Calculating expected value in sports betting requires two inputs: the payout the book is offering and your estimate of the true probability of the outcome. Multiply your win probability by the profit on a win, subtract your loss probability multiplied by your stake, and the result tells you whether the bet is worth taking. A positive number means the price is in your favor. A negative number means you are paying more for the bet than the outcome is worth.
The formula itself takes thirty seconds to run. The work is in building a reliable probability estimate to feed it, because a positive EV result from a bad probability input is not an edge — it is a maths error with a false positive sign. This article covers the full calculation mechanics, how to strip vig from book prices to find the fair probability benchmark, and how to apply both across different odds formats and market types. If you want the conceptual foundation first, what is EV betting covers that ground.
01 — The Core Formula
Expected Value: The Calculation Step by Step
The expected value formula expresses what a bet returns on average across an infinite number of identical trials at the same price and probability. It does not predict what happens on any individual bet. It describes the long-run mathematical direction of the strategy.
EV = (Pwin × Profit) − (Plose × Stake)
Pwin = estimated true probability of winning (decimal). Plose = 1 − Pwin. Profit = amount won if bet succeeds. Stake = amount risked.
Walk through a concrete example. A recreational book is offering +120 on an outcome you estimate has a 52% true probability of occurring. Your stake is $100.
The bet produces $14.40 in expected profit per $100 staked. That is a 14.4% edge, which is unusually large — most qualifying opportunities will sit in the 1–4% range. The same arithmetic applies regardless of odds format; only the profit figure changes based on how you convert the price.
02 — Converting Odds to Probability
Implied Probability and Why It Includes Margin
Before you can calculate EV, you need to convert the book’s price to implied probability — the win probability the price assumes. This is not the same as the true probability of the outcome. It includes the book’s margin, which is why the implied probabilities of both sides of a two-way market always sum above 100%.
American Odds Conversion
P = |odds| ÷ (|odds| + 100)
Example: −110 → 110 ÷ 210 = 52.38%
P = 100 ÷ (odds + 100)
Example: +130 → 100 ÷ 230 = 43.48%
The combined implied probability of a standard -110/-110 two-way market is 52.38% + 52.38% = 104.76%. That 4.76% excess is the book’s margin. It is built into the price before you place a single bet, and it compounds across every wager you make at those prices.
Decimal and Fractional Odds
Decimal odds convert directly: implied probability equals 1 divided by the decimal odds. A price of 2.10 implies 1/2.10 = 47.6%. Fractional odds convert by dividing the denominator by the sum of numerator and denominator. 6/4 implies 4/(6+4) = 40%. American format is the dominant format in North American markets, but sharp consensus lines are sometimes displayed in decimal format by aggregators, so being comfortable with both is worth the two minutes it takes.
Standard US spread price
Corresponding other side
03 — The No-Vig Conversion
Finding the Fair Probability Benchmark
Implied probability from the book’s price includes the margin, which makes it an unreliable input for an EV calculation. What you need is the no-vig probability — the book’s actual assessment of the outcome stripped of their cut. This is the benchmark you compare against the recreational book’s price to find the edge.
The no-vig conversion is a three-step process for any two-way market. First, convert both sides to implied probability using the formulas above. Second, sum the two figures — the total will be above 100% by the margin amount. Third, divide each side’s implied probability by the total. The result is the no-vig probability for each outcome, and the two figures will now sum to exactly 100%.
No-vig P = Implied Pside ÷ (Implied Pside1 + Implied Pside2)
Works for any two-way market. For three-way markets (soccer with draw), divide each of three implied probabilities by their sum.
With the no-vig probabilities in hand, you now have the benchmark. Take those figures to any recreational book and compare their implied probability for the same outcome. When the recreational book’s implied probability is lower than the no-vig benchmark, the price is better than fair and the bet carries positive expected value at that price.
04 — Applying the Calculation
Full Worked Examples Across Market Types
Example 1: NFL Spread — Identifying a +EV Underdog
A sharp-market no-vig conversion puts the underdog’s true probability at 45.73%. A recreational book is offering +120 on the same side, implying 100/220 = 45.45%. That looks close, but run the EV calculation:
A $0.61 edge per $100 staked is a 0.6% edge — thin but genuine. Across 500 bets at this price, that is $305 in expected profit before variance. This is the realistic end of the EV spectrum for main lines on liquid markets. The price discrepancy is narrow because sharp action has already done most of the corrective work.
Example 2: Player Prop — Higher Edge in a Less Efficient Market
Player props are priced with less precision than main lines, which means the gap between fair probability and the recreational price is typically wider. A receiver’s receiving yards prop opens at over/under 64.5 at -110 on both sides. A sharp bettor tracking the receiver’s target share in zone coverage estimates the true probability of the over at 57%.
An 8.82% edge is exceptional and reflects a market where the book’s model is materially wrong relative to a well-researched probability estimate. This kind of discrepancy closes fast as sharp action corrects the line, which is why speed matters in prop markets considerably more than it does in main line betting.
Super Bowl LVI: Cooper Kupp Receiving Yards — Prop Mispricing in Practice
Before Super Bowl LVI, several books opened Cooper Kupp’s receiving yards prop at 90.5 yards. Bettors who had tracked Kupp’s target share across the Rams’ 2021 season — he ran 35% of LA’s routes and generated a 26% target share — found the number conservative relative to what the San Francisco defense had allowed to slot receivers during the playoffs. Sharp money hit the over early, and the line moved to 94.5 at most books before kickoff. Kupp finished with 92 yards. Bettors who got the opening number captured a meaningful price advantage over those who waited for the line to settle, with the edge shrinking by roughly half as the market corrected.
05 — Edge Percentage and What It Means
How to Express and Evaluate Edge
Expected value in dollar terms is useful for sizing a specific bet, but edge percentage is the more portable metric for comparing opportunities and evaluating process quality across a portfolio. Edge percentage is simply EV divided by stake, expressed as a percentage.
Edge % = (EV ÷ Stake) × 100
Example: $8.82 EV on a $100 stake = 8.82% edge. Use this to compare opportunities across different stake sizes and odds.
In practice, a 1–3% edge is a strong and repeatable result on competitive markets. Below 1% requires very high volume to produce meaningful returns. Above 5% in a main line market should prompt a second look at the probability estimate — edges that large on liquid markets are either genuine mispricings that will close within minutes or errors in the calculation. In prop markets and less liquid markets, higher edge percentages are more common and more durable.
to produce meaningful returns
well-run EV operations
normal in props, rare in main lines
Edge percentage is also how you calculate the Kelly stake. Full Kelly stake = edge percentage divided by the decimal odds minus 1. Most serious operators use a quarter to half Kelly to manage variance. The bankroll management mechanics are covered in the EV betting guide.
06 — Common Calculation Errors
Where the Math Goes Wrong
Using implied probability as the true probability
The book’s implied probability includes the vig. Plugging it directly into the EV formula as if it were the fair probability produces a calculation that will almost always show negative EV, because you are comparing the book’s marked-up price against itself. Always strip the vig first to get the no-vig probability before using it as your benchmark input.
Treating a sharp line as the probability estimate for the same book
The no-vig conversion from a sharp consensus line gives you the fair probability benchmark. That benchmark then gets compared against a different book’s price — typically a recreational book offering a better price on one side. Comparing a sharp book’s no-vig probability against the same sharp book’s price will show zero edge by definition, because the fair probability and the offered price are derived from the same number.
Overestimating the probability input
The single most expensive error in EV calculation is feeding an overconfident probability estimate into the formula. A 55% probability estimate on an outcome the market puts at 48% produces a large positive EV figure that may have no basis in reality. Anchoring probability estimates to the sharp consensus no-vig conversion, rather than to personal conviction, is the discipline that separates genuine EV calculation from optimistic arithmetic.
07 — Vig, Platform, and Effective Edge
Why Where You Bet Changes the Calculation
The EV calculation assumes you are placing bets at the price you identified. The structural vig at the book you use determines how much of any edge survives after margin drag. At standard -110, the break-even win rate is 52.4%. At reduced vig pricing of -105, it drops to 51.2%. That 1.2 percentage point improvement applies structurally to every single bet you place, regardless of your selection process.
On a bet where your true probability estimate gives you a 2% edge at -110, moving to a book offering the same outcome at -105 increases that effective edge to roughly 3.2%. The selection is identical. The edge is 60% larger simply because of where the bet was placed. At bet105, the reduced vig structure and stable limits mean the calculation you run is the edge you actually capture — without the structural drag that compounds against you at recreational pricing across thousands of bets.
“Bookmakers do not appear to set prices to balance the book. Rather, they shade their lines to exploit the systematic biases of bettors.”
Steven D. Levitt
Why Are Gambling Markets Organised So Differently from Financial Markets? | The Economic Journal, Vol. 114 | University of Chicago, 2004
Levitt’s research identifies the structural reason why the no-vig conversion from a sharp consensus is the right probability benchmark: books are not trying to price accurately. They are pricing for public consumption. The gap between public-facing pricing and sharp-consensus no-vig probability is precisely where positive EV betting finds its edge, and the calculation mechanics in this article are what turn that gap into a quantified number you can act on.
FAQ
Frequently Asked Questions
How do you calculate expected value in sports betting?
Multiply your estimated probability of winning by the profit on a win, then subtract your estimated probability of losing multiplied by your stake. The result is your expected profit or loss per bet at that price and probability. The accuracy of the calculation depends entirely on how reliable your probability estimate is.
What is the expected value formula for betting?
EV = (P_win × Profit) − (P_lose × Stake). P_win is your estimated true probability of winning expressed as a decimal. P_lose is 1 minus P_win. If the result is positive, the bet has positive expected value at that price.
How do you convert American odds to implied probability?
For negative odds, divide the absolute value by that value plus 100. For -110, that is 110/210 = 52.38%. For positive odds, divide 100 by the line plus 100. For +130, that is 100/230 = 43.48%. These figures include the book’s margin, so both sides of a two-way market will sum above 100%.
What is a no-vig probability?
The no-vig probability removes the sportsbook’s margin from both sides of a market, leaving the fair probability estimate for each outcome. To calculate it, convert both sides to implied probability, sum them, then divide each side’s implied probability by the total. The result is the book’s actual assessment of the outcome without the markup.
What is a good edge percentage in EV betting?
A consistent 1–3% edge per bet is a strong result in a competitive market. Most qualifying opportunities will sit toward the low end of that range. Edge percentage matters less than consistency across volume — a reliable 1.5% edge applied to 1,000 bets produces more total profit than an inconsistent 4% edge applied to 100.
How much does vig affect expected value?
At standard -110, the vig forces a 52.4% break-even win rate instead of 50%. That 2.4% structural drag applies to every bet you place. Moving to a reduced-vig book at -105 drops the break-even to 51.2%, effectively improving your edge on every qualifying bet without changing your selection process.
Can you calculate EV without a sharp consensus price?
You can, but the calculation is only as reliable as the probability estimate you substitute in. Without a sharp consensus benchmark, you are estimating true probability from your own model or analysis, which introduces more error. The sharp no-vig conversion is the most accessible and reliable probability input for most bettors.