# Devig

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Canonical: https://novigapi.com/learn/devig

To devig is to strip the bookmaker margin out of a set of odds so the implied probabilities sum to exactly 100%, leaving an estimate of the fair price.

```
multiplicative: p_i = q_i / sum(q); additive: p_i = q_i - (sum(q) - 1) / n
```

Devigging turns a sportsbook's prices into fair probabilities. A book's implied probabilities add up to more than 100% because of the vig. Devigging rescales them so they add up to exactly 100%, which gives you the market's best guess of each outcome's true chance. That fair probability is the yardstick for expected value, closing line value and every other edge calculation.

## How it works

First convert each price to an implied probability. Then choose a method to remove the excess. The multiplicative method, the most common, divides each implied probability by their sum, so each side keeps its share of the total. The additive method subtracts an equal slice of the excess from every outcome. The power and Shin methods push more of the margin onto long shots, which matches how many books actually price favorites and underdogs.

- Multiplicative: p_i = q_i / sum(q). Simple, and the default in most tools.
- Additive: p_i = q_i - (sum(q) - 1) / n. Treats every outcome as carrying the same absolute margin.
- Power: find k so that sum(q_i ^ k) = 1. Shrinks long shots more than favorites.
- Shin: models a share of informed money and assigns more margin to long shots. Best on markets with many outcomes.

## Worked example

Take a moneyline of -150 and +130. The implied probabilities are 60.000% and 43.478%, a sum of 103.478%, so the overround is 3.478%.

Devigging -150 / +130

| Method | Favorite fair | Underdog fair | Favorite fair odds | Underdog fair odds |
| --- | --- | --- | --- | --- |
| Raw implied | 60.000% | 43.478% | -150 | +130 |
| Multiplicative | 57.983% | 42.017% | -138.0 | +138.0 |
| Additive | 58.261% | 41.739% | -139.6 | +139.6 |


The methods agree to within about 0.3 percentage points on a two-way market with a small margin. The gap grows on long-shot-heavy markets and on futures with dozens of outcomes. The [no-vig calculator](https://novigapi.com/no-vig-calculator) runs all four methods side by side.

## On Novig

On Novig there is no house margin to remove, because every price comes from traders on an exchange. What you devig instead is the bid-ask spread. With a best Yes bid of 55% and a best No bid of 42%, the implied Yes ask is 1 - 0.42 = 58%, and the fair Yes price is the midpoint, 56.5%. Our `/fair-price` endpoint returns that midpoint for every two-sided Novig market, and the [Novig odds converter](https://novigapi.com/novig-odds-converter) turns it into American and decimal odds.

## When it matters

Devigging matters most when you compare a soft book's price to a sharp reference. If you devig a sharp market and the fair probability is higher than the implied probability of a price you can get elsewhere, that price is positive expected value. Devigging a soft, high-margin market gives a noisy fair price, so always devig the sharpest source you have.

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