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<title>Four ways to remove a bookmaker margin, and why the choice matters</title>
<meta name="description" content="Proportional, additive, power and Shin de-vigging explained on one worked three-way market, with the probabilities each method produces and when the difference matters.">
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<h1>Four ways to remove a bookmaker margin</h1>
<p class="lead">A market's quoted prices imply probabilities that add to more than 100%. To use them as forecasts you have to decide how to give the excess back. Four common methods give four different answers for the same market.</p>

<h2>The worked market</h2>
<p>A three-way result market quoted at 2.10 / 3.40 / 3.50. The implied probabilities are 47.62%, 29.41% and 28.57%, which add to 105.60%: a margin of 5.60% to remove.</p>

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<thead><tr><th>Method</th><th>Rule</th><th>Home</th><th>Draw</th><th>Away</th></tr></thead>
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<tr><td>Raw implied</td><td>1 / price</td><td>47.62%</td><td>29.41%</td><td>28.57%</td></tr>
<tr><td>Proportional</td><td>divide each by the total</td><td>45.09%</td><td>27.85%</td><td>27.06%</td></tr>
<tr><td>Additive</td><td>subtract margin ÷ n from each</td><td>45.75%</td><td>27.54%</td><td>26.70%</td></tr>
<tr><td>Power</td><td>raise each to the k that makes them sum to 1 (k = 1.054)</td><td>45.75%</td><td>27.54%</td><td>26.71%</td></tr>
<tr><td>Shin</td><td>solve for an insider share z, then adjust (z = 0.028)</td><td>45.58%</td><td>27.62%</td><td>26.80%</td></tr>
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<p>Proportional keeps the raw shape; power and additive take more from the two outsiders and give it to the favourite, and Shin sits between. On this fairly even market the methods differ by under a point. On a lopsided market (1.10 against 7.00) they can differ by two to three points on the outsider, which is a large fraction of a 12% chance.</p>

<h2>What each method assumes</h2>
<p><strong>Proportional</strong> assumes the margin is spread in proportion to each outcome's probability. It is the simplest and the usual default. <strong>Additive</strong> assumes an equal slice per outcome, which can push a tiny outsider below zero on extreme markets. <strong>Power</strong> (one exponent applied to all implied probabilities) and <strong>Shin</strong> (a model in which a share <em>z</em> of money comes from informed bettors) both assume the margin sits more heavily on outsiders, which is the pattern that measurements of settled markets tend to support.</p>

<h2>Why it matters</h2>
<p>Štrumbelj (2014) compared these allocations on large samples and found the choice affects forecast accuracy, mostly in the tails. The <a href="https://betbetter.world/studies/market-calibration">market calibration study</a> uses the proportional method as a conservative baseline on 36,476 observations and finds exactly the tail signature the Shin and power views predict: outsiders slightly overperform their proportional margin-free price. Its open data set lets anyone re-run the band table under another method.</p>
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<p><strong>Practical rule.</strong> For near-even markets use proportional and move on. For markets with an outcome under about 20%, compare proportional with Shin or power before trusting the outsider's probability, and read the margin size first: the <a href="https://betbetter.world/studies/margin-index">daily bookmaker margin index</a> shows that three-way markets carried about 7.6% in July to September 2026 against about 4.8% for two-way match results, so there is more to allocate. The <a href="https://betbetter.world/studies/bookmaker-margins">method notes</a> describe how those margins are measured.</p>
<p style="margin:0">Margin-free model probabilities, already allocated, are published through a <a href="https://betbetter.world/api/">free API with no key</a>.</p>
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<footer>Compiled by Bet Better Pty Ltd, Melbourne. Worked figures are computed from the stated prices; Shin and power values are rounded solutions. Educational reference, not betting advice.</footer>
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