Understanding and Finding Positive Expected Value Wagers: A Step By Step Guide

You’ve probably heard sports bettors talk about ‘value’ betting. But, quantifying what bettors mean by “value” isn’t always so easy.

Often, “value” is anecdotal, purely a reflection of someone’s feelings or opinion about a game. Sometimes however, “value” is calculated in a significantly more mathematical way and is more accurately referred to as “Expected Value” (EV).

Expected Value is where sports betting meets analytics. Done right, bettors can make decisions based on the probabilities of a particular bet hitting rather than relying completely on their gut. So how easy is it to figure out Expected Value and place smarter sports bets? Well, all you have to do is follow four simple steps, each of which we’ll explain each below:

Step 1: Understand the Juice
Step 2: Convert Betting Odds into Implied Probabilities
Step 3: Evaluate Bets Using an Expected Value Framework

Step 1: Understand The Juice

Sportsbooks take a commission for booking bets. This tax is called the “vig” or the “juice.” To complete an expected value calculation, you have to calculate and remove the juice.

Here’s an example to help understand the juice: Flipping a coin is a 50/50 proposition. Without any juice, the odds should be set at EVEN (+100), meaning that if you bet \$10, you stand to win \$10. Here, the expected value is 0. You should win half of the coin flips (earning \$10) and lose half of the coin flips (losing \$10). After 100 flips, you should have the exact amount of money you started with.

But, how would a sportsbook ever make money under this model? They wouldn’t. So they change 50/50 odds to -110. This means that if you bet \$10 on heads, and the coin comes up heads, you’ll only win \$9. Meanwhile, the person who bet tails will lose \$10. So, assuming there is one player betting on either side of the coin, the sportsbook will automatically make \$1 per flip (paying the loser’s wager to the winner, minus \$1). Inclusion of the sportsbook’s juice has rendered this 50/50 bet a “negative EV” bet, where bettors would expect to lose money if they continued to bet into this market for any statistically significant amount of time.

However, imagine that the odds for the coin flip were +105. This would be a “positive EV” or “+EV” bet, since your \$10 bet on a 50/50 probability would net you \$10.50. You’d want to take this bet, at these odds, all day every day, as many times as you were allowed. Now you understand the juice.

Step 2: Converting Betting Odds Into To Implied Probabilities

In the coin flip example, it’s pretty easy to convert the odds and pop them into the equation because we know it’s EVEN money. Using the expected value calculation from above, let’s say you bet \$50 on each side and there’s a 50% chance of landing on heads or tails, then the EV equation would look like this:

(10 * 0.5) – (10 * 0.5) = 0

What many bettors struggle to figure out is manipulating the equation when the odds are not so obvious. The short answer is that you can simply use an EV calculator tool to do the work for you.

What you’re looking to do is to convert the sportsbook’s odds into the implied probability of the bet hitting. or example:

 Betting Odds Implied Probability Miami Heat +400 Heat: 20% Boston Celtics -400 Celtics: 80%

Once converted to an implied probability, you’ll see that the sportsbook is predicting that the Miami Heat have a 20% chance of winning the game, while the Celtics have an 80% chance.

Some tools like Outlier, automatically list the implied odds of every single available bet so that you don’t have to plug lines into a EV calculator one-by-one.

Step 3: Use Your Own Models To Find +EV

Now that you know how the sportsbook is valuing particular bets, it’s time to determine how you value them, or said another way, what you think the chances of a particular bet hitting are. Here, the challenge is that you’re charged with quantifying what you believe the probability of a particular bet hitting is. Not an easy task.

If you’re a pro, you might have developed a model that spits out a score for every NFL game, which you can then take and compare to the sportsbooks’ implied probabilities. Sharp sports bettors usually have developed this type of tool.

If you don’t have a tested model, there are two easy ways to inform your EV calculation: (1) Referencing historic hit rates and (2) Comparing sportsbooks’ odds against each other.

Referencing Historic Hit Rates

One simple way to get a sense of a bet’s chances of hitting is to look at the bet’s “historic hit rate.” For instance, when deciding whether Jimmy Butler will score over 25 points in his matchup against the Hornets in tonight’s game, you’d want to know how often Butler has scored over 25 points in his last 5 games, 10 games, during the current season, during all of last season, and every time he’s matched up against the Hornets.

Let’s say the Caesars has set the odds at +120, which is an implied probability of 45.5%. When you look at Butler’s 25 point historic hit rate, you notice that he’s gone over 25 points in 5 of his last 5 games (100%), 9 of his last 10 games (90%), 27 of the 35 games this season (77%), 70 of the 82 games last season (85%), and 6 of his last 6 games against the Hornets (100%). No doubt there are more variables to consider and research (injuries, lineup changes, load management concerns, etc.), but at first glance, you might have found a +EV bet, since Caesars is saying that Butler has a 45.5% chance of scoring more than 25 points, when in fact, he has historically performed significantly better against this prop.

The same can be done for spreads, total, moneylines, game props, team props, and player props of all types. Hit rates are a great way to get a quick sense of whether a particular bet might be +EV.

Comparing Sportsbooks’ Odds Against Each Other

If you’re hesitant to conduct and rely on your own research, you can piggyback off the sportsbooks’ research. This method of determining EV is pretty straightforward. Simply calculate the implied probabilities from the other sportsbooks to see if any one of the sportsbooks is undervaluing the bet or has otherwise departed from the consensus implied probability.

Let’s go back to our Jimmy Butler 25 point over example. Remember that Caesars priced the line at +120 (45.5% implied). Now, let’s say that the other books have priced the line as follows: BetMGM +110 (47.62% implied), DraftKings -110 (52.38% implied), FanDuel +105 (48.78% implied), WynnBet +105 (48.78% implied). The average outlook on Butler’s points over is that he has a 48.6% chance of scoring more than 25 points. That’s a 3.1% better chance than Caesars projected. You might have just found yourself a +EV bet.

Some bettors look at particularly “sharp” books like Pinnacle and compare Pinnacle’s implied odds against other available odds to find +EV bets

Once you’ve identified your +EV bets, you simply need to pull the trigger and track your bet’s performance. Note however, that +EV betting requires patience. At the end of the day, it’s easy to get excited about +EV betting and assume that every +EV opportunity will result in a win. Sadly, that’s not the case.

Let’s go back to the coin flip example. Even if a sportsbook pays you +200 for heads and you bet on heads (a fantastic +EV bet), that doesn’t mean the coin will land on heads the first, second, or even third time you bet it. All it means is that, if you continue to play this exact game at these exact odds, over a long period of time, you will eventually and assuredly be profitable.

The same is true for +EV sports betting. Your +EV edge on the sportsbook might not immediately translate to wins, but, if you are correctly evaluating bets and actually betting on +EV opportunities, then you will become a profitable bettor over the long run.

Pro Tip: Try Using Promos to Profit from +EV Betting

One of the best and safest ways to deploy expected value betting is with the help of some sportsbook promos. Sportsbook oddsmakers can be pretty sharp with their opening and closing odds, and you might not be able to perfectly find +EV bets on your own. However, when the books start to give handouts, you don’t have to be perfect in your expected value analysis– the promo will help you out on the margins.

Let’s say you’re trying to evaluate whether the New York Giants are a good spread bet at +115. After researching the Giants’ track record of covering the spread and checking with the other sportsbooks to see if there is significant variance in odds, you might still be worried that +115 is not quite a +EV bet. However, if DraftKings is giving you an odds boost and has increased the odds to Giants +135 (+20 more than any other sportsbook), then you can confidently conclude that the Giants’ spread is a +EV bet.

Done right, bettors can make decisions based on the probabilities of a bet hitting rather than on what their gut is telling them. This is +EV betting. Now that you understand the juice, are able to convert betting odds into implied probabilities, and have an idea how to evaluate bets using an expected value framework, you should be well equipped to start placing your first +EV bets.

Can you live bet every college basketball game?

Yes, every mainstream sportsbook will have in-game betting available on every major college basketball game. Nowadays, if the game is available in pre-match wagering, it will be available for live betting too. You might find that a rare game between smaller school that’s not available.

Are there times that you can’t bet in-game while the action is happening?

The sportsbooks will remove the odds, readjust and re-hang them throughout the game. This is done in a very swift manner these days, so you’ll simply just notice the odds changing as various aspects of the game take place. However, there are times when the line will be off the board. For example, if there’s a key injury or if a play is under review, the oddsmakers may pull the line off the board until there is more clarity. Also, if the results are becoming clear and the odds are becoming quite high (I.E. when a team is about to win the game), the odds also won’t be available.

What types of bets can you make in-game?

Almost every sportsbook will allow you to bet on the moneyline, spread and total in-game. However, the better sportsbooks will have a much bigger offering in terms of options. You might find things like first halves and first quarters being updated. Then you’ll also have options for player props, team props and game props. Some sportsbooks even have in-game options for small segments like will the player make the next free throw or what will be the result of the next possession?

Are you able to cash out bets in-game?

Some sportsbooks will allow you to cash out your bets at any point in the game. You’ll have to check the rules with the sportsbook you’re playing at as not all of them work the same way. Some sportsbooks don’t offer cash out at all, some don’t offer it in-game and some will allow you to cash at almost any point. Having that extra flexibility can come in handy, so you’d obviously rather bet at a sportsbook that offers the cash out feature.

Outlier Team
February 26, 2023
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