Markets Are Information - Beating the Sportsbooks at Their Own Game
In July of 1654 Blaise Pascal wrote to Pierre Fermat about a gambling problem which came to be known as the Problem of Points: Two players are interrupted in the midst of a game of chance, with the score uneven at that point. How should the stake be divided?
The Empire of Chance, 1.1 Introduction
Perhaps unsurprisingly, the study of probability has an inextricable link to games of chance. We can trace the birth of modern probability theory back to 1654 where Blaise Pascal and Pierre Fermat exchanged a series of letters to answer questions centered around gambling. These questions were proposed to them by notable 17th century liberal thinker and gambling degenerate Antoine Gombaud who was interested in what we now refer to in statistics as “expected value” and a question about a specific dice game which would not be out of place in an “Introduction to Probability” textbook.1
Human nature hasn’t changed much since the 1600s. Over the past few years in the US the chosen outlet for those who would like to gamble is increasingly in the form of sports betting. Since a 2018 Supreme Court ruling that lifted a federal ban on sports betting the spread of legalized online sports betting across states has been rapid and ubiquitous. It is impossible to consume any media that has an audience for which the demographic skews male without seeing an ad promoting a sportsbook. After all, sportsbooks operate a business where it is difficult to differentiate the underlying product so it is left to the marketing departments to figure out how to capture a newly legalized, highly profitable market for would-be sports bettors.
I figured it would be thematically appropriate to follow up my last post on poker with another “hobby” that involves a bit of luck. My sports betting journey started surreptitiously at the start of this year - the Youtube algorithm must have identified my interest in poker as being adjacent enough to sports betting that it started recommending me a bunch of sports betting content with videos which claimed to have a system to beat the books. This, of course, caught my eye and a healthy degree of skepticism. How could I, someone who barely knows the rules of the most watched professional sports, hope to overcome the legions of analysts that sportsbooks employ to set the odds?
Where you may expect the answer to lie is with the stereotypical “sharp bettor” who is portrayed as a personification of Moneyball – a sports nerd who runs some sophisticated proprietary model that integrates every possible signal to predict the outcome of a future sporting event and then uses that to identify where value is in the market. Thankfully for most of us, there are also sports betting strategies which require you to know almost nothing about the underlying thing you’re betting on. On first glance… this seems sort of insane? In the vast majority of activities that people are compensated to do, we generally expect some degree of competency or knowledge about that activity. So how can it be possible to construct a profitable sports betting strategy without understanding anything about the sport itself?
The actual answer turns out to be surprisingly simple. My goal with this post is to demonstrate how and why it is possible for anyone with a basic understanding of how coin flips work and a little bit of faith in how markets represent information to beat the books. This is a strategy that I have been implementing over the past 10 months having placed over 1,400 bets across a variety of sports and sportsbooks. As much as showing off results gets the people going, I am going to refrain from leaning on my results as a proof point for whether or not the strategy works or not. I would like to emphasize that in luck dominated activities, to some degree, the results are at best a secondary concern and you really should try to evaluate the merits of the process on its own. That being said, we will cover how I have fared at the end of this post.
How do Sportsbooks Work?
For those uninitiated to the world of sports betting, the general idea is that sportsbooks (“bookies”, “books”) allow their clients to make wagers on whether a particular event will happen in the future. Sportsbooks will have a menu of possible events to wager on and for each of those they will specify a payout which creates implied odds for that event occurring. Once an event has been resolved, books keep the money wagered on the losing side and pay out the winners based on the odds they received when they placed the bet.
So, how does a sportsbook make money? If you deposit money into a sportsbook and place a wager, you will notice that there are no explicit fees that a book charges you for making a wager. The catch is that their fees are baked into the odds they offer. Unless something has gone very, very wrong with the odds that a book is offering or they’re offering some sort of promotion, if you sum up the implied odds for every possible choice in a particular betting market, you will notice that the implied odds sum up to more than 100%! They are, in effect, systemically underpaying whomever is on the winning side of the bet compared to the estimated true odds of an event occurring. That amount over 100% is called the “vigorish” / “vig” / “juice” and is the effective fee that the book collects.
Taking inspiration from “Introduction to Probability” courses, we can use a simple coin flipping game to demonstrate how a vig works. Imagine you’ve been offered to play a simple coin flipping game where you pay $1 to flip a fair coin. You are given the choice of either heads or tails and, if you guess correctly, you will be paid $1.90 total. Clearly this is a losing proposition for the player and the $0.05 they are losing per toss on average can be interpreted as the fee or “vig” that the person offering the game takes. The game offerer could even open this up for anyone to place a wager on heads or tails before they flip the coin. In theory, assuming the book has a large enough bankroll to cover the winners, the book is agnostic as to which outcome occurs as no matter how “unbalanced” the wagers are between heads and tails for any given coin toss, over a large enough sample of flips all of that evens out and they simply collect their fee in the form of “underpaying” the winners. This is more or less how sportsbooks make their money.
The House (Almost) Always Wins
“Edward O. Thorp…obviously doesn’t know the facts of gambling life. There has never been a system invented that overcomes…the advantage the house enjoys in every game of chance.”
Edward A. Olsen, Gaming Control Board chairman referring to the Father of Card Counting
So how do we beat the books? Using the coin flipping analogy, it seems like the house wins by definition. No matter what, they get their cut by overselling the odds. The catch here for the sportsbooks is that they have to do some work to estimate the correct odds of an event happening so they can offer payouts such that they’re not “overpaying” a wager.
Returning to the coin flip example, let’s say the book continues to offer $1.90 if you correctly guess the side the coin lands on. However, you now possess a new piece of information that the book doesn’t have - it turns out the coin is weighted such that it lands on heads 75% of the time! Armed with this new information, it is obvious that you should bet on heads as the $1.90 payout far exceeds the break even payout. In this case, the book got the underlying odds so wrong that a bettor armed with the right piece of information can effectively beat the book.
Conceptually, this is very simple - if we want to beat the book we should be looking for bets that are so mispriced that they are profitable even when factoring in the sportsbook’s vig. However, this can be very challenging in practice. Compared to coin flips, modeling the odds of sporting events is much more complex. Sportsbooks are heavily incentivized to accurately predict the future for the bets they offer. Large casino organizations such as Caesars and MGM are companies worth billions of dollars which invest heavily in personnel whose entire job it is to accurately price these bets. We already revealed earlier that we’re not taking a sophisticated modeling approach to beating the books. So how in the world is someone with very little sports knowledge meant to beat the books?
Turning the Tables - Markets Are Information
The tool that we have against the all powerful sportsbooks is by leveraging their greatest strengths against them. As it turns out, sportsbooks also exist along a spectrum of skill. Some books are better at their jobs than others and we can use this knowledge to make profitable bets. There are a few properties of the sports betting market that allow us to find potentially profitable bets:
Sportsbooks, in general, unilaterally set and adjust the odds for every bet that they offer.
Sportsbooks publicly post their odds.
Multiple sportsbooks exist and independently operate.
Some sportsbooks are better at setting and adjusting odds than others.
The modern sportsbook offers on the order of hundreds of possible bets for major sporting leagues (e.g. NBA, NFL, MLB). This results in a large surface area of bets that each book has to manage.
The odds for bets can change in the days and hours before the bet settles as news is integrated into the markets.
The resulting dynamic allows us to place profitable bets by simply observing the odds that the sharper books2 are offering and placing bets at other, less skilled books on wagers that they have mispriced. An important detail is that you cannot expect to profit by only doing “line shopping”, which is looking across all of the books to see who is offering the best price/odds. We have to remember that the books have a vig so therefore the mispricings have to be large enough to overcome the padding that is built into the odds. These mispricings also don’t have to be all that common. If a book has to manage 10,000 betting lines on a particular day and 0.1% of those bets are mispriced at some point, that gives us 10 profitable bets per day per book.
To once again return to the coin flipping analogy, we can think of sharper books as those which can more accurately identify weighted coins. If every sharp book is saying that a coin has a 75% chance of landing heads then we can shop around the other books to see if anyone else is offering better than 1:3 odds. If we are able to find a book offering better than 1:3, then we can place that bet and can be pretty sure that bet is profitable.
This is a very tangible example of how markets abstract information and how certain market structures allow savvy participants to profit. For the sports betting market, there are strong incentives for books to be as sharp as possible and do all the hard work of trying to accurately predict the future. We don’t need to know anything about the underlying bet because all of the relevant information that we care about for making our bet should already integrated into the odds that the sharper book is offering. The way that we profit is by exploiting mispricings by weaker books. Note that this strategy doesn’t identify “sure” bets. This strategy is a form of statistical arbitrage - we don’t expect to win every bet that we make using this strategy. Instead we expect to profit over the long run over a large number of bets due to being “overpaid” when we win.
The Downsides of a Free Lunch
The first thing that most people ask me when I outline this strategy is: why don’t more people do this? The only thing you really need is a system that aggregates odds for you - and if you don’t feel like building your own there are many paid services3 that will do this for you. There are few practical reasons for which why more people don’t do this that I can think of:
Marketing. The strategy is fairly easy to understand, however, out of the market of people who would even consider sportsbetting, a very small % of potential bettors even know that these market inefficiencies exist.
Picking Up Pennies. Sharp sports betting shares this characteristic with poker - it is very much a grind. In general, most bets that you will be able to find have a small edge generally on the order of 1%-5%. For example, if you are placing $100 bets and average a 5% edge (which would already be considered very good), you are only expected to make $5 per bet. If you can find 20 bets on average per day, that’s $100/day for risking $1,000. Over the long run this adds up, but it requires a certain willingness to put in the time to grind it out. You have to get a lot of volume in to make it worth it and the reward may not be worth it to some.
Bankroll Constraints & Risk Aversion. Many people lack the means to be betting the sizes that are required to make this activity worth it while taking on a risk of ruin that is acceptable. At the end of the day sports betting is a game of chance. Even if you are only making positive EV wagers, there is still a chance that you can go through losing streaks. Personally, I’ve hit 30 unit losing streaks before and, understandably, most people are not going to feel good about potentially losing 30 bets in a row and/or have the bankroll to sustain that type of downswing.
Legality. There are still many states in the US which simply have not legalized sports betting. As an aside, you might be thinking “hang on Jonathan, don’t you live in California where sports betting is not legalized?” And that is a good question (obligatory “I am Not A Lawyer”). Many of the betting operators in CA are attempting to skirt California law by claiming their products are a subset of fantasy sports. Personally, I think their apparent legal cover is paper thin but it appears no one has challenged them… yet. It is telling that many of these books have already been thrown out of New York and Florida for trying the same thing.
A related question that I get asked is: why don’t you quit your job and do this full time?
The books will eventually limit you. Turns out sportsbooks don’t like winners and it is inevitable that a sharp bettor will have the size of their bets limited. This has happened to me a few times and, while the first time feels like a badge of honor, it will drastically cut into your profitability as you won’t be able to put down as much as you would like on highly +EV bets. Due to this dynamic, for the true professional sharp bettors there is an entire cottage industry that provides services to source new accounts for these people.
The books get sharper. This is especially true in markets where a bunch of new books are operating. Initially it seems like it is raining money due to the inexperience of the new books in setting odds. Sadly, this is not something that lasts forever. As books operate they tend to get better at doing their jobs and your relative edge using a market based strategy will shrink over time.
There simply isn’t that much opportunity in sportsbetting relative to a full time white collar job that I’m privileged to have. The opportunity cost of sports betting will, of course, differ based on your particular circumstances. I probably put in on the order of 30min - 1hr of time a day and generate maybe +$50 of EV a day. Due to the limited number of +EV bets there are in a given day, 10xing the amount of time I spend on this is not going to 10x my returns.4
To put it in simpler terms: No free lunch lasts forever and some free lunches are not worth it.
The Results of Glorified Coin Flipping
Now that we have established the system and how it works, I can finally pull down the curtain to reveal how I have fared over the past 10 months.
Assorted stats:
Bets placed: 1,451
Amount wagered: $91,3635
Average bet size: $63
Estimated EV generated: +$9,630
Estimated Average Bet Size Weighted EV %: +10.6%6
Realized $: +$22,446
Worst losing streak: -$2,300 over a 90 bet period
Best winning streak: +$9,500 over a 75 bet period
The above chart is from Pikkit which is a bet tracking app that syncs directly from sportsbooks. My profile on Pikkit is @rudiscoo if you want to independently verify. Overall I would generally be skeptical of people’s betting results even if they show you something from Pikkit as it is definitely possible to manipulate results that make it look like you are a bigger winner than you actually are. The sports betting industry is full of scammers and grifters and you should not by default trust anything anybody says especially if they are trying to sell you something.
Some general observations and reflections on my results:
The discrepancies between the Pikkit and the summary stats I provided are due to Pikkit not supporting some of the other books that I have placed bets on. I have my own spreadsheet to keep track of results for this reason.
I am running very, very good / getting very, very lucky this year. As you can see, my results are way over the estimated expected value. I haven’t done a variance calculation, but I imagine it’s over 2-3 standard deviations above EV. To be clear, this has nothing to do with my skill as a bettor! I am only executing this strategy of looking for discrepancies in pricing in the market and being up this much above EV is purely a product of luck. Either that or the EV calculations I’ve been doing are too conservative.
Over a long enough sample of betting you will experience some very unlikely runs. It’s one of those “a specific sequence of coin toss results is unlikely, but if you toss a coin enough times you are almost guaranteed to observe that sequence at least once”. The almost $10,000 upswing over 75 bets is an example of that. I effectively had a series of events equivalent to flipping a fair coin and it landing on heads something like 15 times in a row. Does this mean I’m good at flipping heads? Probably not, but maybe the market is helping me find coins that land heads slightly more often.
Sports betting at volume gives you a pretty visceral understanding of variance and expected value. I think I’m used to it at this point, but no matter how much you intellectually understand the numbers, experiencing a +/- $1000 swing off of +$50EV in a day reminds me of the amount of risk that I am taking.
As covered in the previous post, these endeavors require quite a bit of volume for you to realize your edge. I was lucky that I was net positive after my first hundred bets, but could have just as easily lost a bunch of money and decided to quit. My overall results over a long enough number of bets should resemble a random walk with positive drift, but nothing is guaranteed in the short term.
How much should these results tell you about whether or not the market based strategy I’ve described actually works? I would personally consider it “weak” evidence in the sense that it probably shouldn’t convince you on its own. Observing positive results suffers greatly from survivorship bias - it’s pretty unlikely that you are ever going to come across a blog post claiming a strategy works and then posting results that contradict that. However, given that you have some trust in the results I am presenting and that I am executing the strategy correctly, 1400+ bets should be a large enough sample to serve as some evidence that this strategy is truly +EV. We are still profitable even if you remove the two most obvious upswings where we had an insane run of luck and went up almost $10,000 in a two week period.
The sports betting market is weird. The 17th century European gambling aficionado mind could not possibly comprehend a world with on demand wagering through the comfort of your mobile device. Even by modern standards the existence of such a market is unusual. The only real comparable market that the average person might interact with is the stock market, but even then the stock market doesn’t generally consist of a bunch of institutional players independently and unilaterally set a price and then allow you to buy or sell that asset.7 It is this structure that paves the way for a profitable market based betting strategy. It is a structure that, unfortunately, only exists because the vast majority of the participants in this market are unsophisticated, losing bettors where even weak sportsbooks have a shot at being profitable.
As someone who has had a passing interest in financial markets - mostly in the form of enjoying Matt Levine’s Bloomberg newsletter - it has been a fun roleplaying as someone sitting at a trading desk, albeit a highly simplified one trading in bets. For folks who want the experience of beating a market, and the swings that can potentially come with it, sports betting is one of the few where the average person armed with the right strategy can hope to have an edge and come out ahead.
Thanks for reading! This post is meant to serve as a high level explanation for how and why a market based approach to sports betting works. There is a lot more to get into on this topic, which include things like pure arbitrage strategies where a bet is priced so differently across books that you can take both sides and be guaranteed a profit. I’ve personally stuck with this hobby since getting started in January because the extra income it generates is worth it for me relative to the amount of time I spend on it and there is just something about taking money from enterprises that engage in predatory practices that is satisfying.8 If there is enough interest in folks learning more, I may do a write up of my experiences traveling to the great state of Colorado earlier this year to take advantage of what was a very soft sports betting market to give a more concrete example of what it is like to execute on the strategy I’ve outlined in this post.
If you have any questions don’t hesitate to reach out via Substack or through my Twitter DMs.
Support Me Through Affiliate / Referrals!
If you are interested in learning more or implementing this flavor of +EV sports betting strategy and would like to support my writing, I have a few affiliate / referral links to various services and books which are compiled below. If you are interested in getting into this world, it is entirely in your interest to sign up for as many books as possible because 1) most books have “free” money in the form of sign up deposit bonuses and 2) the more books you have access to, the more possible bets you have access to, and therefore the more opportunity you have to identify and profit from mispricings.
OddsJam - Odds screener that I personally use. I have also tried a few others on the market, but this is the one that I like the most in terms of how it presents information and having a bet tracking feature to alert you to potentially correlated bets. The OddsJam Youtube channel also has a decent library of videos that go a bit more in depth on +EV sports betting strategies and how to get the most out of their screener.
PrizePicks - “Pick’em” book that offers really good promotions. Generally less sharp on esports. Unfortunately they’ve limited me on promos, but somehow have not limited me on my bets (yet).
Underdog - “Pick’em” book that offers some of the best odds for 3 and 6 leg parlays. Also not very sharp on esports.
HotStreak (use code “RUDISCO”) - Parlay book that has some of the sharpest esports lines which are used to benchmark. Good book to have if you’re based in California because it’s one of the few books that operate in CA where you can effectively place a “straight” bet by using their round-robin feature. This allows you to reduce your variance if your bankroll is limited or you’re more risk averse.
Betr - Parlay book owned by Jake Paul. They offer some decent promotions, but have generally gotten sharper over time. Worth signing up for the deposit match and I expect them to have more value after basketball season kicks off.
ParlayPlay - Another parlay book that’s legal in CA. They offer some decent promotions, but their vig is super high and it can be hard to regularly find profitable bets outside the promos.
Sportsbooks can be evaluated for sharpness by back testing the odds they offered. In general, Caesars and Pinnacle are widely regarded as the sharpest books for traditional sporting events. Hotstreak, a relatively new book, is known for their skill in setting esports lines.
OddsJam is an odds aggregating service that helps you identify profitable betting opportunities. I get affiliate revenue from OddsJam if you use this link to sign up.
As I’ve alluded to, an additional constraint I face is living in California where the books I have access to is limited. Residents of more mature sports betting markets such as Colorado or New Jersey enjoy access to more books and more opportunity.
Because I’m making bets over time, a lot of this is “recycled” money from my bankroll. I certainly don’t have $90k in bets outstanding at any given point in time.
Given that I said 5% would be “really good”, this number may look high to you. There are a couple reasons for this: 1) this includes promos and free bets for which the EV can be 100%+, 2) there are a number of newer books in CA that are really bad at setting some lines, and 3) this is ultimately an estimate, though I don’t have a sense on whether or not it’s biased up or down.
There are some newer sportsbooks such as Novig springing up which operate on more exchange-like market structure principles.
As an aside, Betr is owned by the one and only Jake Paul and there is some extra utility in taking money from him.
Great article! Thanks for such clear thinking and explaining.