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Why you need to devig
A book's prices imply probabilities that add up to more than 100%. To get a fair probability you have to remove that extra, the vig, and there's no single correct way to do it. Each method makes a different assumption about where the book put its margin. The no-vig calculator shows every method side by side for any prices you enter.
The methods
Start from each outcome's implied probability qᵢ = 1 ÷ dᵢ, with S = Σ qᵢ.
| Method | Formula | Assumption |
|---|---|---|
| Multiplicative | pᵢ = qᵢ ÷ S | Vig in proportion to each price. |
| Additive | pᵢ = qᵢ − (S − 1) ÷ n | The same vig on every side. |
| Power | pᵢ = qᵢ^k, k solves Σ qᵢ^k = 1 | More vig on longshots. |
| Shin | Solves for a share z of insider money | The book defends against informed bettors. Equals additive on two-way markets. |
| Probit | pᵢ = Φ(Φ⁻¹(qᵢ) − c), c solves Σ pᵢ = 1 | The same shift on the normal-quantile scale. |
Two more options use these: worst case takes whichever of multiplicative, additive and power gives the lowest probability for the side you're betting (the most conservative fair), and best case takes the highest (for comparison only).
Worked example: a lopsided market
A −300 favourite against a +240 underdog. Implied: 75.00% + 29.41% = 104.41%, a 4.41% hold.
| Method | Favourite | Underdog | Fair underdog odds |
|---|---|---|---|
| Multiplicative | 71.83% | 28.17% | +255 |
| Additive | 72.79% | 27.21% | +268 |
| Power | 73.31% | 26.69% | +275 |
| Shin | 72.79% | 27.21% | +268 |
| Probit | 72.84% | 27.16% | +268 |
Multiplicative: 0.2941 ÷ 1.0441 = 28.17%
Additive: 0.2941 − 0.0441 ÷ 2 = 27.21%
Underdog spread across methods: 28.17% − 26.69% = 1.48 points
Imagine a book offering the underdog at +265. Under multiplicative (fair +255) it looks −EV; under power (fair +275) it looks +EV. On lopsided markets, the method can decide the answer. Worst case would use power here, 26.69%, for the underdog.
All seven methods on a bigger favourite
A −400 favourite against a +300 underdog: implied 80.00% + 25.00% = 105.00%, a 5.00% hold.
| Method | Favourite | Underdog | Fair underdog odds | EV of the dog at +330 |
|---|---|---|---|---|
| Multiplicative | 76.19% | 23.81% | +320 | +2.38% |
| Additive | 77.50% | 22.50% | +344 | −3.25% |
| Power | 78.24% | 21.76% | +359 | −6.41% |
| Shin | 77.50% | 22.50% | +344 | −3.25% |
| Probit | 77.58% | 22.42% | +346 | −3.59% |
| Worst case (dog) | 78.24% | 21.76% | +359 | −6.41% |
| Best case (dog) | 76.19% | 23.81% | +320 | +2.38% |
A +330 underdog elsewhere is +2.38% EV under multiplicative and −3.59% under probit. That six-point swing is the whole reason the method matters on lopsided markets. Further out it gets bigger: at +500 / −800 (a 5.56% hold), the longshot's fair probability is 15.79% multiplicative (+533), 13.89% additive and Shin (+620), 13.70% probit (+630) and 12.69% power (+688).
All seven methods on a 3-way soccer market
Home +150, Draw +240, Away +190: implied 40.00% + 29.41% + 34.48% = 103.89%, a 3.89% hold. Worst and best case are shown for the Draw.
| Method | Home | Draw | Away |
|---|---|---|---|
| Multiplicative | 38.50% | 28.31% | 33.19% |
| Additive | 38.70% | 28.11% | 33.18% |
| Power | 38.69% | 28.13% | 33.18% |
| Shin | 38.65% | 28.16% | 33.19% |
| Probit | 38.63% | 28.19% | 33.18% |
| Worst case (draw) | 38.70% | 28.11% | 33.18% |
| Best case (draw) | 38.50% | 28.31% | 33.19% |
On three outcomes, Shin and additive finally differ (38.65% vs 38.70% for Home). The spread is small here because no outcome is a big favourite; a 3-way market with a heavy favourite spreads the methods much further apart, mostly on the draw and the longshot.
One detail: additive subtracts the same amount from every side, which can push a deep longshot below zero. When that happens the engine floors it at a tiny positive value and renormalises.
When it barely matters
Near 50/50, the methods agree. At −115 / −105 (a 4.71% hold), the favourite's fair probability is 51.08% multiplicative, 51.13% additive and Shin, 51.14% probit and 51.16% power: within 0.08 points. A typical prop at −120 / −102 gives the Over 51.93% multiplicative and 52.08% power, with additive, Shin and probit all at 52.03%: a 0.15-point spread. Most player props sit close to even money, so the method rarely changes a prop's answer. It matters most for big favourites and longshots, and for markets with three or more outcomes.
A soccer 1X2 at +150 / +240 / +190 (3.89% hold) gives the home side 38.50% multiplicative and 38.63% to 38.70% under the others: a small but real difference on the favourite.
How probit works
Probit converts each implied probability into a z-score on the normal curve, Φ⁻¹(qᵢ), subtracts the same constant c from every side, and converts back. The engine solves for the c that makes the fair probabilities add up to exactly 1, by bisection to a tolerance of 10⁻¹². Because the normal curve is flat in the tails, the same shift takes less probability from the favourite and more from the longshot than multiplicative does. On the −400 / +300 market above, probit gives the underdog 22.42%: between multiplicative (23.81%) and power (21.76%), and close to additive (22.50%).
Our default and why
We default to probit. Multiplicative is simple but systematically overstates longshots and understates favourites on lopsided markets. Published studies of closing odds find additive-family and probit methods well calibrated and close to one another; probit is our pick among them. You can change the method in the Devig method section of the Fair value & filters sheet or on the Account page.
Exchanges are handled differently whatever method you choose. An exchange's two asks are a spread, not a vig, so we take the mid of its net asks after fees.
Pitfalls
- Method shopping. Picking the method that makes a bet look best is just bias. Decide once, or check the edge survives worst case.
- Garbage in. No method fixes a stale price or a mislabelled side.
- One book is a small sample. Blending several devigged books is more reliable than any one book under any method.
In build
This tool is in build on the same tested engine. The app shows what is coming and what already runs.