Expected Value

EV, expected value, is the average result of a bet if it were placed many times, weighted by probability. It is the only metric that connects the price you get with the probability you believe in, the bridge between CLV, which reads the same edge through the market’s final price, and ROI, which reports what the settled bets actually returned.

The EV Formula

EV per unit staked = (P × odds) − 1

P is your estimated win probability, odds the decimal price. Bet at 2.00 on an event you estimate at 55%, and the EV per unit is 0.10, a 10% expected profit on every unit staked over the long run.

The same expectation in dollars. For a decimal price, the win profit is the stake multiplied by the price minus one:

EV = (P × win profit) − ((1 − P) × stake)

Stake $100 at 2.10 on an event estimated at 50%. A win pays back $210, a profit of $110; a loss costs the stake. EV = (0.50 × 110) − (0.50 × 100) = $5.00. The bet is worth five dollars over the long run. The dollar figure is the per-unit EV multiplied by the stake, so the EV percentage stays the same whatever the amount.

An exchange takes commission out of the win, which cuts EV. At a 5% rate the same 2.10 bet at 50% pays $104.50 net profit per $100, and EV = (0.50 × 104.50) − (0.50 × 100) = $2.25 instead of $5.00.

American prices plug into the same equation once the win profit is known. A positive price pays its face value per $100 staked, so +120 pays $120; a negative price pays 100 divided by the price, so −200 pays $50 on $100.

+120 at a 48% estimate: (0.48 × 120) − (0.52 × 100) = $5.60 per $100, an EV of 5.6%. A −200 favorite you estimate at 60%: (0.60 × 50) − (0.40 × 100) = −$10.00 per $100. The favorite wins more often than not and still loses money: the price never pays for the risk.

EV hits zero when your probability equals the price’s implied probability, 1 divided by the decimal odds. At 1.91 you need 52.4% winners just to stand still; at 1.30 the bar rises to 76.9%. This is the same break-even Hit Rate that Average Odds predicts.

The Bookmaker Margin

Before any estimate enters the calculation, every market carries negative EV. Decimal odds imply a probability, 1 divided by the price, and the implied probabilities of all outcomes in a market sum to more than 100%. The excess is the bookmaker’s margin, the built-in tax on every price. A two-outcome market priced at 1.90 and 1.90 implies 105.3%, a 5.3% margin; remove the tax and the fair price of both sides is 2.00.

The tax varies by market and book. According to the Bet Better bookmaker margin study, the average margin on head-to-head markets across 31 bookmakers and nine sports in July 2026 was 4.78%, with a median of 4.71% over 205,491 markets. By sport the average ran from 4.54% on NHL to 5.61% on WTA tennis; by bookmaker, from 3.16% to 5.78%. Head-to-head is the cheapest class of market: Pinnacle holds main markets near 2%, about half the measured average, while props and exotics run markedly steeper.

What Good EV Looks Like

Edges on efficient markets are small. A sustained positive EV in the low single digits is a strong result; below about 1% the edge is real but variance eats it for long stretches. A number above 10% on a real market is almost always an error in the probability estimate, not a market that cheap.

Scanning tools set the same bar: SharpAPI’s default EV threshold is 2%, and the EVBets scanner shows only bets between +1% and +20%, treating anything above that as a data error.

EV vs ROI and CLV

EV is forward-looking: what a bet should return on average before the result lands. ROI is backward-looking: what the settled bets actually returned. Over many bets the two converge, because the expected ROI of a sample is simply its average EV; a bettor with consistent positive EV lands at positive ROI in the end. In any short window they diverge, since results swing around the expectation.

EV and CLV describe the same edge through different probability sources. EV reads it through your own estimate; CLV through the market’s final price. The two can disagree on a single bet: your estimate can beat the close or trail it. They reconcile over a sample only when your probabilities are right. A tracker that computes EV against its own closing line reports CLV under an EV label, the same signal in different packaging.

Finding Positive EV

Positive EV starts with a probability estimate, and the recoverable proxy is the market’s own line. Split the implied probabilities of a two-way market proportionally and the margin falls away:

fair probability = implied probability / total implied probability

The result is the no-vig price, the market’s collective estimate of the true probability and the benchmark behind CLV. Any price better than it is positive EV by definition, relative to the market if not to your model.

Line shopping raises EV without changing the estimate. At a 52% estimate of an even game, −110 loses $0.73 per $100 staked while −105 wins $1.52: the same opinion, opposite results, decided by price alone.

Where the estimate can beat the market is the domain of value betting, hunting slow markets, stale lines, and niche prices; its guaranteed cousin arbitrage locks in positive EV with no probability estimate at all. In-play bets need a live estimate rather than a settled one, and the market charges a higher margin for the privilege. Scanners run the comparison across thousands of markets at once: OddsJam computes EV% against a sharp book’s no-vig line and flags every price that beats it.

Parlays and Props

Parlays multiply odds and margins alike. The combined margin of legs at a 4.77% per-leg margin compounds:

combined margin = 1 − (1 / 1.0477)ⁿ

where n is the number of legs. Three legs stack to 13.0%, five to 20.8%, seven to 27.8% of every dollar staked. The market prices the longshot ticket worse than the compounding suggests: according to a 2026 study of parlays on Kalshi, a parlay whose price implies a 30% chance wins about 24% of the time, and the gap grows with the number of legs.

Props are a worse base to build on. They average near 8% margin against the 4.78% head-to-head figure, and a five-leg prop parlay compounds from there toward a third of every dollar staked. Prop probabilities are also priced less accurately, so a reliable estimate is harder to come by exactly where the margin gets bigger.

Sample Size and Variance

EV is a long-run number, and the long run is longer than most people expect. A bettor with a genuine 3% edge at even money still loses almost every other bet and endures runs of ten or more losses; an honest coin eventually lands twenty heads in a row. Results settle slowly. A few hundred bets show the direction and a few dozen prove nothing; at even money a 3% edge needs roughly four thousand bets before it sits two standard errors above zero. Yield carries the significance math; the practical read is that variance, not edge, decides the short term.

Positive EV decides whether to bet; Kelly decides how much. Without sizing, even a real edge is ruined by a stake too large for the variance the bets carry.

Probability Estimation

The probability is the entire game. EV is only as good as the estimate that feeds it, and the estimate has to beat the market’s own number, a high bar. According to a calibration study of 18,238 settled markets, realized frequencies track the no-vig probabilities within about two percentage points on main markets, so a price that beats the fair line by more than that is either genuinely sharp or simply wrong.

The market’s one systematic error runs against the casual read. The favourite-longshot bias prices heavy favorites a touch more likely to win than they are and longshots a touch less likely, so the EV of underdogs is understated and the EV of favorites overstated. A favorite can be a bad bet even when it wins often. The distortion concentrates at the far ends of the odds scale and is roughly twice as large on props as on main markets.

Limits

EV measures expectation, not outcome.

An estimate that merely repeats the implied probability produces an EV of zero minus the margin; an inflated estimate produces an EV that exists only in the calculation. The metric rewards a genuinely better estimate, not a more confident one.

EV per unit is scale-free: it says nothing about stake size, risk, or drawdowns, which live in Sharpe Ratio and Bankroll Charts. Sustained positive EV is also perishable: bookmakers limit accounts that consistently beat the price, which caps the EV a bettor can actually realize.

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