An expected value calculator is the single most important tool for serious sports bettors who want to move beyond gut instinct and start pricing bets like a professional. Instead of asking "do I like this team?" you learn to ask "does this bet offer positive expected value?" Our free expected value calculator helps you answer that question in seconds, showing you exactly how much edge (or disadvantage) any wager carries over the long run.
Expected value (EV) measures the average profit or loss you can expect per bet if you were to place the same wager thousands of times. A positive EV bet does not guarantee you will win today. It means the math is on your side, and if you consistently bet +EV opportunities while managing your bankroll properly, you give yourself the best chance of long-term profit. This is the fundamental shift from recreational betting to strategic betting.
Whether you are evaluating NFL spreads, NBA player props, MLB moneylines, or promotional odds boosts, the expected value calculator below will help you understand your true edge. New to the concept? Keep reading for a complete breakdown of what expected value means, how to calculate it step by step, and strategies for finding +EV bets in real markets. For a deeper dive into EV theory, check out our Expected Value Betting Guide.
Important note: Sports betting involves real financial risk. Even mathematically sound +EV bets can and do lose. This calculator and guide are educational tools to help you make more informed decisions, not guarantees of profit. Always bet responsibly, only with money you can afford to lose, and only where sports betting is legal for adults 21 or older.
Use the OddsIndex expected value calculator below to instantly compute the EV of any bet. This tool takes American odds, your stake, and win probability to show you whether a wager has positive or negative expected value.
What the calculator shows you:
How to use the calculator:
The fair odds toggle is particularly useful if you do not have your own win probability model. It strips the vig (house edge) from the market odds to estimate fair probability, then calculates EV based on the difference between that fair price and the odds you are actually getting.
Remember: This calculator shows long-term mathematical expectation, not what will happen on your next bet. A +5% EV edge means that over many bets at these odds and this win rate, you would expect to profit 5% of your stake on average. Individual results will vary widely.
For more betting calculators, visit our calculator hub.
Understanding what happens inside an expected value calculator helps you trust the output and identify when manual adjustments might be needed.
The core EV formula in words: Expected Value equals (Win Probability times Profit if Win) minus (Loss Probability times Amount Lost if Wrong).
Let us break that down:
Win Probability is your estimated chance of the bet winning, expressed as a decimal (for example, 55% becomes 0.55).
Profit if Win is what you gain if the bet hits. For American odds, this depends on whether the odds are positive or negative. At +150 with a 100 dollar stake, your profit is 150 dollars. At -110 with a 100 dollar stake, your profit is approximately 90.91 dollars.
Loss Probability is simply 1 minus your win probability. If you estimate 55% to win, there is a 45% chance of losing.
Amount Lost if Wrong is your stake. If you bet 100 dollars and lose, you lose 100 dollars.
Putting it together with an example: You bet 100 dollars at +150 odds (potential profit of 150 dollars). You estimate a 45% chance of winning.
EV = (0.45 times 150) minus (0.55 times 100) EV = 67.50 minus 55.00 EV = +12.50 dollars
This means you would expect to profit 12.50 dollars per bet on average if this scenario repeated many times. That is a +12.5% EV relative to your stake.
The fair odds toggle automates the win probability step. It takes the American odds from a sharp market or the no-vig line, converts those odds to implied probability, removes the built-in vig, and uses that cleaned probability as your baseline. Learn more about this process with our Implied Probability Calculator and Vig and True Odds Calculator.
Expected value in sports betting is the mathematical measure of how much you can expect to win or lose on average per bet over the long run. It answers a simple question: if I placed this exact same bet thousands of times, would I make money or lose money?
Think of expected value as your betting compass. It does not tell you whether this specific bet will win or lose. It tells you whether the bet is priced in your favor. A +EV bet means the potential payout is larger than the risk justifies based on the true probability. A -EV bet means you are paying more than the opportunity is worth.
A non-sports example for intuition:
Imagine a coin flip game. A fair coin has a 50% chance of landing heads and 50% tails. If someone offers you even money (bet 100 dollars to win 100 dollars) on a fair coin, the expected value is zero. You would break even over time.
Now imagine they offer you 2-to-1 odds on heads with a fair coin. You bet 100 dollars to win 200 dollars, still with a 50% chance.
EV = (0.50 times 200) minus (0.50 times 100) EV = 100 minus 50 EV = +50 dollars
That is a massively +EV bet. You would be foolish not to take it. Of course, you might still lose the first flip, or the first five flips. But mathematically, you should keep betting as long as these odds are offered.
A sports betting example:
The Buffalo Bills are -3 against the Miami Dolphins. One sportsbook offers Bills -3 at -110 odds. A sharp market consensus suggests the true probability of Bills covering is 54%.
Convert -110 to implied probability: approximately 52.4%
If the true probability (54%) exceeds the implied probability (52.4%), this is a +EV bet. Let us calculate:
At -110 with 100 dollar stake, profit if win = 90.91 dollars
EV = (0.54 times 90.91) minus (0.46 times 100) EV = 49.09 minus 46.00 EV = +3.09 dollars (approximately +3.1% EV)
This bet has positive expected value. It does not guarantee the Bills will cover, but it means the odds offered are better than they should be based on the true probability.
Key distinction: Expected value describes the average result over many bets, not the outcome of a single wager. You can lose a +EV bet. You can win a -EV bet. But over hundreds of bets, +EV betting puts you in position to profit while -EV betting guarantees long-term losses.
A positive EV bet (also called a +EV bet or value bet) is any wager where the odds offered exceed the true probability of winning. In other words, you are getting paid more than the bet is worth.
Sportsbooks make money by offering odds that imply a slightly higher probability than the true chance of each outcome. This difference is the vig or juice. When a sportsbook offers -110 on both sides of a spread, they are implying each side has about 52.4% chance of covering, but both sides cannot each have 52.4% true probability. The extra 4.8% (52.4 + 52.4 = 104.8%) is the house edge.
Positive EV bets arise when:
Comparing fair odds to sportsbook odds:
| Scenario | True Win Probability | Fair Odds | Sportsbook Odds | EV Status |
|---|---|---|---|---|
| Standard spread bet | 50% | +100 | -110 | Negative EV |
| Mispriced prop | 40% | +150 | +180 | Positive EV |
| Odds boost promo | 35% | +186 | +220 (boosted) | Positive EV |
| Sharp vs soft book | 55% | -122 | -110 | Positive EV |
The goal of sophisticated sports betting is to consistently identify and bet +EV opportunities while avoiding -EV traps. This requires discipline, bankroll management, and accepting that short-term results do not always reflect long-term edge.
Knowing how to calculate expected value manually helps you understand what the calculator is doing and allows you to quickly estimate EV when you are away from a computer. Here is the step-by-step process.
Step 1: Convert American odds to implied probability
American odds tell you how much you win relative to your stake, but to calculate EV you need probabilities.
For negative American odds (favorites): Implied Probability = Absolute Value of Odds divided by (Absolute Value of Odds plus 100)
For positive American odds (underdogs): Implied Probability = 100 divided by (Odds plus 100)
Example conversions:
For a deeper dive and instant conversions, use our Implied Probability Calculator.
Step 2: Determine or estimate the true win probability
This is the hardest part. The implied probability includes the vig. To find true probability, you need either:
For this example, assume you have determined through line shopping that the true probability of your bet winning is 55%.
Step 3: Calculate potential profit
For positive American odds: Profit = Stake times (Odds / 100) For negative American odds: Profit = Stake times (100 / Absolute Value of Odds)
Examples with 100 dollar stake:
Step 4: Apply the EV formula
EV = (Win Probability times Profit) minus (Loss Probability times Stake)
Worked Example 1: NFL Point Spread
You want to bet the Kansas City Chiefs -3.5 at -108. Your research suggests the Chiefs have a 54% chance of covering.
Convert -108 to implied probability: 108 / 208 = 51.9% True probability: 54% Stake: 100 dollars Profit if win: 100 times (100/108) = 92.59 dollars
EV = (0.54 times 92.59) minus (0.46 times 100) EV = 50.00 minus 46.00 EV = +4.00 dollars (+4% EV)
This is a positive EV bet worth making.
Worked Example 2: NBA Player Prop
Jayson Tatum over 27.5 points at +105. Based on his recent form and matchup, you estimate a 50% chance of hitting the over.
Convert +105 to implied probability: 100 / 205 = 48.8% True probability: 50% Stake: 50 dollars Profit if win: 50 times (105/100) = 52.50 dollars
EV = (0.50 times 52.50) minus (0.50 times 50) EV = 26.25 minus 25.00 EV = +1.25 dollars (+2.5% EV)
Small but positive. Whether to bet depends on your confidence in the 50% estimate.
Worked Example 3: MLB Moneyline
The New York Yankees are +145 underdogs. You believe they have a 42% chance of winning.
Convert +145 to implied probability: 100 / 245 = 40.8% True probability: 42% Stake: 100 dollars Profit if win: 100 times (145/100) = 145 dollars
EV = (0.42 times 145) minus (0.58 times 100) EV = 60.90 minus 58.00 EV = +2.90 dollars (+2.9% EV)
Another +EV opportunity.
| Bet | Odds | Implied Prob | True Prob | Stake | EV ($) | EV (%) |
|---|---|---|---|---|---|---|
| Chiefs -3.5 | -108 | 51.9% | 54% | $100 | +$4.00 | +4.0% |
| Tatum o27.5 pts | +105 | 48.8% | 50% | $50 | +$1.25 | +2.5% |
| Yankees ML | +145 | 40.8% | 42% | $100 | +$2.90 | +2.9% |
Getting accurate EV calculations is straightforward once you understand the inputs. Here is a detailed walkthrough for using the OddsIndex expected value calculator effectively.
Step 1: Enter the American odds
Type in the odds exactly as shown by your sportsbook. Include the plus or minus sign. For example, -110, +150, or -200.
Step 2: Input your stake
Enter the amount you plan to bet. The calculator will show EV in both dollar terms and as a percentage, so the stake amount matters for the dollar figure but the percentage EV is the same regardless of stake size.
Step 3: Enter your win probability
This is the critical input. If you have your own model or strong conviction about the true probability, enter it here. For example, 55 for 55%.
Step 4: Review your results
The calculator displays:
If you do not have your own win probability estimate, the fair odds toggle helps by deriving probability from market odds.
When to use it:
How it works:
Example: A betting exchange has an NBA spread priced at essentially +100 / -100 (no vig). Your retail sportsbook offers -108 on the same side. Enable the fair odds toggle, enter the +100 sharp price, and see how much edge you have at -108.
Advanced bettors who build their own models can input their projected probability directly.
Tips for custom probability:
Check multiple sportsbooks: Before betting, see if the same bet is available at better odds elsewhere. A bet that is -EV at -115 might be +EV at -105.
Try different scenarios: Adjust the win probability up and down a few percentage points to see how sensitive your EV is to estimation error.
Log your calculations: Keep a record of your EV estimates alongside actual results. Over time, you will learn whether your probability estimates are accurate.
Remember the limitations: The calculator shows mathematical expectation, not guaranteed outcomes. Use it as one input into your decision-making, not the only factor.
You may encounter the term value betting calculator in your research. In practice, value betting calculators and expected value calculators are essentially the same tool with different branding.
Both measure whether a bet offers positive edge by comparing the odds offered to the true probability of winning. Some sites express the result as value percentage rather than expected value dollars, but the core calculation is identical.
The terminology differences:
Use whichever framing makes more intuitive sense to you. The underlying math is the same: you are looking for bets where the price is better than the true probability justifies.
Expected value principles apply to every type of sports bet, but the complexity of calculating EV varies depending on the bet structure. Here is how to approach EV for different wager types.
Straight bets are the simplest to evaluate. You have one outcome, one set of odds, and one probability to estimate.
Moneylines: The true probability is your assessment of which team wins. Compare to implied probability from the odds.
Spreads: The true probability is your assessment of the team covering the point spread. More complex because you need to estimate not just who wins, but by how much.
Totals: The true probability is your assessment of the combined score going over or under the posted number. Factors like pace, weather, and injuries all influence your estimate.
For all straight bets, the EV calculation follows the formula exactly as shown above.
Parlays are high-variance bets where you combine multiple selections. All legs must win for the parlay to pay.
Key EV considerations for parlays:
Worked parlay example:
You build a 2-leg parlay:
Combined true probability: 0.54 times 0.53 = 28.6%
Parlay odds at standard sportsbook pricing: approximately +264
Break-even probability at +264: 100 / 364 = 27.5%
Since 28.6% exceeds 27.5%, this parlay has positive expected value.
Same Game Parlay complications:
SGPs involve legs from the same game that may be correlated. If you bet a team to win AND the game to go over, those outcomes are not independent. Sportsbooks adjust SGP pricing to account for correlation, often in their favor.
Calculating EV on SGPs requires estimating correlated probabilities, which is significantly more complex. The calculator provides a baseline, but treat SGP EV estimates with extra caution.
For more on parlay strategy, see our parlay betting guide.
Player props: These bets on individual performance (points, rebounds, passing yards) can offer significant EV because:
Estimating true probability requires player-specific research. Track historical performance, matchup data, and situational factors.
Futures: Long-term bets like championship winners or MVP awards.
Futures have unique EV challenges:
A +EV futures bet today might become -EV as circumstances change. Factor in opportunity cost when evaluating futures EV.
Sportsbook promotions can create +EV opportunities that would not exist in normal markets.
Odds boosts example:
Standard odds: Lakers moneyline +180 Boosted odds: Lakers moneyline +220
If you estimate Lakers have a 35% chance of winning:
At +180: EV = (0.35 times 180) minus (0.65 times 100) = 63 minus 65 = -2 dollars (-2% EV) At +220: EV = (0.35 times 220) minus (0.65 times 100) = 77 minus 65 = +12 dollars (+12% EV)
The boost flipped a slightly -EV bet into a clearly +EV opportunity.
Free bet EV:
Free bets have special EV math because you risk nothing. The EV of a free bet equals the expected profit only, since you cannot lose the stake.
Free bet EV = Win Probability times (Stake times Odds / 100)
A 50 dollar free bet at +200 with 35% win probability: Free bet EV = 0.35 times 100 = 35 dollars
Convert free bets at the highest possible odds to maximize expected value.
| Bet Type | EV Calculation Complexity | Key Considerations |
|---|---|---|
| Straight bets | Simple | Single probability estimate, direct formula application |
| Parlays | Moderate | Multiply independent probabilities, high variance |
| Same Game Parlays | Complex | Correlated outcomes, sportsbook pricing adjustments |
| Player props | Moderate | Player-specific research, situational factors |
| Futures | Complex | Probabilities shift over time, opportunity cost |
| Odds boosts | Simple | Standard EV formula with boosted odds |
| Free bets | Simple | No downside risk, maximize odds for highest conversion |
Understanding expected value is only half the battle. The other half is managing variance and your bankroll so that short-term losses do not wipe you out before the long-term edge materializes.
A common frustration among new +EV bettors: "I'm betting positive EV but I keep losing. What gives?"
The answer is variance. Expected value describes the average outcome over many thousands of bets. Individual results can and will deviate wildly from this average.
The coin flip analogy:
Imagine a coin that lands heads 55% of the time. You bet heads at even money every flip. Your EV is +10% per bet. But in any given 20-flip session:
Sports betting works the same way. A 54% win rate is excellent, but over 100 bets you might easily go 48-52 or even 45-55. This is normal variance, not evidence that +EV betting does not work.
Small sample sizes tell you almost nothing about whether your betting is profitable.
Approximate sample sizes needed to detect edge:
Most recreational bettors do not place enough bets to distinguish skill from luck. This is why tracking, discipline, and patience are essential.
Your bankroll is the money specifically set aside for sports betting. It is money you can afford to lose entirely without affecting your life.
Key bankroll principles:
The Kelly Criterion is a mathematical formula for optimal bet sizing based on your edge and the odds offered. It maximizes long-term growth rate while minimizing risk of ruin.
Kelly formula (simplified):
Kelly % = (Edge / Odds) where Edge = (Win Probability times (Odds + 1)) - 1
Example:
You have a 55% chance of winning at -110 (decimal odds 1.91).
Edge = (0.55 times 1.91) - 1 = 1.05 - 1 = 0.05 or 5% Kelly % = 0.05 / 0.91 = 5.5% of bankroll
Full Kelly is aggressive. Most sharp bettors use fractional Kelly (one-quarter to one-half Kelly) for a smoother ride with lower risk of devastating losses.
For a complete guide and calculator, see our Kelly Criterion Calculator.
| Estimated Edge | Full Kelly Stake | Half Kelly Stake | Quarter Kelly Stake |
|---|---|---|---|
| 2% | 2.2% | 1.1% | 0.55% |
| 5% | 5.5% | 2.75% | 1.4% |
| 10% | 11% | 5.5% | 2.75% |
Important: Kelly assumes your edge estimate is accurate. If you overestimate your edge, Kelly will suggest oversized bets that can be devastating. Always use conservative probability estimates and fractional Kelly.
Closing Line Value (CLV) measures whether you bet at better odds than the final line before a game starts. It is closely related to expected value but not identical.
Why CLV matters:
The closing line represents the market's most informed view of the true probability after all information and sharp money has been absorbed. If you consistently bet at better odds than the closing line, you are demonstrating an ability to identify value before the market does.
The relationship:
In practice, beating the closing line over a large sample is the strongest evidence that you are betting +EV. It removes the subjectivity of your probability estimates and uses the market as the truth benchmark.
Example:
You bet Patriots -3 at -105. The line closes at Patriots -3 -115. You beat the closing line by 10 cents, showing positive CLV. Over hundreds of bets, positive CLV strongly suggests positive EV.
For a deep dive, see our Closing Line Value guide.
Knowing how to calculate expected value is useless if you cannot find +EV opportunities. Here are practical strategies for sourcing edge in competitive US sports betting markets.
The simplest way to improve your expected value is to always take the best available price. Different sportsbooks hang different lines, and the gaps can be significant.
How line shopping creates +EV:
If your true probability estimate makes this bet marginal at -110, Book B's -105 might push it clearly into +EV territory while Book A's -115 might make it -EV.
Line shopping best practices:
For comprehensive line shopping strategies, see our Betting Line Shopping guide.
Some sportsbooks cater to recreational bettors and have softer lines. Others welcome sharp action and have tighter, more accurate prices. The sharp books' odds are generally closer to the true probability.
Strategy:
Use the sharp book line to estimate true probability, then bet at recreational books when they offer better prices than the sharp reference.
Example:
Sharp book: Cowboys -6.5 at -110/-110 (no vig true probability approximately 50%) Recreational book: Cowboys -6 at -110
Getting Cowboys -6 instead of -6.5 at the same price is a significant edge. The half-point discount on a key number like 6/7 is valuable.
Sportsbooks spend heavily on bonuses, odds boosts, and free bet promotions to acquire customers. Smart bettors use these offers to create +EV situations.
Types of exploitable promos:
Caution:
Do not chase every promotion blindly. Calculate the EV of each offer. Some promos have terms that make them -EV despite appearing generous.
The most sustainable source of +EV bets is developing your own probability models that are more accurate than the market.
Model building basics:
This is advanced work that requires significant time and skill. Start simple (one sport, one bet type) and expand as you develop proficiency.
US sportsbooks want recreational bettors who lose money. They do not want sharp bettors who consistently win. If you are successful at +EV betting, expect:
This is frustrating but reality. Manage expectations and maximize your edge while you can access full betting privileges.
Even with a calculator doing the math, users frequently make errors that lead to bad betting decisions. Here are the most common mistakes and how to avoid them.
American odds look different from decimal or fractional odds. Entering -1.91 (decimal) when the calculator expects -110 (American) produces garbage output.
Solution: Double-check your odds format before calculating. Our calculator uses American odds by default. If you have decimal or fractional odds, convert them first using our Odds Converter.
Some users enter what they want to win instead of what they are risking.
Solution: Stake is the amount you wager, not your potential profit. A 100 dollar bet at +150 has a 100 dollar stake and 150 dollar potential profit.
Your favorite team feels like they have an 80% chance of winning because you want them to win. This is not probability estimation, it is wishful thinking.
Solution: Use objective methods to estimate probability. Reference sharp lines, consider historical base rates, and be brutally honest about uncertainty.
A 2% EV bet is not "free money." It is a slight long-term advantage that requires many bets to manifest.
Solution: Understand that small edges require large sample sizes. Do not overbet small edges expecting quick profits.
Your EV calculation might show +3%, but if you are paying -115 juice while the fair line is -105, part of that edge goes to the house.
Solution: Always account for the vig in your EV calculations. The fair odds toggle helps by stripping vig from your reference probability.
Many bettors run EV calculations but never track whether their probability estimates are accurate.
Solution: Log every bet with your probability estimate, the EV calculation, and the actual result. Over time, compare your predictions to outcomes to calibrate your models.
Losing streaks happen even when betting +EV. The temptation is to increase bet sizes to "get back to even."
Solution: Stick to your staking plan regardless of recent results. Variance evens out over time, but only if you survive the downswings with proper bankroll management.
The calculator shows positive EV only if you input a win probability higher than the implied probability. Anyone can type in 60% and see +EV. The question is whether that 60% is accurate.
Solution: Be conservative with probability estimates. When uncertain, round down. It is better to pass on bets than to bet false positives.
What is an expected value calculator in sports betting?
An expected value calculator is a tool that computes the average profit or loss you can expect from a bet over the long run. You input the odds, your stake, and your estimated probability of winning. The calculator outputs your expected value in dollars and as a percentage of your stake, helping you identify whether a bet is mathematically profitable (+EV) or not (-EV). It automates the EV formula so you can quickly evaluate any betting opportunity.
How do you calculate expected value on a bet?
To calculate expected value manually, multiply your estimated win probability by the profit if you win, then subtract the product of your loss probability and your stake. For example, with a 55% win chance, 100 dollar stake, and 90 dollar potential profit: EV = (0.55 times 90) minus (0.45 times 100) = 49.50 minus 45 = +4.50 dollars. Our calculator automates this process and handles the odds conversions for you.
What is a positive EV bet?
A positive EV bet (also called a +EV bet or value bet) is a wager where the odds offered by the sportsbook are better than the true probability of winning would justify. In other words, you are getting paid more than the bet is mathematically worth. Positive EV bets do not guarantee wins, but consistently betting +EV opportunities is the foundation of profitable sports betting over the long term.
Are positive EV bets guaranteed to win?
No. Positive EV bets are not guaranteed to win. Expected value describes the average result over many repetitions of the same bet, not the outcome of any single wager. You can lose a +EV bet, and you can even have losing streaks while betting +EV. The mathematical edge only manifests over large sample sizes. Short-term results are dominated by variance, which is why bankroll management is essential.
Why am I losing money even though I am betting +EV?
Losing money while betting +EV is normal and happens because of variance. A 55% win rate over 100 bets can easily produce only 48 wins due to random fluctuation. Additionally, your probability estimates might be slightly off. If you are overestimating your win probability, what you think is +EV might actually be -EV. Track your bets over a large sample (500+ wagers) before concluding whether your strategy is profitable.
How much should I bet on a positive EV opportunity?
Bet sizing depends on your edge size and bankroll. The Kelly Criterion provides a mathematically optimal formula: stake a percentage of your bankroll proportional to your edge divided by the odds. Most sharp bettors use fractional Kelly (one-quarter to one-half of the full Kelly recommendation) to reduce volatility. As a general rule, risk 1-3% of your bankroll on typical +EV bets and never more than 5% on any single wager. See our Kelly Criterion Calculator for detailed guidance.
Sports betting should be entertaining, not a source of financial stress. Even with sophisticated tools like the expected value calculator, betting involves real risk.
Key reminders:
If you or someone you know is struggling with problem gambling, help is available 24/7 through the National Council on Problem Gambling at 1-800-522-4700 or ncpgambling.org.
Gamble responsibly. If you or someone you know has a gambling problem, call +1-800-GAMBLER.