The phrase “positive expected value,” or “+EV” for short, gets bandied about a lot in the sports betting community. If you’ve been betting frequently and consuming serious content (i.e., OddsShopper’s YouTube Channel) then you’ve probably heard the term. You might even have a general sense of what +EV means. Nevertheless, let’s get deeper into answering the what is +EV question.
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What is +EV? Positive Expected Value Explained
In short, for a bet to be +EV, it means that the probability of cashing on the bet is higher than it is priced at the book where you are placing the wager. Conversely, if your wager’s shot at hitting is less than what you need to breakeven, then it’s a -EV play.
Let’s say you want to bet on the Bears to cover as 3.5-point home underdogs versus the Packers. The book is offering dime lines of Bears +3.5 (-110) and Packers -3.5 (-110). Without getting into details of how the Vig is handled, just know that it means that sportsbooks are holding approximately 2.4% of the wagers on markets priced at -110/-110 (you can use OddsShopper’s Hold Percentage Calculator to find this number for any two-way betting market). So in the case of the Bears +3.5, you will need that bet to hit more than 52.4% of the time to have an edge. With 52.4% set as a breakeven point, if you think the Bears will cover more than 52.4% of the time, then the bet is +EV.
Luckily, OddsShopper has a tool that can help you figure out if your bet is +EV, and by precisely how much. The Expected Value Calculator can run this for any bet so that you don’t have to spend time memorizing hold percentages or figuring them out on your own.
The OddsShopper bet shopping tool will display this information and then some. It’s a turnkey way to approach +EV betting. However, as you get more involved in sports gambling, you will want to get a better feel for this concept. It will help you build an intuition of your own as you shop for bets and grow your betting chops. Yes, OddsShopper will always make things quicker, but the more you know about +EV sports betting, the more that you’ll build your intuition, ability to spot good betting opportunities and your appreciation for the tools at your disposal.
With that in mind, there are a few more nuanced points to discuss about Expected Value that will get you started.
Expected Value is Theoretical
You’ve probably already realized that figuring out your “edge,” or the percent chance of your bet hitting, is the critical component to +EV vetting. But how do you know the true chance of a bet coming through before a game has been played? The reality is that, in sports betting, you never will know anything for certain.
The concept of EV got its start in formal statistics and investing and was later exported to card games like poker. All of these mediums are quite different from sports gambling. That is especially true for card games. Consider the percent chance of something happening in a poker game that uses a 52-card deck. Unlike investing or sports, the “world” of cards is bracketed to those 52 possibilities, including their various numbers and suits. The key is that the number of possibilities is set and never changes. Precise probabilities can be calculated, as can a precise Expected Value because you can specifically gather the likelihood of pulling something out of the deck.
Sports are completely uncertain. We can get an idea for how often something happens by building models that take a possible range of outcomes and compare them to the average or mean outcomes. You can try playing out scenarios or different variations or variables on a sports game and seeing how they would affect the model (known as a regression), but those are always assumptions. We can only input our own assumptions about sports, teams and players before the actual sporting event. In the end, reality happens and the game is played with all the uncertainties that humans bring and cards do not.
That is why you must think of EV as something theoretical. It is an estimate of your percentage chances based on assumptions, whether you are using quantified models or your own “take” on a game or player prop. OddsShopper’s models are back-tested to ensure that they come as close to real game outcomes over a large sample size. Nevertheless, they are models that estimate probabilities and do not compute finite scenarios like a deck of cards.
The +EV opportunities you’ll have in gambling are going to come when the model is slightly off from Vegas. That is where you spot opportunities in a line. But it raises a question of, how off is the model? And how precise is it on any given bet? It’s impossible to answer. You will never know exactly what your percent chance of winning a bet is because sports do not have set parameters like a card game. Your best bet is to have a theoretical +EV.
This concept of EV, in theory, has important implications for how you size your bet and the volume of bets you place. Both will depend on how confident you are in your perceived edge. First, let’s look at some ways to think of betting sizing in relation to expected value.
Uniform Bet Sizing vs. Kelly Criterion Betting
One way to mitigate the uncertainty in your chances of winning is to control your bet sizing. Uniform bet sizing is a straightforward way to do this despite some flaws. If you bet the same amount on every bet, then you won’t have to worry about over-betting your bankroll when your theoretical win probability is lower than you thought. The downside to that approach is you will also be over-betting your roll in the times that your win chances are lower than you thought they were.
The other issue is that you will be missing out on opportunities to grow your bankroll when you spot large +EV situations. If you notice a bet that has a huge expected ROI, you might want to “hammer” it by betting more, even if that ROI is only theoretical.
There’s a method that accounts for this called the Kelly Criterion. We’ll cover it more in-depth in future articles and get into the weeds of its history and mathematics. For our purposes here, what’s important is that the method helps you adjust your bet size depending on the percentage EV that you have. Likewise, you can size your Kelly bets to the full equation or some fraction of it depending on your confidence in a single bet or the entire projection source. Kelly Criterion betting allows you to make the most of EV and to lower your risk a bit in scenarios where the edge is present but smaller.
Before moving on, there are a few other considerations you have to consider when varying your bank size based on theoretical EV or plain confidence. For one, if you are frequently betting into small theoretical edges, you are likely to increase your variance. A 10% edge is going to come through for you 10x more than a 1% edge. Not all value is created equal, so if you are unable to sustain larger swings in your bankroll, you may want to avoid some bets, even if they are technically +EV. When you do make 1% bets, your expected ROI is going to be lower, so in the case that you are playing even small edges like those, you will also need significant betting volume to steadily grow your bankroll.
When you do spot a large, highly +EV bet, even if a Kelly Criterion calculator suggests betting a large portion of your bankroll (at a fraction of Kelly, even), you still must consider your own personal risk tolerance. You may even want to question the robustness of your projections or personal “take” on the bet. Making huge bets can be tough for your bankroll and tough for your “life EV” if they put you at risk. So being completely stuck to the process and its suggestions for +EV betting can be something to avoid to stay within your comfort zone.
These are just some of the finer points of bet sizing as they relate to expected value.
Line Shopping Still Key
Considering how fragile EV is, and how you can never be completely certain how robust your prediction is, you can start to see another reason why line shopping is so important. Given that your real edge varies a small amount from your estimated EV, then a few cents on every bet is crucial.
If you think your win probability for a bet is 55% and it’s a -110 line, then you’ll have $5.00 of EV for every $100 you bet. However, what if your theoretical edge, in reality, was 54%? That would take your EV down to approximately $3. And the more your theoretical win chances are off from your estimate, the more risk you run of going in the red. But if you happen to shop for the best lines (using OddsShopper’s tools, of course), you may find the best at a -105 Vig. In that case, your EV would be around $5, even if you overestimated your win probability.
Margins are slim in sports betting, but getting the best lines available will add up over time. They’ll also give you some cushion on your EV and mitigate losses when you might unknowingly be placing -EV wagers. Shopping, bet sizing and understanding the nuances of EV itself are just three concepts to think about whether you are beginning as a sports bettor or fine tuning your process.
