Calculating a wager’s expected value is an important risk management tool. If you’re planning to bet on the NFL, NBA, or NHL all season, you’ll need to guard your bankroll carefully. Use this simple formula to bet strategically, identifying opportunities with more upside than others.
The expected value calculation shows how much you can expect to profit if you repeatedly placed the same wager at the same odds. In a way, it’s a mathematical simulation. While it doesn’t necessarily indicate what will happen with any single wager, it does show what would happen if you made the same bet infinitely.
Below, we’ll walk you through the formula and an example calculation.
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What is Sports Betting Expected Value?
The expected value calculation shows how much you can expect to profit if you repeatedly placed the same wager at the same odds. This calculation is useful for assessing the profitability of a particular bet. It’s an ideal sports betting handicapping tool, especially if you plan to bet consistently throughout the year.
Here’s how to understand the calculation in words. Expected value is the difference between the probability of a win times the profit amount, less the probability of a loss times the wager amount.
The following is the basic equation, where “wager” is the dollar amount you plan to bet:
EV = (Win Probability * Potential Win) – (Loss Probability * Wager)
Note that we’ll need to do a little prep work to get the right win probability. More on that below.
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Example Expected Value Calculation
We mentioned above that we’ll need to do a little prep work before making the expected value calculation. First, we’ll need to calculate each side’s implied probability. Next, the overround, which is the sum of both side’s implied probabilities. Finally, the no vig win probabilities for each side.
The “no vig” probability value is important because it doesn’t include the sportsbook’s vigorish. That means it’s closer to the side’s actual probability of winning. We’ll use this as our “win probability” in the expected value formula from above.
| Team | Odds | IP% | NoV W% | Loss% |
|---|---|---|---|---|
| Ravens | +125 | 44.44% | 42.55% | 57.45% |
| Chiefs | -150 | 60.00% | 57.45% | 42.55% |
| Total | 104.44% Overround | 100.00% |
Expected Value Win Probability Values
The following steps and equations show how we calculated the values in the table above.
- Calculate each side’s implied probability using the following formulas for each moneyline value:
- Minus ML IP = (-1 x (Odds)) / (-1 x (Odds) + 100)
- Plus ML IP = 100 / (Odds + 100)
- Calculate the overround by summing each implied probability value. We need this to find the no vig win probability:
- Overround = IP1 + IP2
- Divide each IP by the Overround. The quotient is No Vig Win Probability. The sum of both quotients should equal 100.00%
- No Vig Win1 = IP1/OR
- No Vig Win2 = IP2/OR
- Loss Probability is the probability that side will lose. Subtract each No Vig Win percentage from 100.00%.
- LP1 = (100 – No Vig Win1)
- LP2 = (100 – No Vig Win2)
- Hint: One side’s win probability is another side’s loss probability.
Calculate Expected Value Using No Vig Win Probabilities
Finally, let’s calculated the EV for a wager on either side. Recall our formula from above. We’ll substitute values from the table above into the equation with a $100 bet.
Remember that a +125 underdog means you risk $100 to win $125. Also, that a -150 favorite means you risk $150 to win $100.
EV = (Win Probability * Potential Win) – (Loss Probability * Wager)
Ravens +125 EV = (0.4255 * $125) – (0.5745 * $100) = -$4.26
Chiefs -150 EV = (0.5745 * $100)) – (0.4255 * $150) = -$6.38
As you can see, the expected value for each side is negative. In fact, most bets will have a negative expected value. The key is to identify those with EV as close to zero as possible.
Positive Expected Value Bets
If you can find one with positive expected value, or +EV, that’s even better. Consistently identifying and betting positive expected value bets can produce long-term sports betting profits.
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How to Calculate Sports Betting Expected Value
Time needed: 6 minutes
How to calculate sports betting EV
- Find each side’s moneyline values.
Search for the matchup’s 2-way or 3-way moneyline values.
- Calculate each side’s Implied Probabilities.
Negative ML IP = (-1 x (Odds)) / (-1 x (Odds) + 100). Plus ML IP = 100 / (Odds + 100).
- Calculate the overround by summing each implied probability value. We need this to find the no vig win probability.
Overround = IP1 + IP2
- Divide each IP by the Overround. The quotient is No Vig Win Probability. The sum of both quotients should equal 100.00%.
No Vig Win1 = IP1/OR. No Vig Win2 = IP2/OR.
- Loss Probability is the probability that side will lose. Subtract each No Vig Win percentage from 100.00%.
LP1 = (100 – No Vig Win1). LP2 = (100 – No Vig Win2). Hint: One side’s win probability is another side’s loss probability.
- Calculate each side’s expected values using the no vig win probabilities and loss probabilities. Determine the win and loss amounts using your wager and moneyline odds.
EV = (Win Probability * Potential Win) – (Loss Probability * Wager)
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FAQs
The EV calculation shows how much you can expect to profit if you repeatedly placed the same wager at the same odds. In a way, it’s a mathematical simulation. While it doesn’t necessarily indicate what will happen with any single wager, it does show what would happen if you made the same bet infinitely.
Calculating a wager’s EV is an important risk management tool. It helps you identify which bets are better than others. This leads to better bankroll management and potentially higher profits.
First, you’ll need to calculate each side’s implied probability. Next, the overround, which is the sum of both side’s implied probabilities. Finally, the no vig win probabilities for each side. We’ll use this as our “win probability” in the expected value formula.
EV = (Win Probability * Potential Win) – (Loss Probability * Wager)
Sports Betting Lessons
- What + and – mean in betting
- What +125 and -125 odds mean
- What +1000 and -1000 odds mean
- +2.5 and -2.5 point spread
- +7 and -7 point spread
- 3 Game Parlay Bet Payout
- 5 Game Parlay Bet Payout
- 3-Way Moneyline
- +1.5 and -1.5 run line
- +1.5 and -1.5 puck line
- PK Point Spread Line
- Asian Handicap Lines
- What a Push Means
- Alternate Betting Lines
- “No Action” Bet
- Betting Line Movements
- Sports Betting Expected Value
- Prop Parlay Bet
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Sports Betting Resources
- How to Read Sports Betting Odds – Our helpful tutorial explains what the numbers mean for point spread, moneyline, total, and Asian Handicap bets.
- Sports Betting Questions and Answers – Common sports betting questions and answers, a simple quick reference for beginners.
- Sports Betting vs Casino Gambling – Learn how sportsbooks and casinos make money, and the important differences between each business model.
- How to Read NFL Odds – Short and sweet guide to NFL point spreads, totals, and moneylines. We’ve got live example bets from upcoming NFL matchups.
- Point Spread Bet – Understanding the point spread is key to betting on football and basketball. Learn how the point spread bet works with our tutorial video and text.
- Over-Under Total Bet – Bet over or under the sportsbook’s line. We explain how to place this bet with easy examples, a video, and text explainer.
- Moneyline Bet – Whether it’s a 2-way or 3-way moneyline, we’ve got you covered. Moneylines are available for almost every major sport league, including football, basketball, baseball, hockey, soccer, tennis, and combat sports.
- Teaser Bet – A teaser is a modified parlay that lets you buy points to shift point spread and total lines in your favor. Our fun tutorial video and detailed text article explain how to place this bet.
- If Bet Win-Only – Sequence multiple bets together in an if-then sequence. Your next bet only sees action if the previous one wins. Ideal for bettors with small bankrolls.
- Futures Bet – We explain what a futures bet is, how it works, and when to bet on a future sporting event. Common futures bets include the winners of the Super Bowl, Final Four, Stanley Cup, World Series, and NBA Finals.
- Parlay Bet – Combine multiple selections into one bet that returns a huge payout if all your selections were correct. We explain how parlay bets work and provide common parlay payout tables.
- Progressive Parlay Bet – Also known as a “Close Call Parlay”, this parlay variant can win even if one or more of selections lose. Our article describes this bet in detail.
- Parlay Card Betting – Parlay cards are issued by major sportsbooks midweek, allowing bettors to make multiple point spread, total, and prop bet selections that can return big payouts. Not to be confused with an “off the board” parlay!
- Prop Bets – We explain what a prop bet is, how to place a prop bet, and provide an expansive list of sports leagues with plenty of props to bet on right now.