A bookmaker's prices are not probabilities. They are probabilities plus a margin, spread across the outcomes in a way the bookmaker does not publish. Devigging is the process of removing that margin to recover a fair probability for each outcome, and because the spreading is unknown, there are several ways to do it. This guide measures the margin, walks through five methods on one market so the differences are visible in the numbers, then compares them on three markets of different shapes. Every figure below comes from the devig calculator, which runs all five methods on any market you paste in.
Overround and margin
Add up the implied probabilities of every outcome in a market. The result exceeds 100%, and the excess is the overround.
S = Σ 1 / odds_i overround = S − 1 margin (share of turnover) = 1 − 1 / S
A soccer 1X2 at 2.20 / 3.40 / 3.60
Implied: 45.45% + 29.41% + 27.78% = 102.64%. Overround: 2.64%. Margin on turnover: 1 − 1/1.0264 = 2.58%. This is a low-margin market, typical of a sharp book on a major league; recreational books run 5–8% on the same fixture.
Two figures are quoted because they answer different questions. The overround says how far the probabilities overshoot 100%. The margin says what fraction of all money staked the bookmaker keeps if the money is spread in proportion to the prices. They are close for small margins and diverge for large ones: a 40% overround is a 28.6% margin.
For a symmetric two-way market such as -110 / -110, the overround is 4.76% and the margin 4.55%, and every method below gives 50% / 50%. The methods only disagree when the outcomes are not equally likely.
Method 1: multiplicative (normalisation)
Divide each implied probability by the sum.
p_i = implied_i / S 2.20 / 3.40 / 3.60 → 44.28% / 28.65% / 27.06% fair odds → 2.26 / 3.49 / 3.70
Simple, always sums to 100%, and the default almost everywhere. Its assumption is that the bookmaker applied the same proportional margin to every outcome. Bookmakers do not: they shade longshots more, because the public overbets them and because a small absolute change in a longshot's price is a large proportional one. Multiplicative devigging therefore overstates the fair probability of longshots and understates favourites — the favourite-longshot bias, in reverse.
Method 2: additive
Subtract an equal share of the overround from every outcome.
p_i = implied_i − (S − 1) / n 2.20 / 3.40 / 3.60 → 44.57% / 28.53% / 26.90% fair odds → 2.24 /
3.51 / 3.72
This takes the same number of percentage points from each outcome, which is a heavier proportional cut on the longshots and a lighter one on the favourite. On this market it moves the favourite up by 0.3 points and the outsider down by 0.2 relative to multiplicative. The weakness is at the extremes: with a large overround and a very long outsider, the subtraction can push the outsider's probability below zero, at which point the method has nothing sensible to say. The calculator clamps such values to a small minimum and flags them.
Method 3: power
Raise every implied probability to the same exponent k, chosen so that the results sum to one.
p_i = implied_i ^ k, with k such that Σ p_i = 1 2.20 / 3.40 / 3.60 → k = 1.025 → 44.57% / 28.53% /
26.90%
k is above one whenever there is an overround (raising a number below one to a power above one makes it smaller). Because the effect of the exponent grows as the base shrinks, the method takes proportionally more from longshots than from favourites — matching how bookmakers actually price. On this low-margin market the power method lands almost exactly on the additive result; on a heavy-favourite market it sits between additive and multiplicative. The exponent is found numerically (the calculator bisects to one part in ten billion).
Method 4: Shin
Shin's method comes from a model in which a fraction z of bettors are insiders who know the result. A bookmaker facing that fraction has to shade every price, and shades longshots most, because an insider betting a longshot is more expensive to the book. Solving the model for z given the observed prices gives both the fair probabilities and an estimate of the insider share.
p_i(z) = [ √(z² + 4(1 − z) implied_i² / S) − z ] / (2(1 − z)), with z such that Σ p_i = 1 2.20 /
3.40 / 3.60 → z = 0.0132 → 44.50% / 28.56% / 26.94%
The result here is between multiplicative and power, with a small z of 1.3%. Shin's z is a useful diagnostic on its own: large z means a market where the book expects informed money, typically low-liquidity or in-play markets. z is undefined when there is no overround (the calculator reports 0 and says so).
Method 5: worst case
Not a model but a rule: for each outcome, take the lowest fair probability any of the other methods produced.
p_i = min over methods of p_i 2.20 / 3.40 / 3.60 → 44.28% / 28.53% / 26.90%
The result does not sum to 100% and is not meant to. It is the most conservative probability a bettor can assume for each outcome, and a price that shows value against the worst case shows value under every model. Use it when the method choice is uncertain and the bet is marginal.
Side by side
| Method | Home | Draw | Away | Note |
|---|---|---|---|---|
| Implied | 45.45% | 29.41% | 27.78% | sums to 102.64% |
| Multiplicative | 44.28% | 28.65% | 27.06% | even proportional cut |
| Additive | 44.57% | 28.53% | 26.90% | even absolute cut |
| Power (k = 1.025) | 44.57% | 28.53% | 26.90% | longshots cut more |
| Shin (z = 0.013) | 44.50% | 28.56% | 26.94% | insider model |
| Worst case | 44.28% | 28.53% | 26.90% | per-outcome minimum |
On a 2.6% overround the methods differ by three tenths of a point at most. That is the normal case for sharp two- and three-way markets. Run the same comparison on a golf outright with an 18% overround — 8.00 / 10.00 / 12.00 / 15.00 / 18.00 / 22.00 / 25.00 and a 1.50 field — and the spread opens up: the field is 56.4% under multiplicative, 60.8% under Shin (z = 2.8%), 63.2% under power (k = 1.13) and 64.4% under additive; the 25.00 shot is 3.4% under multiplicative and 1.7% under additive. The multiway guide goes through that market in detail.
Three markets, five methods
The same five methods on three markets of different shapes: a symmetric two-way market at -110 / -110, the soccer 1X2 above, and an eight-runner outright at 8.00 / 10.00 / 12.00 / 15.00 / 18.00 / 22.00 / 25.00 with the field at 1.50 (overround 18.3%). For the outright the table shows the two ends of the market: the 1.50 field and the 25.00 shot.
| Method | -110 / -110 | Soccer home / draw / away | Outright field / 25.00 shot |
|---|---|---|---|
| Implied | 52.38% | 45.45% / 29.41% / 27.78% | 66.67% / 4.00% |
| Multiplicative | 50.00% | 44.28% / 28.65% / 27.06% | 56.37% / 3.38% |
| Additive | 50.00% | 44.57% / 28.53% / 26.90% | 64.38% / 1.72% |
| Power | 50.00% | 44.57% / 28.53% / 26.90% | 63.16% / 2.60% |
| Shin | 50.00% | 44.50% / 28.56% / 26.94% | 60.76% / 2.56% |
| Worst case | 50.00% | 44.28% / 28.53% / 26.90% | 56.37% / 1.72% |
Three things stand out. On the symmetric market the method is irrelevant. On the low-margin three-way market the methods differ by three tenths of a point, less than the noise in most probability estimates. On the outright the field's fair probability ranges over eight points and the longshot's is halved between multiplicative and additive: the method is the estimate. The larger the overround and the longer the longest price, the more the choice matters, and the less any method should be trusted on the longshots.
What the literature says
The Shin method comes from Hyun Song Shin's early-1990s papers modelling a bookmaker who faces a share of insider bettors, which is why its parameter is read as an insider fraction. The power method appears in the academic comparisons of overround adjustments from the late 2000s onward, where it and Shin's method tend to calibrate better than plain normalisation on markets with uneven prices, and the additive method is the simplest alternative to normalisation in that same literature. Practitioner write-ups from sharp bookmakers reach the same conclusion from the closing-line direction: the margin is applied unevenly, with more of it on the longshots, so a method that removes more from longshots recovers the fair line better. None of that makes any single method correct; it makes the multiplicative method the one with the weakest case outside symmetric markets.
Which method to use
- Symmetric two-way markets (spreads, totals, even matches): any; they agree.
- Two-way with a clear favourite: power or Shin; multiplicative will overrate the underdog.
- Three-way soccer: power or Shin; the draw and the away side carry most of the margin.
- Outrights and large fields: power or Shin, and treat the longshot numbers with suspicion under every method.
- When it matters and you are unsure: worst case.
Whatever the method, the input should be a sharp market. Devigging a recreational bookmaker's prices recovers that bookmaker's opinion, margin removed; devigging a sharp bookmaker's or an exchange's prices recovers something closer to the truth.
Using the result
The devigged probability feeds two calculations. Compared with a price you are offered elsewhere, it gives expected value: p × offered − 1. Divided by the offered price's net odds, it gives the Kelly stake. The devig calculator shows all five methods for any market and, in its price-check panel, the edge and Kelly fraction under each for a price you type in. A price that is value under the worst case is the one to take.
Margin by market type
Overrounds are not uniform across a bookmaker's offering. Main markets on major events — moneylines, spreads and totals in the biggest leagues — carry the smallest margins, typically 2–5%, because they attract the most informed money and the most price comparison. Derivative markets (player props, correct scores, first goalscorer) carry 8–20%, and outrights on large fields 20–40% or more. Live markets add a few points to whatever the pre-match margin was. The pattern matters for devigging in two ways. A high-margin market gives the devig methods more room to disagree, so method choice matters more there. And a high-margin market is a worse source of fair probabilities, whatever the method: devigging a 25% overround recovers the bookmaker's shaded opinion, not the truth. Take fair probabilities from the lowest-margin market available for the same event, which is usually a sharp bookmaker's main market or an exchange, and use the devig of a high-margin market only to price the high-margin market itself.
Checking a devig against the closing line
The way to find out which method suits a market is to test it against outcomes. Devig a set of pre-match prices with each method, record the fair probabilities, and compare them with the results over a few hundred events: the method whose probabilities are best calibrated (outcomes at 30% happen about 30% of the time) is the one to use for that market type. A quicker proxy is the closing line at a sharp book, which is close to fair; the method whose devigged probabilities from an early price come nearest to the devigged closing probabilities is the one that models the market's shading correctly. In published tests of this kind the power and Shin methods tend to beat multiplicative on markets with uneven prices and tie with it on even ones, which is the pattern the worked examples above show in miniature.
Two-way markets from one price
Sometimes only one side of a market is visible. If the market is symmetric (a spread or total), the other side is usually the same price and the devig is trivial: both sides are 50%. If it is not symmetric, no method can recover the fair probability from one price alone; the margin's split between the sides is unknowable without the other price. Find the full market before devigging.
Run the numbers yourself
Paste any market into the devig calculator to see all five methods and, in the price-check panel, the edge and Kelly stake for a price you are offered under each of them. The EV & Kelly calculator turns a fair probability into a stake, and the multiway arbitrage and devigging guide applies these methods to large fields.