Picking the right side is not the same as finding a profitable wager.
A running back may look more likely than not to clear 62.5 rushing yards—but at -150, “more likely than not” is insufficient. That price requires a 60% break-even win rate. If the estimated chance is 56%, the prediction may be reasonable while the wager still has negative value.
This distinction matters when learning how prop bets work: the outcome and its price must be judged together. “After juice” means using the actual net payout, not merely deciding which result seems likelier. A $100 bet at -150 earns only $66.67 when correct but loses the full $100 when wrong. Prediction asks what will happen; expected value asks whether the payout justifies the risk.
Gather the three required inputs
Every prop-bet EV calculation needs three inputs:
- Stake: the amount risked, excluding any returned principal.
- Posted American odds: the sportsbook price actually available.
- True-probability estimate: an independent estimate of how often the bet wins.
The prop line alone is not enough. “Over 24.5 points” identifies the threshold, but it does not show whether the player clears it 45%, 55%, or 65% of the time. That probability must come from projections, historical distributions, matchup adjustments, or another defensible method—not simply from the offered price.
Whole-number lines may also push. A $100 bet on over 24 points returns the $100 stake if the player scores exactly 24, producing zero profit and zero loss. With pushes included, the probabilities of winning, losing, and pushing must total 100%.
Convert the odds into payout and break-even probability
For positive odds +A:
- Net profit = stake × A / 100
- Break-even probability = 100 / (A + 100)
At +120, a $100 winner earns $120 net, and the break-even rate is 45.45%.
For negative odds −A, using A as the absolute value:
- Net profit = stake × 100 / A
- Break-even probability = A / (A + 100)
At −150, a $100 winner earns $66.67 net, and the break-even rate is 60%.
The expected-value formula is:
EV = (win probability × net profit) − (loss probability × stake)
A push contributes zero. Most importantly, the posted payout already reflects the sportsbook’s pricing. After using that net profit in the formula, juice should not be subtracted again. Doing so would penalize the wager twice.
Estimate the true probability
Expected value is only as credible as the probability fed into it. A defensible estimate may come from several sources:
- Projections: Minutes, usage, pace, and expected game conditions can produce a forecast for the relevant statistic.
- Historical rates: The share of comparable games in which the player cleared the line offers a baseline, provided the sample reflects the current role.
- Matchup adjustments: Opponent tendencies, injuries, venue, and likely defensive assignments can move that baseline.
- Pricing models: A statistical distribution can turn a projection into an over, under, or exact-outcome probability. This is the core of learning to calculate player prop odds.
The sportsbook’s offered odds should not determine this estimate. Otherwise, the calculation merely repackages the market price and may create false confidence.
Treat small samples and recent streaks cautiously. Regress extreme results toward a longer-term average, document each adjustment, and use a probability range when uncertainty is high. Precise EV math cannot rescue a weak probability estimate.
Remove the vig from market probabilities
For a two-way market priced at -120 / +100, first convert each side to implied probability:
- -120: 120 ÷ (120 + 100) = 54.55%
- +100: 100 ÷ (100 + 100) = 50.00%
The total is 104.55%, with the extra 4.55 percentage points representing the sportsbook’s margin. To remove it, divide each implied probability by the combined total:
- Favorite: 54.55% ÷ 104.55% = 52.17%
- Underdog: 50.00% ÷ 104.55% = 47.83%
These no-vig probabilities sum to 100% and provide a cleaner market benchmark. They can serve as a reasonableness check when estimating touchdown probability for EV, but should not replace an independent estimate.
De-vigging only approximates the market’s fair probability. Specialized props may reflect uneven limits, thin liquidity, or different margins, so a separate model is still needed to identify an edge.
Calculate expected value and EV percentage
- Write the full EV formula
Use EV = (P(win) × win profit) + (P(loss) × loss) + (P(push) × 0). EV is the average theoretical profit or loss per wager.
- Define the outcomes
P(win), P(loss), and P(push) are estimated probabilities and should total 100%. Win profit excludes the returned stake; loss is entered as a negative amount.
- Treat pushes as zero profit
A push returns the stake, producing neither profit nor loss. Its EV contribution is therefore zero, though its probability still belongs in the outcome distribution.
- Calculate EV per dollar
For a $1 stake, use EV/$ = (P(win) × b) − P(loss), where b is the net profit per dollar at the offered odds.
- Convert EV to a percentage
Use EV% = (EV ÷ stake) × 100. At -110, with 55% wins, 43% losses, and 2% pushes: (0.55 × 0.9091) − 0.43 = 0.07, or +7% EV.
A $100 stake in the example has a theoretical EV of +$7.
A +7% EV wager can still lose. The figure describes an estimated average return across many comparable bets, assuming the probabilities are accurate—not the outcome of a single prop.
Example: A -110 prop with a small edge
Suppose a prop is priced at -110, the stake is $100, and an independent estimate gives it a 55% chance of winning. At -110, a $100 stake returns $90.91 in net profit when successful.
- Net win payout: $100 × (100 ÷ 110) = $90.91
- Expected gain: 55% × $90.91 = $50.00
- Expected loss: 45% × $100 = $45.00
- EV: $50.00 − $45.00 = +$5.00
- EV ROI: $5.00 ÷ $100 = +5.00%
The break-even probability is 52.38%, so the estimated 55% win rate supplies an edge of 2.62 percentage points. That margin is not especially forgiving: a 53% estimate produces about +$1.18 EV, while 52% produces roughly −$0.73 EV. Small changes in the probability estimate can therefore flip the decision.
Example: Plus money can still be negative EV
Consider a +140 prop with a $100 stake and an estimated 40% win probability. A win earns $140, but the bet must win 41.67% of the time to break even.
- Net win payout: $100 × 1.40 = $140
- Expected gain: 40% × $140 = $56
- Expected loss: 60% × $100 = $60
- EV: $56 − $60 = −$4
- EV ROI: −$4 ÷ $100 = −4%
Despite the attractive plus-money price, the bet loses an average of $4 per $100 staked under this probability estimate.
Shopping between sportsbooks can change the conclusion without changing the projection. At +150, the same 40% estimate gives $60 in expected gains and $60 in expected losses, making the bet break-even. At +160, expected gains rise to $64, producing +$4 EV and +4% EV ROI. The underlying prop is identical; only the offered price changes its value.
EV mistakes
Weak models, correlated inputs, stale prices, and early rounding can erase a 1–2% edge. Keep full precision and recalculate at the available line.
Positive EV is an estimate and can lose. Practical arbitrage and EV checks describe a locked return—but only if every leg, limit, and settlement rule holds.
Apply a disciplined pre-bet standard
- Compare prices
Check multiple sportsbooks; even a small odds improvement can materially change EV.
- Recalculate at the offered line
Use the actual juiced price available, not an earlier quote or a market average.
- Stress-test the probability
Recompute EV after lowering the estimated win probability by one or two percentage points. If the edge disappears, the bet is fragile.
- Account for practical constraints
Factor in uncertainty, stake size, and planning around prop-bet limits. A positive percentage may still produce little practical return.
- Pass on marginal edges
When assumptions are weak or EV is barely positive, restraint is usually more defensible than forced action.
A prop is positive EV only when the estimated probability justifies the exact price being offered. Price shopping improves the threshold, but it cannot rescue an unsupported probability estimate.
Small theoretical edges deserve caution: modest forecasting errors, low limits, or both can erase their practical value.