To remove the bookmaker margin from a market, turn every price into an implied chance with 1 / decimal odds, add the chances up, then shrink them until they total exactly 100%. One divided by each shrunken chance is that outcome's fair price, also called its no vig price, and the whole process is called devigging, or de-vigging, after "vig", a US word for the bookmaker's cut.
How you shrink the chances is the choice that matters. The four common methods are multiplicative, additive, power and Shin, and each assumes a different spread of the margin across the market: they agree on close two-way markets and part ways on long shots. How betting odds work explains implied probability and why a market totals more than 100% in the first place.
How to devig odds, step by step
- Take every outcome in one bookmaker's market at one moment: both teams and the draw in a soccer match, every runner still in a race.
- Turn each price into an implied chance: implied chance = 1 / decimal odds.
- Add the chances. The total is the market percentage, and everything above 100% is margin.
- Shrink the chances so they total 100%, using one of the four methods below.
- Turn each fair chance back into a price: fair odds = 1 / fair chance.
- Check that the fair chances add up to 100%. If they do not, an outcome is missing or a price is mistyped.
Only step 4 changes with the method. The fair odds calculator runs any of the four, one at a time, on a market of two to 30 prices.
Multiplicative: the same share off every chance
The multiplicative method, also called the proportional method, divides every implied chance by the market total. Written as a price, it multiplies every price by the total:
fair chance = implied chance / market total
fair odds = decimal odds x market total
It assumes the bookmaker shortened every price by the same proportion, so a favourite and an outsider give up the same share of their implied chance. It is the simplest of the four and a sound default where prices sit close together. Its weak point is the long shot: if the bookmaker put more of its margin on the outsiders, multiplicative leaves their fair prices too short.
Additive, power and Shin: more off the long shots
The other three methods all take a bigger share of the margin off long shots than off favourites, each for a different reason.
Additive: the same points off every chance
fair chance = implied chance - (market total - 1) / number of outcomes
In a three-way market totalling 107.70%, each outcome loses 7.70 / 3 = 2.57 points of chance. Those 2.57 points are 4% of a 64.52% favourite but 14% of an 18.18% outsider, so the outsider's fair price lengthens the most. In a big field the same cut can be larger than a long shot's whole implied chance, which leaves it a fair chance below zero.
Power: small chances shrink fastest
fair chance = implied chance raised to the power k
Here k is the one number above 1 that makes the fair chances add up to 100%, found by trial or with a spreadsheet's goal seek. Any chance below 100% shrinks when raised to a power above 1, and a 5% chance loses a far bigger share than a 60% one, so long shots carry more of the margin. The power method entry has more on outsiders.
Shin: the margin as protection against better-informed money
The Shin method, named after the economist Hyun Song Shin, assumes a share z of the money in a market comes from punters who know more than the bookmaker, and that the margin is the bookmaker's protection against them. In that model the protection weighs most on long shots, so the method moves margin onto them:
fair chance = (square root of (z x z + 4 x (1 - z) x implied chance x implied chance / market total) - z) / (2 x (1 - z))
z is found by trial, like k. On a two-way market this formula gives exactly the same fair prices as the additive method; with three or more outcomes the two part ways. The Shin method entry explains the model in plain terms.
One three-way market de-vigged four ways
Example: a soccer match with three outcomes at one bookmaker: the home side at $1.55, the draw at $4.00 and the away side at $5.50. Illustrative prices, not a real match.
The implied chances are 1 / 1.55 = 64.52%, 1 / 4.00 = 25.00% and 1 / 5.50 = 18.18%, a total of 107.70%. Each method shrinks them to 100%, with k about 1.0863 for power and z about 0.039 for Shin:
| Outcome | Price | Implied | Multiplicative | Additive | Power | Shin |
|---|---|---|---|---|---|---|
| Home | $1.55 | 64.52% | 59.90%, $1.67 | 61.95%, $1.61 | 62.12%, $1.61 | 61.42%, $1.63 |
| Draw | $4.00 | 25.00% | 23.21%, $4.31 | 22.43%, $4.46 | 22.18%, $4.51 | 22.63%, $4.42 |
| Away | $5.50 | 18.18% | 16.88%, $5.92 | 15.62%, $6.40 | 15.70%, $6.37 | 15.96%, $6.27 |
| Total | 107.70% | 100% | 100% | 100% | 100% |
The working for the home side:
- Multiplicative: 0.64516 / 1.07698 = 0.5990, a fair price of 1.55 x 1.07698 = $1.67.
- Additive: 0.64516 - 0.07698 / 3 = 0.6195, and 1 / 0.6195 = $1.61.
- Power: 0.64516 raised to the power 1.0863 = 0.6212, and 1 / 0.6212 = $1.61.
- Shin: 0.64516 x 0.64516 / 1.07698 = 0.38648; 4 x 0.961 x 0.38648 + 0.039 x 0.039 = 1.48715, whose square root is 1.21949; (1.21949 - 0.039) / (2 x 0.961) = 0.6142, and 1 / 0.6142 = $1.63.
All four put the home side between $1.61 and $1.67. They disagree on how much margin sat on the draw and the away side:
| Share of the implied chance taken off | Home | Draw | Away |
|---|---|---|---|
| Multiplicative | 7% | 7% | 7% |
| Additive | 4% | 10% | 14% |
| Power | 4% | 11% | 14% |
| Shin | 5% | 9% | 12% |
Multiplicative spreads the margin evenly. The other three load it onto the longer prices, and Shin sits between multiplicative and the other two on every outcome. The away side's fair price runs from $5.92 to $6.40, a gap of 6.40 / 5.92 - 1 = 8.1%.
That gap decides bets. Say another bookmaker offers the away side at $6.20:
| Method | Fair away price | Edge on $6.20 |
|---|---|---|
| Multiplicative | $5.92 | 6.20 / 5.92 - 1 = +4.7% |
| Shin | $6.27 | 6.20 / 6.27 - 1 = -1.1% |
| Power | $6.37 | 6.20 / 6.37 - 1 = -2.7% |
| Additive | $6.40 | 6.20 / 6.4038 - 1 = -3.2% |
The same price is a value bet under one assumption and a negative-edge bet under the other three.
Risk: Betting involves risk. An edge measured against a de-vigged price is only as sound as the method behind it, and a bet with a positive edge can still lose, and often does. See responsible gambling for limits and support.
Which method suits two-way markets and which suits racing
The shape of a market matters more than how many outcomes it has. With illustrative prices:
| Market | Prices | Total | Multiplicative | Additive and Shin | Power |
|---|---|---|---|---|---|
| Close two-way | $1.88 and $1.94 | 104.74% | $1.97 and $2.03 | $1.97 and $2.03 | $1.97 and $2.03 |
| Lopsided two-way | $1.25 and $4.00 | 105.00% | $1.31 and $4.20 | $1.29 and $4.44 | $1.28 and $4.59 |
On the close market all four agree to the cent, so the quickest, multiplicative, is enough. On the lopsided one the outsider's fair price runs from $4.20 to $4.59, a range of 4.595 / 4.20 - 1 = 9.4%, although the market has only two outcomes. Working for the outsider: 4.00 x 1.05 = $4.20; 0.25 - 0.05 / 2 = 0.225, and 1 / 0.225 = $4.44; 0.25 raised to the power 1.10 = 0.21764, and 1 / 0.21764 = $4.59.
A race field is where the choice matters most: more outcomes, a bigger margin and prices that run out to long shots. An illustrative 10-runner market at one bookmaker adds up to 118.29%, with k about 1.0968 and z about 0.022 (the table uses their unrounded values):
| Price | Implied | Multiplicative | Additive | Power | Shin |
|---|---|---|---|---|---|
| $2.60 | 38.46% | $3.08 | $2.73 | $2.85 | $2.89 |
| $4.50 | 22.22% | $5.32 | $4.90 | $5.21 | $5.11 |
| $6.00 | 16.67% | $7.10 | $6.74 | $7.14 | $6.94 |
| $8.00 | 12.50% | $9.46 | $9.37 | $9.78 | $9.48 |
| $11.00 | 9.09% | $13.01 | $13.77 | $13.87 | $13.51 |
| $15.00 | 6.67% | $17.74 | $20.67 | $19.50 | $19.32 |
| $21.00 | 4.76% | $24.84 | $34.10 | $28.20 | $29.04 |
| $26.00 | 3.85% | $30.76 | $49.59 | $35.64 | $38.11 |
| $41.00 | 2.44% | $48.50 | $164.05 | $58.74 | $71.09 |
| $61.00 | 1.64% | $72.16 | Below zero | $90.82 | $129.95 |
The favourite's fair price runs from $2.73 to $3.08, and the $61.00 outsider's from $72.16 to $129.95. Additive takes 18.29 / 10 = 1.83 points off every runner, more than the outsider's whole 1.64%, so it cannot price this field at all. The other nine additive chances add up to 100.19%, and the fair odds calculator refuses the market.
The decision rule that follows:
- Close two-way markets: the methods agree to about a cent, so use multiplicative.
- Markets with a short favourite, two-way or three-way: run multiplicative and at least one other method, and treat any gap on the price you want as the size of your doubt.
- Race fields: where the favourite-longshot bias holds and outsiders pay back less per dollar than favourites, multiplicative leaves the long shots too short; Shin and power both move margin onto them. Avoid additive in big fields, and check any method against an exchange market with plenty of money matched.
Why a de-vigged price is an estimate, not a probability
Three things stand between a de-vigged price and the true chance:
- The method is an assumption. None of the four can see how the bookmaker spread its margin, and their guesses differ most where the margin is biggest.
- The input is one opinion. A bookmaker's prices carry its own errors, its shading of popular selections and any lag behind other markets, as how bookmakers set odds explains, and de-vigging removes only the margin.
- Prices move. A fair price describes, at best, the moment its prices were read.
To test a method, record its fair chances for every market you de-vig, with the date, and compare them with results by price band once you have hundreds of markets. If outcomes a method rated at about 10% won about one time in 10, it suited those markets. Fair odds covers the other places a fair price can come from, the exchange included.
Mistakes that skew a de-vig
| Mistake | What it does | The fix |
|---|---|---|
| Leaving an outcome out | Without the draw, the soccer market totals 64.52% + 18.18% = 82.70%, and multiplicative prices the home side at $1.28 | Include every outcome, the draw and every runner |
| Leaving a scratched runner in | Its chance inflates the total, so every fair price comes out too long | Remove it and de-vig the runners still in the race |
| Mixing bookmakers' prices | A market of best prices can add up to under 100%, and no method can make that fair | De-vig one bookmaker at a time |
| Scaling a place market to 100% | A three-place market's fair total is 300%, not 100% | Scale it to the number of places paid |
| Trusting one method on a long shot | The away side was $5.92 or $6.40 depending on the method | Run two methods and treat the gap as uncertainty |
How B337's +EV screener de-vigs a market
B337's +EV screener de-vigs prices across sports markets. The margin comes out of prices across the market, exchanges and global market references included, and the results are combined into one fair price for each selection. Bookmaker prices above that fair price are listed by edge. Its adjustable de-vig lets you choose which prices count and how much margin each one gives up, and it recalculates every edge to match. Terminal View adds your own de-vig settings for the fair price on the Terminal.
To see the screener's rows you need Terminal Pro, Full Automation or a Screeners plan arranged with the team; Terminal View does not include them. A free account sees each screener's live count and the +EV screener's best edge, with the rows locked. Placing any bet stays with you, in accounts you hold.
For free and confidential support call 1800 858 858 or visit gamblinghelponline.org.au.
Risk: Betting involves risk. A price above a de-vigged fair price is a bet on an estimate: it can lose, and bookmakers can limit your stakes or void bets under their terms. See responsible gambling for limits and support.