Four ways to remove a bookmaker margin

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.

The worked market

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.

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.

What each method assumes

Proportional assumes the margin is spread in proportion to each outcome's probability. It is the simplest and the usual default. Additive assumes an equal slice per outcome, which can push a tiny outsider below zero on extreme markets. Power (one exponent applied to all implied probabilities) and Shin (a model in which a share z 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.

Why it matters

Štrumbelj (2014) compared these allocations on large samples and found the choice affects forecast accuracy, mostly in the tails. The market calibration study 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.