bettors
Addict bettors are the lifeblood of oddsmakers business—regardless if bookmakers or bettors want to admit. Addict bettors are primarily fueled by hope. They see large payouts—especially from parleys or teasers—and look to cash in with big winnings. A few large scores propel them through tremendous, long-term losses.
And this is reflected directly in both the public reports these bookmakers must make to investors—where they talk up how they are going to capture more of the parley and in-game betting markets (which offer high payouts, but terrible odds)—and how the companies market themselves to users: again, an emphasis on same-game parleys, which offer relatively terrible (and hard to calculate odds).
What does this mean for oddsmakers?
As we have seen, oddsmakers are constrained only slightly by the public. The public is willing to bet large amounts of absurd propositions because it provides them entertainment and satisfies a fantasy of obtaining a high-payout event. These things are not tethered to reality.
As a result, professional gamblers can beat lines set by oddsmakers. But as we noted in the previous post, this is not the same as beating the oddsmakers themselves. In many ways, oddsmakers use the professional bettors to diversify their portfolio and align the size of their bets—which they do not have perfect, direct control over.
Provided you can open a book and offer lines, you should have access to what is effectively an infinite money machine. The trouble, of course, is your competitors. Line shopping—a behavior that only sharps do in practice—forces oddsmakers to offer better lines than they otherwise would, reducing their profits. That said, because line shopping is hard, the name of the game is customer acquisition.
A bookmaker wants to acquire as many customers as possible, because each customer is substantially positive EV for them—potentially up to $75/mo. based on recent research.
What does this mean for you?
Your first order rule should be not to bet. Just don’t do it.
We make recommended bets on this site, and our bets have paid out well above breakeven. Further, we put some nominal stake behind each recommended bet on FanDuel. But we do this primarily to “put our money where our mouth is”. It would be dishonest to recommend lines and not bet them.
Since this blog started, we’re getting a near 50% return on investment. If we have bet $100 to date, we would have $150 in our bankroll. That’s not exactly how it has worked, because the bets take place through time and we don’t stake each bet with even sizing (see the Kelly Strategy in the last post) — but it’s close enough.
And all that said, you shouldn’t bet. Betting now increases your likelihood of becoming an entertainment bettor or an addict bettor, and both of those are negative expected value shifts. Again, as an entertainment bettor, the more you bet, the more your u/eq and u/ep will both increase — causing you to bet (and lose) more money.
If you want to bet, come up with a system. You need a system for assessing what you think the odds are, comparing that with the odds that are actually offered by the book, and then sizing a bet based on that. Ideally, you can do this with a bankroll approach, where you set some palatable number as your bankroll and only bet fractions of that.
If you used a crude approach, and bet 6% of your bankroll for your favorite game each week of the NFL season and 3% of your bankroll for two other games, you should be able to make it through at least 20 seasons of football without needing to re-up your bankroll. If you want to bet and have some skin in the game—this is a measured and safe way to do it.
Should betting be legal?
Because sports betting’s legality is so recent, an obvious question that many are asking is: did we make the right decision?
The responses to this generally take two paths:
Sports betting is bad because the oddsmakers are predatory and people make bad decisions with their money when given the opportunity
Sports betting is just another thing and we shouldn’t make it illegal just because some people choose to spend lots of money on it
Similar—better—arguments can be made for a whole host of vices: alcohol and marijuana are two that come to mind because they have both been illegal in the near-past. These are also things that have massive negative effects on society, and yet, we choose to make them legal.
Why? Because the vast majority of consumers indulge in these things responsibly, and outlawing the practice creates a black market with its own (negative) knock on effects. Instead of funneling money to American corporations that can be taxed, black market revenue by and large goes to organized crime. It is no coincidence that the Mafia has strong associations with both prohibition and gambling.
So yes, sports betting should be legal. There is no reason that a sports fan should need to interact with violent criminal organizations to enhance their enjoyment of a sporting event—even if doing so costs them $1,000 per year. $1,000 per year might be a large number, but it might also be a reasonable number, given the amount of enjoyment that many derive from sports fandom.
Further conversation is warranted on the matter of how sports betting might be restricted. For example, we already have restrictions limiting betting to those over the age of majority. Could further restrictions apply to limit the most addictive behaviors? Certainly.
As a bettor myself, I would be reluctant to see the user experience for betting get significantly worse. As it is, complying with location restrictions and session time limits is burdensome enough. And as one adds restrictions, one needs to be careful not to tip the scales to make it a better experience to bet through a black-market bookies and illegal sports-betting sites. Today, about $60B in bets each year goes to illegal, online oddsmakers. Those oddsmakers do not conform to the restrictions put in place to provide a better experience—so we have to be careful about how much we disadvantage the lawful players in the market.