The single most important calculation in sports betting
Every analytical workflow — line shopping, Kelly sizing, CLV measurement, +EV identification — depends on knowing the fair price. The fair price is the no-vig price. It is the bookmaker's actual probability estimate, stripped of the commission embedded in the public quote. Without it, you are comparing apples (your model probability) to oranges (vig-loaded market probability) and concluding edge that may not exist.
The no-vig price is also the answer to the most common bettor question: "How sharp is this line?" A no-vig price within 1-2 cents of your model price = no edge. A no-vig price 4-6 cents off your model = potential edge worth investigating. A no-vig price 10+ cents off = either your model is broken or the book has badly mispriced — usually the former.
Method 1 — Multiplicative (proportional)
The industry default for two-way markets. Divide each side's implied probability by the overround.
# Lakers -150 / Celtics +130 implied_LAL = 150/250 = 0.6000 implied_BOS = 100/230 = 0.4348 overround = 1.0348 novig_LAL = 0.6000 / 1.0348 = 0.5798 → -137.9 American novig_BOS = 0.4348 / 1.0348 = 0.4202 → +137.9 American # Fair price: -138 / +138. Implied probabilities sum to 100%.
Assumes vig is distributed proportionally across outcomes. Accurate for balanced two-way markets where favorite-longshot bias is minimal. Breaks down on heavy favorites or extreme longshots.
Method 2 — Shin (additive)
Subtract an equal slice of the overround from each side's implied probability. Adjusts for asymmetric vig loading on lopsided markets.
# Same Lakers -150 / Celtics +130 example overround_excess = 0.0348 slice = 0.0348 / 2 = 0.0174 novig_LAL_shin = 0.6000 − 0.0174 = 0.5826 → -139.6 American novig_BOS_shin = 0.4348 − 0.0174 = 0.4174 → +139.6 American # Shin assigns slightly more value to the favorite than multiplicative.
Hyun Song Shin's 1992 paper introduced this method to model bookmaker behavior when insider trading is present. Empirically, Shin's no-vig prices fit horse racing and futures markets better than multiplicative, because vig is asymmetrically loaded on longshots.
Method 3 — Power (logit) method
The academic gold standard for three-way markets. Apply a power exponent k to each implied probability so that the result sums to exactly 1.
# EPL match: Liverpool 2.10 / Draw 3.40 / Arsenal 3.80 p_LIV_raw = 0.4762; p_DRW_raw = 0.2941; p_ARS_raw = 0.2632 sum_raw = 1.0335 # Solve for k such that p_LIV^k + p_DRW^k + p_ARS^k = 1 k ≈ 1.0532 # numerical solve via Newton-Raphson novig_LIV = 0.4762^1.0532 = 0.4628 → 46.28% novig_DRW = 0.2941^1.0532 = 0.2829 → 28.29% novig_ARS = 0.2632^1.0532 = 0.2543 → 25.43%
Štrumbelj's 2014 paper documents that the power method consistently produces the best probabilistic forecast in three-way markets across 50,000+ soccer matches. Most professional toolchains default to power for 1X2 markets.
How the three methods disagree
| Market | Multiplicative | Shin | Power | Best method |
|---|---|---|---|---|
| NFL spread -3 (-110/-110) | 50.00% | 50.00% | 50.00% | Any |
| NBA moneyline (-150/+130) | 57.98% | 58.26% | 58.10% | Multiplicative |
| EPL 1X2 (2.10/3.40/3.80) | 46.08% | 46.20% | 46.28% | Power |
| NFL futures longshot (+5000) | 1.90% | 1.75% | 1.82% | Shin |
| Player prop O/U (-115/-115) | 50.00% | 50.00% | 50.00% | Any |
| Tennis Grand Slam outright (128 players) | varies | varies | most accurate | Power |
In symmetric two-way markets, all three methods agree exactly. Differences emerge on lopsided lines, longshot futures, and three-way markets — exactly where the bettor needs the most accuracy.
Real-world workflow — model vs. market
A professional bettor's typical Sunday morning routine:
- Pull Pinnacle closing odds from previous week as training labels.
- Run private model on this week's slate — outputs probability for every team/total.
- Pull current odds across 8-10 books in real time.
- For each market, compute no-vig price using the appropriate method.
- For each book's posted price, compute edge: edge_% = (model_prob × posted_decimal) − 1.
- Filter to bets with edge > 1.5% AND limit > $500 AND no signal of stale line.
- Size each bet at fractional Kelly (typically quarter-Kelly).
The no-vig calculation happens at step 4 and is the foundation. If the no-vig math is wrong, every downstream calculation is poisoned. This is why bettors with custom Python pipelines almost always implement multiple no-vig methods and cross-check.
When no-vig calculations break
- Heavy longshot futures — multiplicative undervalues longshots; Shin is more accurate.
- Same-game parlays — books embed extra correlation-adjustment vig; no off-the-shelf method strips this cleanly.
- Player props with thin two-way markets — wide vig means small inaccuracies in method choice translate to larger fair-price differences.
- Live betting — vig fluctuates rapidly; the no-vig price calculated from a 5-second-old quote may already be stale.
- Books with hidden vig — bonuses, deposit matches, and odds boosts effectively reduce vig below the posted level; the "true" no-vig is harder to compute.
The Pinnacle benchmark
Pinnacle Sports' no-vig closing line is the de facto industry benchmark for "true" probability. Reasons: ① 2.5% overround → vig-stripping introduces minimal noise; ② high limits and welcomes sharp action → reflects best-informed money; ③ global reach → aggregates worldwide modeling intelligence.
Sharp shops typically benchmark every bet against the Pinnacle no-vig closing price. CLV against Pinnacle is the cleanest measure of bettor skill. A bettor consistently beating Pinnacle no-vig close by 2+ cents across hundreds of bets is almost certainly profitable.
For US-licensed bettors who cannot access Pinnacle, Circa Sports (Vegas-licensed, sharp-friendly), Bet365 (when accessible), and the Smarkets/Betfair exchange mid-market are reasonable substitutes.
Common no-vig mistakes
- Using multiplicative on three-way markets. Produces fair probabilities that don't sum to 100% — internally inconsistent.
- Calculating no-vig from one book. Single-book no-vig reflects only that book's view. Cross-book averaging is more robust.
- Ignoring posting-time bias. A no-vig price calculated at opening (Tuesday 9 AM NFL) is much less informative than the same calculation at closing (Sunday 1 PM).
- Treating no-vig as truth. No-vig is the market consensus, not God's eye view. Sharp bettors disagree with no-vig and document their disagreement through CLV.
Sources & further reading
- Shin, Hyun Song. "Prices of State Contingent Claims with Insider Traders, and the Favourite-Longshot Bias." Economic Journal, 1992.
- Štrumbelj, Erik. "On determining probability forecasts from betting odds." International Journal of Forecasting, 2014.
- Clarke, Stephen R. et al. "Adjusting bookmaker's odds to allow for overround." American Journal of Sports Science, 2017.
- Pinnacle Betting Resources — "How to remove the margin from betting odds" (public methodology).
- Buchdahl, Joseph. Squares and Sharps, Suckers and Sharks: The Science, Psychology & Philosophy of Gambling. High Stakes Publishing, 2016.