DawgHousePicks
De-Vigging Sportsbook Odds: American Odds to the No-Vig Fair Line
Your sportsbook never shows you a fair price. Every line carries the vig, and the vig hides inside the implied probability. Convert minus 110 to a win probability and you get 52.38 percent. Add the other side and the two numbers sum past 100 percent. The overflow is the house margin. Measure your edge against the raw number and you overstate the edge on every bet you place.
De-vigging fixes the problem. You strip the margin out and recover the no-vig fair line, the price the market would offer with zero hold. The fair line is what you compare your own probability estimate against. The fair line is what feeds correct bet sizing. Skip the step and every downstream number inherits the vig.
This guide covers the full pipeline. American odds to implied probability, implied probability to the booksum, and the booksum to a clean fair line through four methods. You will see when the method choice changes nothing and when the method choice moves real probability. A de-vig calculator at the end runs the math on your own numbers.
American odds to implied probability
Start with the conversion every bettor needs. American odds map to an implied probability, the win rate baked into the price.
implied = |odds| / (|odds| + 100)
# Positive odds (underdogs):
implied = 100 / (odds + 100)
# Worked:
-200 → 200 / 300 = 66.67%
+150 → 100 / 250 = 40.00%
The implied probability already includes the vig. One side alone looks reasonable. Both sides together expose the margin.
The booksum: where the vig shows up
Add the implied probabilities of every outcome in a market and you get the booksum, also called the overround. A fair market sums to exactly 100 percent. A real market sums higher. The excess is the hold the book keeps.
overround = booksum − 100%
A standard minus 110 / minus 110 spread sums to 52.38 plus 52.38 = 104.76 percent. The 4.76 points is the vig. A minus 400 / plus 320 moneyline sums to 80.00 plus 23.81 = 103.81 percent, a 3.81 point hold. You de-vig by pushing the booksum back down to 100 percent. The methods differ in how they hand the margin back.
Method 1: the basic (proportional) de-vig
The basic method, also called proportional or multiplicative, divides each implied probability by the booksum.
# Balanced spread, -110 / -110:
52.38% / 104.76% = 50.00% per side
# Lopsided line, -400 / +320:
80.00% / 103.81% = 77.06% # favorite
23.81% / 103.81% = 22.94% # underdog
The basic method keeps the ratio of the raw prices intact. The favorite stays 3.36 times more likely than the underdog before and after. OddsJam and most public guides stop here. For a balanced two-way market, stopping here gives you the right answer.
Why the basic method falls short on lopsided lines
The basic method assumes the book spreads its margin evenly across both sides. Real markets do not behave this way. Bettors over-bet longshots and under-bet favorites, a pattern researchers call the favorite-longshot bias. Erik Snowberg and Justin Wolfers studied roughly 6.4 million horse-race bets and concluded the bias comes from misperception of probability, not from a taste for risk (Journal of Political Economy, 2010). Bettors treat small chances as larger than they are.
Books price around the behavior. They shade longshot odds short because the public pays up for the lottery ticket. The result: a longshot's raw implied probability sits above the longshot's true probability. The basic de-vig preserves the inflation, because the basic de-vig keeps every ratio fixed. On a lopsided line, the basic method leaves too much probability on the underdog.
Methods 2 through 4: correcting the imbalance
Three methods adjust for the skew instead of scaling everything by one factor.
- Additive. Subtract the overround in equal probability points from each side. Equal points take a larger share from the smaller number, so the underdog loses more of its probability.
- Power. Raise each implied probability to a single exponent, chosen so the set sums to 100 percent. The exponent pulls the most probability off the longshot. The goto_conversion library frames the basic method as naive for this reason and computes an analytical correction in the same family.
- Shin. Model a fraction of bettors as insiders who already know the outcome. The book widens its margin to cover the informed money, and the model recovers a fair line shifting probability toward the favorite. Hyun Song Shin derived the method in 1992 and 1993. Erik Štrumbelj tested the method against basic normalization across a large multi-bookmaker data set and found Shin produces more accurate probability forecasts (International Journal of Forecasting, 2014). The open-source implied R package implements all four methods plus the odds-ratio variant.
Run the same minus 400 / plus 320 line through each method and the split moves:
| Method | Fair P(favorite) | Fair P(underdog) | What the method does |
|---|---|---|---|
| Raw implied | 80.00% | 23.81% | Sums to 103.81%, not a probability |
| Basic (proportional) | 77.06% | 22.94% | Keeps the 3.36-to-1 price ratio |
| Additive | 78.10% | 21.90% | Equal point subtraction |
| Shin | 78.09% | 21.91% | Moves probability off the longshot |
| Power | 78.65% | 21.35% | Moves the most off the longshot |
The basic method prices the underdog at 22.94 percent. Shin and power price the same underdog near 21.4 to 21.9 percent. More than a full point of probability sits on a single side of one bet. The direction matches the research: the public overpays for longshots, so the fair longshot probability lands below the proportional estimate.
When the method changes your decision
The gap between methods scales with how lopsided the line is.
- Balanced markets (minus 110 / minus 110, minus 120 / plus 100): every method lands within a tenth of a point of the same answer. Use the basic method and move on.
- Lopsided markets (minus 400 / plus 320, minus 900 / plus 600): the methods split by a full point on the favorite and more on the underdog in percentage terms. The basic method overstates the underdog. Reach for Shin or power.
A one-point error on a fair line looks small. Run the error through an edge calculation and a stake size and the mistake compounds. If your fair line says the underdog wins 22.94 percent and the true number is 21.4 percent, you will grade marginal underdog bets as plus EV when they are minus EV, and you will overbet them. The sizing math is in our companion piece on the Kelly criterion, where a small edge error pushes you past the threshold where growth turns negative.
The de-vig calculator
Enter the two American prices on a market. The calculator returns the implied probability per side, the booksum, the overround, and the no-vig fair line under both the basic method and the power method. Watch the two fair lines converge on a balanced market and split apart as you make the favorite heavier. The math runs locally. No server, no tracking.
No-Vig Fair Line Calculator
Inputs are American odds for the two sides of a market. Try -110 and -110, then try -400 and +320.
Side A
Side B
Putting the fair line to work
The fair line is the input to every edge decision you make. The workflow is short.
- De-vig a sharp book. Pinnacle and Circa run thin margins and take sharp action, so their de-vigged line is the closest public proxy for the true price. De-vig the two sides and you get a reference fair probability.
- Compare your number. Your edge is your estimated probability minus the fair probability, not minus the raw implied probability. Use the raw number and you erase your own edge by the size of the vig on every bet.
- Size from the fair line. Feed the fair probability into your staking math. A clean fair line is the difference between a real edge and a rounding error.
Tools like Outlier and Pikkit report closing line value against de-vigged numbers, so the CLV figure you track already accounts for the hold. When you build your own model, run the de-vig first and grade everything against the fair line.
Sharp Line Desk inside the DawgHousePicks Discord de-vigs every market before ranking an edge, and applies Shin-style corrections on lopsided lines so a heavy favorite never gets graded off an inflated underdog price. Raw implied probability is where most bettors start and stop. The fair line is where the real number lives.