Most casual sports bettors base their wagers on what they think may - or may not - happen in a given game. And while that may work up to a point, truly successful players utilize expected value betting, or +EV. It’s a system for determining where you have an edge in mathematical probability over sportsbooks.
In this betting guide, we will break down +EV to give you an additional tool to become a winning sports bettor.
What is expected value?
Expected value is the difference between a bettors' expectations and the sportsbook's odds.
If your view of an NFL game puts the odds of Team A claiming victory at 50% while the sportsbook’s odds are reflecting chances closer to 40%, then you’ve found a line offering superior odds than what you believe should be available.
EV matters in sports betting because it allows you to take advantage of incorrect lines and gives you an edge against the sportsbooks. Utilizing EV also helps you stay away from lines that aren't paying out what they should for a less-likely result.
EV rewards bettors who analyze lines early and jump on those edges before the markets adjust, and over time makes it more likely for you to come out ahead. Think of it as “buying low and selling high” in the betting market.
The components of expected value
1. Probability: Assessing the likelihood of an outcome
Implied probability is a method used to turn betting odds into a percentage that shows what the sportsbooks believe the likelihood of an outcome is. It’s how likely the oddsmakers believe one side of a bet will win versus the other.
To get an estimate of the probability for either side of a betting line, you can utilize one of two equations. For example, if Team A’s odds are +100 and Team B’s odds are -120, you would use the underdog equation for Team A and the favorite equation for Team B.
| Team | Moneyline Odds |
|---|---|
 Boston Celtics |
+100 |
 New York Knicks |
-120 |
For a favorite, the equation is odds divided by the sum of the odds and 100, divided by 100. So for Team A:
120 / (120 + 100) x 100 = 54.55%
Finding the underdog’s implied probability you will use their +100 odds in a different equation—taking the number 100, dividing by the sum of the odds plus 100, and then multiplying by 100 like so:
100 / (100 + 100) x 100 = 50%
And if you’re wondering how those two numbers add up to over 100%, that’s because there is always the “vig”. The vig is the cut the sportsbook takes out of every betting market, usually between 4.5% and 5%. With these two probabilities adding up to 104.55%, it lines up perfectly.
By the way, you don’t need to memorize these formulas. You can use our handy Covers odds calculator to save you time.
2. Payouts: Calculating potential returns
Knowing the implied probabilities is just the first step. Next you need to know how much you stand to win from a wager.
Odds are displayed in one of three methods: American (where odds have a plus or minus), decimal (where odds are listed in a 1.3 or 2.3 style), and fractional (where odds are listed as a fraction).
American odds indicate how much money you would win based on a $100 wager, and do not reflect the returning of your bet should you win. Minus-odds indicate how much you would have to bet in order to return a $100 profit, while plus odds show what you’d win from a successful $100 wager.
Decimal odds indicate what you would win per dollar wagered, and includes the returned stake. For example, a line of 2.30 means you’d win $2.30 for every dollar staked, with a profit of $1.30 per dollar bet.
For fractional odds, the top number indicates what you would return while the bottom is the amount wagered. So a $5 bet on 9/5 odds would return a total of $9. That number is profit, with your stake also being returned to you.
Calculating expected value
Now it’s time to plug in some data to find your expected value. EV is calculated with the following formula:
EV = (Probability of Winning * Potential Profit) - (Probability of Losing * Loss)
For example, let’s take an upcoming NFL game. The Los Angeles Chargers are priced at -178 on the moneyline and the New York Jets are getting +150.
| Team | Moneyline Odds |
|---|---|
 Los Angeles Chargers |
-178 |
 New York Jets |
+150 |
Let’s assume you’ve determined the true odds—or, the odds without calculating the vig—of the Jets winning are 45%, which correlates to odds of +122. Seeing odds of +150 indicates value on your side, as it correlates to implied odds of 40%.
Let’s also say you’re planning to wager $20 on this bet. Thus:
EV = (.45 * 30) - (.55 * 20) = 13.50 - 11.00 = 2.50 Expected Value
Therefore, you have a positive expected value. While it’s not a large amount of profit in this example, those profits add up over time.
Positive EV bets vs negative EV bets
Our previous example is one of a positive EV bet. It’s a wager that, even if it loses, provides a higher return than what the odds indicate should be the case. When you find lines that offer larger positive EV, you will want to bet more on those to maximize profit.
Conversely, you want to avoid negative EV wagers. While it seem fun to bet on those games, you’ll be laying more juice than you should and getting back less profit versus the probable odds.
To find value in betting markets, you want to look at lines and determine your true probability. Calculate the implied probability and run the formula. If your expected return is positive, then you’ve found a value bet. Weigh it against others you’ve found, and cash in on those with the highest differential.
Expected Value in Different Bet Types
Applying +EV to moneyline wagers is easy. The odds are between a winner and a loser, and finding an underdog that you deem to be the favorite is one of the best ways to capitalize on EV.
For spread betting, the rule of thumb is to look for prices that have a significant market width. So if Team A is getting +3 at -105 and Team B is getting -3 at -115, there’s not much market width.
| Team | Spread |
|---|---|
 New England Patriots |
+3 (-105) |
 Miami Dolphins |
-3 (-115) |
But if Team A is getting -130 for +7.5 and Team B is -102, then you’ve found a market with a significant gap between odds. If either has positive EV, then it’s worth playing.
Totals are a bit trickier as you’re not picking a team to win or lose, but instead are looking at how many points or runs or goals will be scored. But the same rules apply. Determine your true odds, look for markets with large splits, and do the math.
Where things get tricky is parlays and teasers. Because the books take vig on every leg of a parlay, your implied odds get warped a bit. But the best rule of thumb is to combine legs that have positive EV. Doing so will ensure you can offset most or all of the vig, and still return positive EV on your parlay or teaser.
Expected value and long-term profitability
If you’re betting on positive EV the majority of the time, you’re much more likely to come away successful. Betting on lines you deem to provide more profit than expected, while avoid those with poor return, allows you to place bigger unit wagers and cash in on lines you correctly deem to be incorrect.
Using EV can help you consistently make a profit. Not only will you be playing better lines, you’ll become more educated in spotting them and capitalizing on closing-line value.
Risks and limitations of expected value
That’s not to say, of course, that you will profit. As we all know, sports can be cruel. You can do the math, find positive EV lines, and make the right call, and still lose on a bad beat or an injury.
Variance happens. How you handle it is important. If you flip a coin 100 times, it should come up heads 50 times. But sometimes it will come up 55 times. That doesn’t mean you need to adjust anything. Don’t get tilted and make drastic changes, but adjust your predictions slightly if you’re seeing long-term losses.
Also track your results, and be aware of sample size. Winning eight of 10 bets, or losing eight of 10, shouldn’t push you to make big changes in your unit size one way or another. Look at long-term trends and understand that you'll typically come out ahead if you're winning 56% of your +EV wagers.
Add EV to your betting toolbox
Expected value betting is an important tool for any successful sports bettor, and one that should be added to your toolbox. Practice by setting probabilities for games and finding what you deem to be +EV bets, and then track them to see if you’re right. Look into algorithms as well, and find a method that works for you.
Once you’ve done so, put your work to the test. Soon you may find yourself betting on leagues and games you never expected, and putting money into your bankroll.
