How to remove the vig from football odds: three methods compared
By FootInsights · Published · 6 min read
Learning how to remove the vig from football odds is the step between reading a price and knowing what it means. A bookmaker’s odds are not a probability estimate — they are a probability estimate with a margin welded on top. Strip the margin off and you get the market’s actual opinion, which is the only version worth comparing your own numbers against. The arithmetic takes one line. The part almost every guide skips is that the one-line version is measurably wrong for football, because a 1X2 book has three outcomes rather than two, and the margin is not spread evenly across them.
What the vig looks like in a three-way football book
Take a hypothetical fixture priced at 1.57 home, 4.10 draw, 5.75 away. Convert each to an implied probability by taking the reciprocal:
| Selection | Odds | Implied probability |
|---|---|---|
| Home | 1.57 | 63.7% |
| Draw | 4.10 | 24.4% |
| Away | 5.75 | 17.4% |
| Total | 105.5% |
The three outcomes are exhaustive and mutually exclusive — exactly one of them happens — so a fair book would sum to 100%. This one sums to 105.5%. That surplus is the overround, and it is the bookmaker’s margin expressed as probability. Bet all three selections in proportion and you are guaranteed to get back about 94.8% of your stake.
The 5.5% figure is typical of a mainstream 1X2 market. It is also the whole problem: those three quoted probabilities cannot all be the bookmaker’s honest estimate, because honest estimates sum to one. Somewhere inside 105.5% is a 100% opinion, and devigging is the attempt to recover it.
How to remove the vig from football odds: the proportional method
The standard approach — variously called multiplicative, proportional or normalisation — divides every implied probability by the total:
- Home: 63.7% ÷ 105.5% = 60.4%
- Draw: 24.4% ÷ 105.5% = 23.1%
- Away: 17.4% ÷ 105.5% = 16.5%
Those sum to 100% by construction. Invert them for fair prices: 1.66, 4.32, 6.06. That is the no-vig book.
The assumption buried in that division is easy to miss because it looks like no assumption at all. Dividing everything by the same constant means the margin was applied to everything by the same constant — that the bookmaker took a proportional cut of each selection. It is the simplest possible story about where the 5.5% came from, and it is the reason the method is everywhere: it needs no parameters, no iteration and no view about bettor behaviour.
Why proportional devigging distorts a 1X2 market
Bookmakers do not load margin evenly. They load more of it onto longshots, because that is where the money is least price-sensitive — the well-documented favourite–longshot bias. A 17.4% away side in a football book typically carries a larger share of the overround than the 63.7% favourite does.
Proportional devigging is blind to this. It hands the longshot back the same relative share it hands the favourite, which systematically leaves the longshot’s fair probability too high — and therefore its fair price too short. If you are shopping for value on outsiders, the naive method quietly makes them look better than the market thinks they are.
Two alternatives correct for it, both by fitting a single parameter instead of assuming one.
The power method raises each implied probability to a power k, choosing k so the results sum to one. Because raising a number below 1 to a power above 1 shrinks small values proportionally more than large ones, this takes a bigger relative bite out of the longshot than out of the favourite — the correction the proportional method lacks. Here k ≈ 1.061.
The odds-ratio method assumes the bookmaker applied a constant multiplier to the odds ratio p/(1−p) rather than to the probability, and solves for that multiplier. It is a gentler version of the same correction. Here the multiplier is ≈ 1.104.
| Selection | Proportional | Odds ratio | Power |
|---|---|---|---|
| Home | 60.4% | 61.4% | 62.0% |
| Draw | 23.1% | 22.6% | 22.4% |
| Away | 16.5% | 16.0% | 15.6% |
| Fair away | 6.06 | 6.24 | 6.40 |
Same book, three defensible answers, and the disagreement is concentrated exactly where the theory says it should be: the favourite moves by 1.6 percentage points, the away price by more than 5%.
A fourth option, Shin’s method, derives the margin from an assumed share of insider money rather than fitting a curve. On this book it lands at 15.8% for the away side, between the odds-ratio and power answers — reassuring, since three unrelated corrections agreeing on a direction is better evidence than any one of them.
The same bet, two verdicts
Suppose you find the away side at 6.20 somewhere else. Against the proportional fair probability of 16.5%, that bet returns 6.20 × 0.165 − 1 = +2.2% expected value. Against the power method’s 15.6%, the same bet at the same price returns −3.0%.
One method says take it, the other says pass, and nothing about the bet changed. On a market where realistic edges live in the low single digits, a devigging choice that moves the answer by five points is not a technicality — it is larger than the edge you are hunting for. Anyone quoting an expected value without saying how they removed the vig has left out half the calculation.
The practical guidance that falls out of this: proportional is acceptable on near-even two-way markets, where all three methods converge and the differences vanish into rounding. On three-way 1X2 books, and on anything with a long price in it, use the power or odds-ratio method. Whichever you pick, pick one and keep it — comparing a number devigged one way against a number devigged another way is not a comparison at all.
What the no-vig numbers are actually for
Devigging is not a betting strategy. It is the measuring instrument that makes other things measurable.
The first use is honest model evaluation. If your model says 20% and the book says 17.4%, you have found nothing until you know whether the market’s real opinion was 16.5% or 15.6% — the gap you are claiming may be entirely margin. Removing the vig is what turns “my number differs from the price” into a testable statement.
The second is closing line value. CLV is the sharpest available proxy for whether a betting process has an edge, and it means beating the no-vig closing price. Beating the raw closing price is trivial and proves nothing, because the raw price includes a margin nobody has to pay on both sides at once.
The third is calibration. Scoring probability forecasts against outcomes — the discipline behind our public track record — only works when the benchmark you are scoring against is a genuine probability distribution. A book summing to 105.5% is not one, and feeding it into a Brier or log-loss calculation produces a number that is not interpretable.
Where devigging still misleads
Two honest limitations are worth carrying.
First, the recovered probabilities are still the bookmaker’s opinion, not the truth. Devigging removes a known distortion; it does not confer accuracy. A soft book with a badly-priced draw yields a clean 100% set of badly-priced numbers.
Second, every method here is an inference from three numbers about a process you cannot observe. None of them is provably correct — they are competing models of margin application, and the right one differs by bookmaker, by league and by market. The defensible position is to know which one you used, state it, and be aware that the away price in the table above could reasonably be 6.06 or 6.40 depending on a choice you made before the match kicked off.