De-vigging odds: how to remove bookmaker margin
Bookmaker odds contain margin, so implied probabilities sum to more than 100%. De-vigging removes it. The three standard methods — multiplicative, power and Shin — disagree most on longshots, which is exactly where value bets live.
De-vigging converts bookmaker odds into probability estimates by removing the built-in margin. Take the implied probability of each outcome (1 ÷ decimal odds), observe that they sum to more than 1, and redistribute the surplus. How you redistribute it is the entire question — the three standard methods produce materially different numbers on the same market.
What is the vig and where does it hide?
Convert every price in a market to implied probability and add them up. In a fair market the sum is exactly 1. In a real one it is more, and the excess — the overround — is the bookmaker's margin.
implied probability = 1 / decimal odds overround = Σ implied − 1Worked example on a three-way football market priced 2.10 / 3.40 / 3.90:
| Outcome | Odds | Implied probability |
|---|---|---|
| Home | 2.10 | 47.62% |
| Draw | 3.40 | 29.41% |
| Away | 3.90 | 25.64% |
| Sum | 102.67% → overround 2.67% |
Those 2.67 percentage points are not a forecast. They are the price of the service. To compare a model against the market you first have to take them out — and the arithmetic of taking them out is not neutral.
Method 1: multiplicative (proportional)
Divide every implied probability by the overround. It is one line of code, which is why almost every public calculator uses it.
p_fair(i) = p_implied(i) / Σ p_impliedIts flaw is structural. It assumes margin is applied as a constant multiple across outcomes. Bookmakers do not price that way: margin is loaded disproportionately onto longshots, so proportional removal leaves too much margin in the outsider's price and takes too much out of the favourite's.
Method 2: power
Raise each implied probability to a power k and solve for the k that makes them sum to 1.
p_fair(i) = p_implied(i)^k, with k chosen so that Σ p_fair = 1Because exponentiation compresses small numbers more than large ones, the power method removes proportionally more margin from longshots than the multiplicative method does. It has no closed-form solution — k is found numerically — but it is a better structural fit to how books actually price.
Method 3: Shin
Shin's model (Hyun Song Shin, 1993) starts from an economic assumption rather than a curve-fit: some proportion z of the money wagered comes from bettors with inside information, and the bookmaker widens prices to protect against them. Solving the model yields fair probabilities and an estimate of z.
Because the protection is concentrated where insiders do the most damage — the longshots — Shin removes the most margin there. Among the three, it is generally the most defensible on football and horse racing, and it is the method that best explains the favourite–longshot bias observed in real markets.
How much do the three disagree?
Enough to matter. On the 2.10 / 3.40 / 3.90 market above, the three methods produce fair probabilities that differ by a few tenths of a point. Widen the market to a genuine longshot and the gap grows:
| Market | Multiplicative on the outsider | Shin on the outsider | Gap |
|---|---|---|---|
| Balanced three-way (2.10 / 3.40 / 3.90) | ≈ 24.97% | ≈ 24.7% | ≈ 0.3 pp |
| Lopsided three-way (1.25 / 6.00 / 12.00) | ≈ 8.0% | ≈ 7.4% | ≈ 0.6 pp |
| Deep longshot (1.08 / 11.0 / 26.0) | ≈ 3.7% | ≈ 3.2% | ≈ 0.5 pp |
Why a half-point matters. At odds of 12.00 a fair probability of 8.0% implies an edge of −4%; 7.4% implies −11%. The choice of de-vig method flips the verdict on the bet without a single input changing. Most published edges in this category are smaller than the disagreement between methods used to compute them.
There are 0-vig calculators online… most are flawed but will get you close enough.
"Close enough" is doing heavy lifting in that sentence. Close enough for a market priced 1.90 / 1.90; not close enough for anything with a longshot in it.
The mistake that is worse than choosing the wrong method
De-vigging assumes you have the complete set of mutually exclusive outcomes. If you de-vig two prices out of a three-way market, or de-vig a market where the group is incomplete, the result is not a fair probability — it is arithmetic performed on the wrong denominator.
The trap that catches people most often is double chance. The three double-chance outcomes (1X, X2, 12) are not mutually exclusive — each covers two of the three base outcomes, so their true probabilities sum to 2, not 1. Normalising them to 1 halves every estimate and manufactures an edge out of nothing.
We hit exactly this in our own engine on live prices. Normalising double chance to 1 produced an apparent 41-percentage-point edge — a number so large it was obviously a bug rather than a discovery. The fix was to give every market family an explicit normalisation target: 1 for exclusive groups, 2 for double chance. It is now a regression test, because the failure was silent and plausible-looking.
Which de-vigging method does CONSENSUS use?
Proportional de-vig is the configured baseline, with power and Shin selectable, and the method used is recorded alongside every priced market so a stored result can always be traced to the arithmetic that produced it. Where a group is incomplete, the market is stored but flagged, and it is never used as a de-vig basis. Where the group is double chance, the normalisation target is 2.
Check any of this against our record
Every signal CONSENSUS publishes carries the bookmaker odds fixed before the event starts and the settled result afterwards — including the drawdowns and the losing runs. The running total is on the front page and every entry is in the log.