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Margin remover
Type a market's prices and strip the bookmaker's margin out four ways: multiplicative, additive, power and Shin. Fractional, decimal or American odds.
Enter one price for every outcome in the market, all from the same firm. The calculator shows the booksum and margin, then the fair probability for each outcome under each method, with the fair decimal price and the nearest price you would see on a coupon. It runs in your browser and stores nothing.
Worked example
The three-way market from chapter 8 of the book, computed by the same maths the calculator uses.
| Outcome | Price | Implied | Multiplicative | Additive | Power | Shin |
|---|---|---|---|---|---|---|
| Home | 4/6 | 60.00% | 57.42% (1.74) | 58.50% (1.71) | 58.55% (1.71) | 58.22% (1.72) |
| Draw | 14/5 | 26.32% | 25.18% (3.97) | 24.82% (4.03) | 24.69% (4.05) | 24.91% (4.01) |
| Away | 9/2 | 18.18% | 17.40% (5.75) | 16.68% (5.99) | 16.76% (5.97) | 16.87% (5.93) |
The four methods
Write each outcome's implied probability as π (one divided by the decimal price) and the booksum as β, the sum of all of them.
Multiplicative
p = π ÷ β. Every outcome gives up the same proportion of itself. Simple and widely used, and it leaves the most probability on long prices, which is exactly where bookmakers tend to load their margin.
Additive, and the odds-proportional shortcut
p = π − (β − 1) ÷ n, for n outcomes. Every outcome gives up the same number of points. In decimal-odds form it is the margin-proportional-to-odds shortcut, fair odds = nO ÷ (n − MO). It fails on long prices in big-margin markets, where the slice is larger than the outcome.
Power
p = πk, with k chosen so the probabilities sum to one. Because small numbers shrink faster when raised to a power above one, long prices give up more.
Shin
Hyun Song Shin modelled a market in which a share z of the money comes from insiders. The fair probabilities are p = (√(z² + 4π²(1 − z)/β) − z) / (2 − 2z), with z solved so they sum to one. On two-outcome markets it gives exactly the additive answer.
The full worked versions are on the chapter 8 workings page, including a nineteen-outcome correct-score audit. To build your own fair prices from expected goals and set them against a bookmaker's, use the Poisson match predictor, which links back here.
Questions
Frequently asked questions
Which de-vig method is the most accurate?
There is no universal winner. Published comparisons have found power at least as good as Shin on tennis and racing data, while a single-season Premier League test found the methods almost inseparable, with multiplicative narrowly ahead. On two-way markets with small margins the four answers barely differ; on correct-score and outright markets they can differ a lot, so look at all four.
Why does the additive column sometimes say below zero?
Additive takes an equal slice of the overround off every outcome. If a price is long and the margin is large, the slice is bigger than the outcome's whole implied probability, and the result goes negative. The test is (booksum minus 1) divided by the outcome's implied probability: if that is bigger than the number of outcomes, ignore additive for that market.
Does the calculator store anything?
No. It runs entirely in your browser, sets no cookies and saves nothing. The prices you type are written into the page address after the # so you can bookmark or share a market, and that part of an address is never sent to any server.
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