Expected Value Betting Calculator
Calculate the expected value of a bet from your estimated probability and offered odds. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Sher, Sports Science & Nutrition Specialist
Expected Value Betting Calculator
Calculator
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Formula: EV = (Probability x Profit) - ((1 - Probability) x Stake)
Worked example — EV: +$12.50 per bet (12.5%) | Edge: 5% | Kelly: 8.3%
Formula
EV = (Probability x Profit) - ((1 - Probability) x Stake)
Expected Value equals the probability of winning multiplied by the net profit if you win, minus the probability of losing multiplied by the amount you lose. A positive EV means the bet is profitable long-term. The Kelly Criterion then determines optimal sizing: Kelly% = (p(odds-1) - (1-p)) / (odds-1).
Worked Examples
Example 1: Positive EV Bet Analysis
Problem:You estimate a team has a 45% chance of winning. The sportsbook offers decimal odds of 2.50 ($100 stake). What is the expected value?
Solution:Profit if win = $100 x (2.50 - 1) = $150 Loss if lose = $100 EV = (0.45 x $150) - (0.55 x $100) EV = $67.50 - $55.00 = $12.50 EV% = $12.50 / $100 = 12.5% Implied prob = 1/2.50 = 40% Edge = 45% - 40% = 5% Kelly = (0.45 x 1.50 - 0.55) / 1.50 = 8.3% of bankroll
Result:EV: +$12.50 per bet (12.5%) | Edge: 5% | Kelly: 8.3%
Example 2: Negative EV Bet Identification
Problem:A coin flip game offers 1.91 decimal odds on heads. You know the true probability is 50%. Is this a good bet?
Solution:Profit if win = $100 x (1.91 - 1) = $91 Loss if lose = $100 EV = (0.50 x $91) - (0.50 x $100) EV = $45.50 - $50.00 = -$4.50 EV% = -4.5% Implied prob = 1/1.91 = 52.4% Edge = 50% - 52.4% = -2.4% Kelly = negative (do not bet)
Result:EV: -$4.50 per bet (-4.5%) | Negative edge | Do not bet
Frequently Asked Questions
What is expected value in sports betting and why does it matter?
Expected value (EV) is the average amount you can expect to win or lose per bet if you placed the same wager thousands of times. It is calculated by multiplying each possible outcome by its probability and summing the results. Positive EV means the bet is profitable in the long run, while negative EV means you will lose money over time. For example, if you have a $100 bet at 2.50 odds with a 45 percent true probability of winning, your EV is (0.45 x $150) - (0.55 x $100) = $67.50 - $55 = $12.50 per bet. This concept is the foundation of all professional sports betting strategies.
How do I determine my estimated probability for calculating EV?
Estimating true probability requires research, data analysis, and experience. Common approaches include building statistical models using historical data, analyzing team and player performance metrics, considering situational factors like injuries and rest days, and studying line movement across multiple sportsbooks. Many serious bettors use power ratings that assign numerical values to each team and calculate win probabilities from the difference. You can also use closing line value as a proxy, since the closing odds at sharp bookmakers are typically very efficient. Start by tracking your estimates against actual results to calibrate your accuracy over time.
What is the Kelly Criterion and how does it relate to expected value?
The Kelly Criterion is a mathematical formula that determines the optimal bet size to maximize long-term bankroll growth when you have identified a positive expected value opportunity. The formula is: Kelly % = (probability x (odds - 1) - (1 - probability)) / (odds - 1). For example, with a 55 percent edge on a 2.00 odds bet, Kelly suggests betting (0.55 x 1 - 0.45) / 1 = 10 percent of your bankroll. Most professional bettors use fractional Kelly, typically half or quarter Kelly, to reduce variance and protect against estimation errors. Kelly only applies when EV is positive; when EV is negative, the formula returns zero or negative values.
Can a bet have positive expected value but still lose money?
Absolutely. Expected value is a long-term statistical concept, not a guarantee for any individual bet or even a series of bets. A bet with positive EV might lose in the short term because variance and randomness dominate small sample sizes. For example, a bet with 5 percent EV and a 40 percent win rate will experience losing streaks of 5 to 10 bets regularly. The law of large numbers means that actual results converge toward expected value only over hundreds or thousands of bets. This is why bankroll management is critical, as you need to survive the inevitable downswings to realize your long-term edge.
What is the difference between expected value and implied probability?
Implied probability is simply the probability suggested by the bookmaker odds, calculated as 1 divided by the decimal odds. Expected value compares your estimated true probability against the implied probability to determine if a bet offers value. If the implied probability from odds of 2.50 is 40 percent but you believe the true probability is 45 percent, you have found a positive EV situation with a 5 percent edge. The implied probability includes the bookmaker margin, so it is always slightly inflated. Understanding the gap between your estimated probability and the implied probability is the key to identifying profitable betting opportunities.
How many bets do I need to place before expected value is reliable?
The number of bets required depends on the size of your edge and the variance of your bets. As a general rule, you need at least 500 to 1,000 bets to start seeing a meaningful signal through the noise. With a 3 percent EV edge on standard -110 bets, you might need over 2,000 bets before your results become statistically significant. The higher your edge, the fewer bets you need. Professional bettors often track their closing line value instead of results in the short term because it provides a more immediate indicator of their skill. Statistical significance testing using p-values or confidence intervals can help determine when your results are unlikely to be due to luck alone.
Is it possible to consistently find positive expected value bets?
Yes, but it requires significant effort, skill, and discipline. Sharp bettors find positive EV through specialization in specific leagues or markets, building quantitative models, exploiting opening lines before they are adjusted, targeting soft bookmakers with less accurate odds, and line shopping across multiple sportsbooks. Steam moves and reverse line movement can also indicate value. However, finding consistent positive EV has become increasingly difficult as the market has become more efficient with the rise of algorithmic odds-making. Most successful bettors operate with thin margins of 2 to 5 percent EV and rely on high volume to generate meaningful profits.
How does variance affect my expected value results in the short term?
Variance is the statistical measure of how widely actual results can deviate from expected results, and it can be enormous in sports betting. Even with a clear positive EV edge, short-term results are dominated by variance. For example, if you make 100 bets at 2.50 odds with a 45 percent win rate, your expected profit is $1,250. However, the standard deviation might be $1,500, meaning a break-even or losing result is well within normal range. Higher odds create higher variance, so a bettor specializing in longshots at 5.00+ odds will experience much wilder swings than someone betting favorites at 1.50 odds, even if both have the same percentage edge.
Should I always bet when I find a positive expected value opportunity?
Not necessarily. While positive EV is a necessary condition for a profitable bet, practical considerations matter. If the edge is very small, say less than 1 percent, transaction costs, time investment, and the possibility that your probability estimate is wrong may make it not worthwhile. Also consider whether the bet fits within your bankroll management strategy and your Kelly Criterion recommendation. Some positive EV opportunities arise from odds errors that will be corrected quickly, meaning execution speed matters. Additionally, if you consistently bet large amounts at certain sportsbooks, you may face account restrictions, so strategic bet placement and account longevity are practical factors beyond pure EV analysis.
What is closing line value and how does it relate to expected value?
Closing line value (CLV) measures whether the odds you received were better than the final closing odds before the event started. If you bet at 2.50 and the line closes at 2.30, you received positive CLV. Closing line value is widely considered the best predictor of long-term betting success because closing lines at efficient markets are extremely accurate reflections of true probability. Consistently beating the closing line indicates you are finding genuine positive EV, even if your short-term results do not reflect it yet. Many professional bettors and syndicates track CLV as their primary performance metric rather than profit and loss, especially when their sample size is below a few thousand bets.
References
Reviewed for accuracy by Sher, Sports Science & Nutrition Specialist · Editorial policy
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