How to devig odds: four methods, worked

To devig odds, convert the price of every outcome in a market to its implied probability, add them up, and scale them back so they total 100%. The simplest way, the multiplicative method, divides each implied probability by the total: −150 / +130 becomes 57.98% / 42.02%, or fair odds of −138 / +138. Other methods take a larger share of the margin from the longshot. On a close market they all agree within a point; on a lopsided one they can disagree by enough to turn a +EV bet into a losing one.

Why devig at all

A book's prices always add to more than 100% implied, because the excess is its margin (see hold and vig). To use a price as an estimate of the true chance, which is what every expected value calculation needs, you have to remove that margin. The fair odds guide shows the easy case, −110 both ways, where every method gives 50%. This guide is about everything else.

Multiplicative (proportional)

Divide each implied probability by the total. Every outcome gives up the same proportion of its probability, so the favourite, having more, gives up more points. It is the default almost everywhere because it is simple and works well on balanced two-way markets.

Additive

Subtract the same number of points from every outcome: the margin divided by the number of outcomes. The longshot, with less probability to begin with, loses a bigger share of it. On extreme longshots additive can push a probability to zero or below, which is why implementations fall back to another method there.

Power

Raise every implied probability to the same power k, choosing k so the results add to exactly 100%. Because a small number shrinks proportionally more than a large one when raised to a power above 1, this takes more of the margin from longshots. It never produces a negative probability.

Shin

Shin's method comes from Hyun Song Shin's early-1990s models, in which a share of the money in a market, called z, comes from bettors who know the outcome, and the bookmaker widens prices to protect itself from them. It solves for the z that makes the fair probabilities add to 100%. Like power, it shifts margin onto the longshot; in the examples below it lands between multiplicative and power.

When the methods disagree

They part company on lopsided markets, and the disagreement is all about the longshot. Studies of betting markets have long found that longshots tend to be overpriced relative to how often they win, the favourite–longshot bias, which suggests books load more of their margin onto them. Multiplicative ignores that and leaves the longshot too much probability. That flatters exactly the long prices that look most tempting.

Worst case: the conservative choice

A worst-case devig is not a new formula. You run the methods and use whichever gives the lowest fair probability for the side you want to bet. If the bet is still positive under that one, it is positive under all of them. On the +750 example it fails; on a close −150 / +130 market it costs you almost nothing. It is a sensible default for longshots and for any market where you are not sure how the book spreads its margin.

The method matters less than the source

Devigging a wide, slow recreational book's price perfectly still gives you a poor estimate. The input should be a market that is hard to beat: a sharp sportsbook, an exchange, or a blend of several. A soft price devigged four ways is four versions of the wrong number.

Doing it without the arithmetic

The Hold Calculator takes the prices for every outcome of a market, two-way or more, and returns the hold and the fair price behind each one, with a selector for Multiplicative, Additive, Power and Shin so you can see how far they disagree. The Positive EV board uses multiplicative by default and shows which method built each fair price. The calculators walkthrough covers both.