How to De-Vig Odds: Find the No-Vig Fair Odds Behind a Line

By · author of the MIT-licensed teachersbettextbook library ·

Every posted price has Brian's cut baked into it. This is how you take the cut back out and see what he actually thinks.

Meet your classmates

Same five. Today we take Brian's board apart.

Add both sides up

Today's race is already on the board. Pip at −130, Chalk at +110.

Turn each price into the percentage it implies. −130 is 56.5%. +110 is 47.6%. Add them and you get 104.1%.

One hamster wins. Exactly one. So those two numbers have to come to 100, and they do not. There are 4.1 points too many, and those 4.1 points are Brian. The word for them is vig.

Squeeze it back to 100

He is not hiding it. He quotes both sides a little short, so whoever wins he keeps a slice. Sales tax works the same way, except a menu never shows you the price before tax.

To read the price without the fee, divide both sides by 1.041. Everything shrinks by the same factor and the pair lands exactly on 100. Pip goes from 56.5% to 54.3%. Chalk goes from 47.6% to 45.7%.

That is de-vigging. That is the whole move.

Joe reads 56.5% off the board and stops there. Evan reads 54.3%. Same board, same second, and one of them is looking at a number with a fee still stuck to it.

What 54.3% is, and what it is not

It is what the price says once the fee is out. Nothing more. The hamsters never saw the board and they are still a coin flip.

It is also the number the rest of this site runs on. Expected value compares it. The board pools it. The report card grades against it. Which took me three goes to get: it is a translation, not a forecast.

Three ways to give the points back

Proportional is what you just did. Shave both sides by the same factor.

Power assumes the cut sits heavier on the longshot, so it shaves the longshot harder. Shin assumes some of the money is better informed than the rest, and backs the cut out of that instead.

On this line all three land within a third of a point of each other. On a real longshot they can be points apart. Nobody can tell you which is right, because nobody ever sees the true probability. So the site prints all three.

Watch it happen

Both prices, drawn as one bar. It runs past the 100% line, the red bit is the overshoot, and then it squeezes.

Average Joe Chalk Bookie Brian Pip +EV Evan What Brian has on the board 100% 4.1 points of vig Chalk +110 Pip −130 47.6% 56.5% 45.7% 54.3% Squeezed back to 100, three different ways method Chalk Pip total Proportional 45.73 54.27 100.00 Power 45.46 54.54 100.00 Shin 45.55 54.45 100.00 Two prices. Turn each one into a percentage. They add to 104.1%. One hamster wins, so it has to be 100. Squeeze both sides down until it is. The 4.1 points you squeezed out were the vig.
A diagram, not a simulation: there is nothing random in a de-vig, so there is nothing to roll. Pip at −130 implies 56.5% (130 / 230), Chalk at +110 implies 47.6% (100 / 210), and 56.5% + 47.6% = 104.1%. The squeeze divides both by 1.041, which is the same as multiplying both by 0.9602, and lands them on 54.3% and 45.7%. The table is the same line through all three methods in teachersbettextbook. All three add to 100. They only disagree about who gives back more, and here by 0.27 of a point.

A price is an opinion with a fee attached. De-vigging is how you read the opinion and ignore the fee.

Four points looks like a rounding error. It is the only part of the price that never has a bad day.

Open the free De-Vig calculator →Free. Shows every step of the math on your own numbers.

Or open it in the live app: the fair-price tool on the board →

Want more math?the Nerd Corner

Nerd Corner

Advanced material. Nothing above depends on it. The line worked here is a different one, −152 / +138, so you get a second example rather than the same one twice.

The three moves, stated

Converting a price to a percentage

American odds map straight to probability. A −152 favorite implies 152152+100=60.3%\tfrac{152}{152+100} = 60.3\%. A +138 underdog implies 100138+100=42.0%\tfrac{100}{138+100} = 42.0\%. The rule:

q={−A−A+100A<0(favorite)100A+100A>0(underdog)q = \begin{cases} \dfrac{-A}{-A + 100} & A < 0 \quad (\text{favorite}) \\[8pt] \dfrac{100}{A + 100} & A > 0 \quad (\text{underdog}) \end{cases}

Add the sides to get the overround, the number to remove:

qa+qb=60.3%+42.0%=102.3%  ⇒  2.3% marginq_a + q_b = 60.3\% + 42.0\% = 102.3\% \;\Rightarrow\; 2.3\%\text{ margin}

A fair market would sum to exactly 100%. None of them do. It is worth knowing what normal looks like, so you can tell an ordinary price from a bad one at a glance:

fair=1.00ordinary two-way line≈1.02 to 1.05exchange quote≈1.00 to 1.01\text{fair} = 1.00 \qquad \text{ordinary two-way line} \approx 1.02 \text{ to } 1.05 \qquad \text{exchange quote} \approx 1.00 \text{ to } 1.01

So the 1.023 worked here is a normal price, on the tighter end. Anything past about 1.05 is a wide market, a thin one, or a book that does not expect to be shopped against.

The worked example, in full

Worked example: de-vigging −152 / +138

Implied:−152→60.3%+138→42.0%\text{Implied:}\quad -152 \rightarrow 60.3\% \qquad +138 \rightarrow 42.0\%
Overround:60.3%+42.0%=102.3%(2.3% margin)\text{Overround:}\quad 60.3\% + 42.0\% = 102.3\% \quad (2.3\%\text{ margin})
Fair (proportional):60.31.023=58.9%42.01.023=41.1%\text{Fair (proportional):}\quad \dfrac{60.3}{1.023} = 58.9\% \qquad \dfrac{42.0}{1.023} = 41.1\%
Margin out, the line was implying a 58.9% favorite, not 60.3%. That gap is the input to every expected-value calculation on a de-vigged line.

The power and Shin methods

Proportional pads both sides by the same factor. Real prices don’t: more of the overround hides in the underdog’s price. Power and Shin remove the vig unevenly, each with a precise rule for how.

The power method raises each implied probability qiq_i to an exponent kk, then solves for the kk that makes the two sides sum to 1:

The power method, stated

pi=qi k,k≥1 solves  qa k+qb k=1p_i = q_i^{\,k}, \qquad k \ge 1 \ \text{solves}\ \ q_a^{\,k} + q_b^{\,k} = 1
One unknown, one equation. No closed form for kk, but bisection nails it in a few dozen steps. k=1k = 1 would mean a vig-free line; the bigger the overround, the higher kk climbs.

Why longshots hardest? Probabilities sit below 1, so a power above 1 shrinks them, and it shrinks a small probability by a larger fraction of itself. The correction lands exactly where the book’s shading does.

Worked example: power method on −152 / +138

Implied:−152→60.32%+138→42.02%(sum 102.3%)\text{Implied:}\quad -152 \rightarrow 60.32\% \qquad +138 \rightarrow 42.02\% \quad (\text{sum } 102.3\%)
Solve for k:0.6032 k+0.4202 k=1  ⇒  k≈1.035\text{Solve for } k:\quad 0.6032^{\,k} + 0.4202^{\,k} = 1 \;\Rightarrow\; k \approx 1.035
Fair (power):0.6032 1.035=59.3%100%−59.3%=40.7%\text{Fair (power):}\quad 0.6032^{\,1.035} = 59.3\% \qquad 100\% - 59.3\% = 40.7\%
Versus proportional (58.9% / 41.1%), power hands the longshot less: more of the margin was hiding in the +138 price.

Shin’s method models why the vig exists: a fraction zz of the money comes from insiders who already know the result. The book pads its prices in defense, heaviest on longshots, where insider money hurts most.[5] Solving the model gives a closed form:

Shin’s closed form

pi= z2+4(1−z) qi2/s   −  z2(1−z),s=qa+qbp_i = \dfrac{\sqrt{\,z^{2} + 4(1-z)\,q_i^{2}/s\,}\; -\; z}{2(1-z)}, \qquad s = q_a + q_b
zz is the insider fraction, fitted (again by bisection) so the fair probabilities sum to 1.[6] Set z=0z = 0 and it collapses to qi/sq_i/\sqrt{s}: every side scaled by the same constant; rescaled to sum to 1, exactly qi/sq_i/s. Proportional is just Shin with no insiders.

Worked example: Shin on −152 / +138

Fit z:fair probabilities sum to 1 at z≈0.023\text{Fit } z:\quad \text{fair probabilities sum to } 1 \text{ at } z \approx 0.023
Favorite: 0.0232+4(1−0.023) 0.60322/1.023 −0.0232(1−0.023)=59.2%\text{Favorite:}\quad \dfrac{\sqrt{\,0.023^{2} + 4(1-0.023)\,0.6032^{2}/1.023\,} - 0.023}{2(1-0.023)} = 59.2\%
Fair (Shin):59.2%40.8%\text{Fair (Shin):}\quad 59.2\% \qquad 40.8\%
The fitted insider share, 2.3%, lands almost exactly on the 2.3% overround: the model attributes the whole margin to insider protection, shifting more of it onto the longshot than proportional does.

The methods disagree by a few tenths of a point on this mild favorite, and by more as lines get lopsided. Method choice is an input; the De-Vig calculator shows the spread on your own prices.

One line, three answers

Proportional: 58.9% / 41.1%⋅Power: 59.3% / 40.7%⋅Shin: 59.2% / 40.8%\text{Proportional: } 58.9\%\,/\,41.1\% \quad\cdot\quad \text{Power: } 59.3\%\,/\,40.7\% \quad\cdot\quad \text{Shin: } 59.2\%\,/\,40.8\%
All three sum to 100%; they differ only in how the 2.3% margin splits.

Which is also the answer to “so which one do I use?”. Nobody can tell you which is right, because nobody ever sees the true probability, which is why the site prints all three. But the size of the disagreement is not random. On a roughly even market the three land within a couple of tenths of a point of each other and the choice barely matters. On a heavy favorite against a long underdog they spread out, because that is exactly where favorite–longshot bias lives. The further the line is from even money, the more the method you pick is doing real work.

One posted price isn’t the last word. Pooling de-vigged numbers across books gives a sturdier benchmark: building a sharp-consensus fair line.

Less vig, better price: why exchanges beat the soft books

De-vig across venues and one fact jumps out: a fat-margin book prices both sides worse than the truth; a thin-vig exchange sits almost on the fair line. The numbers (a typical book near 4.77% against an exchange’s 0.21%, the season-long drag, the per-contract fee, why books limit winners and exchanges don’t) get their own lesson: Books vs. Exchanges.

Where the methods come from

None of this is ours to invent. The reading:

  1. Griffith, R. M. (1949). “Odds Adjustments by American Horse-Race Bettors.” American Journal of Psychology 62(2), 290–294. The first measurement of the favorite–longshot bias.
  2. Thaler, R. H. & Ziemba, W. T. (1988). “Anomalies: Parimutuel Betting Markets: Racetracks and Lotteries.” Journal of Economic Perspectives 2(2), 161–174. The bias surveyed across markets.
  3. Shin, H. S. (1991). “Optimal Betting Odds Against Insider Traders.” The Economic Journal 101(408), 1179–1185. The insider-trading model of the bookmaker’s margin.
  4. Štrumbelj, E. (2014). “On determining probability forecasts from betting odds.” International Journal of Forecasting 30(4), 934–943. Shin-style de-vigging forecasts better than proportional normalization.
  5. Shin, H. S. (1992). “Prices of State Contingent Claims with Insider Traders, and the Favourite-Longshot Bias.” The Economic Journal 102(411), 426–435. Why insider protection shades longshots hardest.
  6. Shin, H. S. (1993). “Measuring the Incidence of Insider Trading in a Market for State-Contingent Claims.” The Economic Journal 103(420), 1141–1153. Fitting the insider fraction z from posted prices.

Every formula here lives on the Formula Sheet for quick reference.

Check your understanding

Frequently asked questions

What does it mean to de-vig odds?

It removes the sportsbook's built-in margin (the vig) from a posted price so the odds reflect fair probabilities summing to 100%.

How do you calculate fair odds from a betting line?

Convert each side to implied probability, add them to find the overround, rescale to sum to 1.0. Proportional divides each side by the overround; power and Shin also correct for favorite-longshot bias.

Proportional vs. Shin de-vig: what's the difference?

Proportional spreads the margin evenly. Shin models part of it as informed money, shifting more onto the longshot. On skewed lines Shin and power are usually more accurate.

Does de-vigging guarantee a winning bet?

No. De-vigging is a calculation that estimates a fair probability from a price. It is an analytical input, not a prediction of any outcome.