How to Calculate Expected Value (EV) in Betting: Formula, Examples & Free Calculator
How to calculate expected value in sports betting. The EV formula explained with 3 worked examples, a free EV calculator, and the complete pipeline from vig removal to bet sizing.
What EV betting actually means
EV betting is placing wagers where the expected value is positive. Expected value (EV) is the average amount you win or lose per bet if you placed it infinite times. It is the single number that determines whether a bet makes money long-term or loses it. There is no third option.
The sports betting expected value formula:
EV = (Win Probability x Profit) - (Loss Probability x Stake)
That is the entire foundation. Every profitable bettor in history is running some version of this calculation. The sportsbook runs it on every line they post. The question is whether you run it before you place your bet.
A positive result means the bet makes money over time. A negative result means it loses money over time. Short-term results are noise. EV is the signal.
The EV formula: 3 worked examples
Abstract formulas are useless without concrete numbers. Here are three real scenarios that show EV betting in practice.
Example 1: NBA underdog at +150
You find a line at +150 on an NBA underdog. After de-vigging Pinnacle's closing line (use the odds converter if you need to convert between formats), you estimate the true win probability at 45%.
- Win probability: 45%
- Loss probability: 55%
- Profit if win: $150 (on a $100 stake)
- Loss if lose: $100
EV = (0.45 x $150) - (0.55 x $100) = $67.50 - $55.00 = +$12.50
That is a 12.5% edge on every $100 wagered. This is a strong +EV bet. Take it every time it appears.
Example 2: NFL spread at -110
You model an NFL game and estimate the favorite covers the spread 54% of the time. The line is standard -110.
- Win probability: 54%
- Loss probability: 46%
- Profit if win: $100 (on a $110 stake)
- Loss if lose: $110
EV = (0.54 x $100) - (0.46 x $110) = $54.00 - $50.60 = +$3.40
Per $110 wagered, you expect to profit $3.40. That is a 3.1% edge. Smaller than Example 1, but still positive. Over 500 bets at this edge, that is $1,700 in expected profit. EV betting is a volume game.
Example 3: A losing proposition disguised as a good bet
A friend tells you to take a +200 longshot. It "only needs to hit 33% of the time." But after de-vigging the sharp line, the true probability is 28%.
- Win probability: 28%
- Loss probability: 72%
- Profit if win: $200 (on a $100 stake)
- Loss if lose: $100
EV = (0.28 x $200) - (0.72 x $100) = $56.00 - $72.00 = -$16.00
Negative EV. You lose $16 per $100 wagered on average. The odds look tempting, but the math says pass. This is why EV betting requires calculation, not intuition. Run any bet through the EV calculator and the number tells you the answer in seconds.
Where the true probability comes from
The EV formula is simple. The hard part is the input: accurate win probability. Your EV calculation is only as good as your probability estimate. Garbage in, garbage out.
There are three common approaches, and serious bettors often use more than one.
Sharp closing lines. Pinnacle's closing line is widely considered the most efficient probability estimate in sports betting. The process: take Pinnacle's closing odds, strip the vig using a de-vig method, and treat the result as your true probability benchmark. If a recreational sportsbook offers you better odds than Pinnacle's de-vigged number, you have an edge. Use the de-vig calculator to strip the margin from any two-way or multi-way market.
Your own model. If you build a statistical model that accounts for variables the market underweights (injuries, rest days, weather, situational spots), your model's output probability becomes the input. This is harder than it sounds. The market is efficient enough that most homegrown models do not beat the closing line consistently.
Prediction market prices. High-liquidity markets on Kalshi or Polymarket can serve as probability benchmarks, especially for non-sports events like elections or economic data releases. A $0.62 contract price on Polymarket implies a 62% probability (before accounting for prediction market fees). These markets are particularly useful when there is no sportsbook equivalent.
EV and the rest of the betting math pipeline
EV does not exist in isolation. It is one step in a sequential system where each concept feeds the next.
Before EV: vig removal. You cannot calculate expected value without a true probability estimate, and you cannot get that estimate without understanding and removing the vig. The bookmaker's margin inflates the implied probabilities on both sides of a market. Strip it first, then calculate EV. The hold calculator shows you exactly how much the book charges on any market.
After EV: bet sizing. Knowing a bet is +EV tells you to take it. It does not tell you how much to wager. Bet too large on a +EV proposition and a losing streak can still destroy your bankroll before the math converges. The Kelly Criterion solves this. It takes your edge and the odds as inputs and outputs the optimal fraction of your bankroll to risk.
For the +150 NBA example above, Kelly says to bet approximately 8.3% of your bankroll at full Kelly. Most serious bettors use half Kelly (4.15%) to reduce variance while capturing roughly 75% of the theoretical growth rate.
After sizing: verification. How do you know your edge is real and not just a lucky streak? Closing line value is the metric that answers this. If the line consistently moves in your direction after you bet, the market is confirming your edge. If it does not, your probability estimates may be off, and your EV calculations are built on a bad foundation.
Why +EV bets still lose (and why that is fine)
You will lose the +150 NBA underdog bet 55% of the time. More than half your bets will lose. This is where most people quit EV betting.
A single bet result tells you nothing about whether the bet was correct. A +EV bet can lose. A -EV bet can win. Over 10 bets, or even 50, variance dominates the results. You cannot evaluate a strategy on a small sample.
Consider: a bet with 55% true probability will produce a losing record about 33% of the time over 100 trials. That is pure math. A bettor who abandons their +EV strategy after a bad 100-bet stretch is making an emotional decision that the numbers do not support.
Expected value reveals itself over hundreds or thousands of bets. If your sample size is under 500, you are evaluating your luck, not your strategy. This is one of the hardest truths in EV betting. The math works, but it demands patience that most people do not have.
The expected value formula works identically on prediction markets. On Kalshi or Polymarket, you buy contracts priced between $0.01 and $0.99. A "Yes" contract priced at $0.55 implies a 55% probability. If you believe the true probability is 65%, your EV on a $100 position:
- Cost: $55 (buying 100 contracts at $0.55)
- Payout if Yes: $100
- Profit if Yes: $45
- Loss if No: $55
EV = (0.65 x $45) - (0.35 x $55) = $29.25 - $19.25 = +$10.00
One difference on prediction markets: platform fees reduce your net payout. Kalshi charges 5-10% on profits. Polymarket has no explicit fee but earns from the bid-ask spread. Either way, factor fees into your EV calculation. The prediction market fee calculator handles this automatically. Read more about how fees eat your edge on different platforms.
How to start EV betting today
The framework is straightforward. The execution takes discipline.
- Pick a sport or market type where you can get sharp closing lines or build a model.
- De-vig the sharp line to get true probability. Use the de-vig calculator.
- Compare against the odds available to you at recreational books or prediction markets.
- Calculate EV on every bet before placing it. Use the EV calculator.
- Size your wager using half Kelly based on the edge.
- Track your closing line value over time to verify your edge is real.
- Repeat hundreds of times. Do not evaluate your results after 20 bets.
Most bettors skip the math and rely on intuition. That is why most bettors lose. EV betting is not complicated. It is multiplication and subtraction. The hard part is the consistency to run the numbers every single time and the patience to trust them when results run bad.
Frequently asked questions
- What does EV mean in sports betting?
- EV stands for expected value. It is the average profit or loss per bet if you placed the same bet infinite times. A +EV bet makes money long-term. A -EV bet loses money long-term. The formula is: EV = (Win Probability x Profit) - (Loss Probability x Stake).
- How do I find the true probability for an EV calculation?
- The most reliable method is de-vigging a sharp sportsbook's closing line. Pinnacle is the industry standard. Strip the vig using a de-vig calculator to get the true implied probability, then use that as your benchmark. You can also build your own statistical model or use high-liquidity prediction market prices.
- Can a +EV bet still lose?
- Yes. A +EV bet will lose regularly in the short term. A bet with 55% true probability loses 45% of the time. Expected value only reveals itself over hundreds or thousands of bets. Short-term results are variance, not signal.
- What is a good EV percentage in betting?
- Any positive EV is worth betting if sized correctly. Professional bettors typically find edges in the 2-8% range. Even a 2% edge, bet consistently over 500+ wagers with proper Kelly sizing, produces meaningful profit through volume.
- Does EV betting work on prediction markets?
- Yes. The formula is identical. Buy contracts where the market price implies a lower probability than your estimate. The only difference is accounting for platform-specific fees on Kalshi or Polymarket, which reduce your net EV.