How to Remove the Bookmaker Margin: Overround, Fair Odds and the Shin Method

The question

"The bookie has the away side at 7.00. What would the fair price be without their cut?"

Knowing how to remove the bookmaker margin lets you turn any bookmaker's odds into fair probabilities. You need that whenever you compare a bookmaker price with your model, or with the price on Betfair.

The idea in one sentence

A book's implied probabilities add up to more than 100%, and removing the margin means shrinking them back to 100% using a rule for where the margin was added.

The picture

In Lesson 2.1 you turned each price into a percentage. For a complete market the true percentages must add up to exactly 100%, because one outcome has to happen. A bookmaker's never do. The amount over 100% is the overround, and it's where the bookmaker's profit comes from.

On Betfair it's different. Nobody sets the prices, so the best back prices typically add up to just over 100% and the best lay prices to just under. That small gap is competing offers from other users, not a margin. You can treat Betfair prices as close to fair already.

The hard part is how to take the margin off. There are three common rules:

Proportional. Shrink every percentage by the same factor. Simple, but it leaves outsiders too short.
Power. Raise every percentage to a power just above 1. Small percentages shrink more, so outsiders get longer fair odds.
Shin. Assumes a small share of the money comes from well-informed bettors, and that the bookmaker guards against it by loading the longshots. The result usually sits between the other two.

The last two reflect the favourite-longshot bias: bookmakers put more of their margin on outsiders.

Try it · Margin remover

RunnerOddsCompare

Compare is optional: a price you can actually get (for example the Betfair back price), checked against each method's fair odds.

Book total

104.76%

Overround

4.76%

Power k

1.0554

Shin z

0.0241

Home @ 1.50raw 66.67%

Proportional	63.64%	1.571
Power	65.19%	1.534
Shin	64.71%	1.545

Draw @ 4.20raw 23.81%

Proportional	22.73%	4.400
Power	21.99%	4.548
Shin	22.34%	4.475

Away @ 7.00raw 14.29%

Proportional	13.64%	7.333
Power	12.83%	7.797
Shin	12.95%	7.724

The book is 4.76% over the odds. On the longest price, Away, fair odds run from 7.33 (proportional) to 7.80 (power), with Shin at 7.72. Proportional leaves outsiders too short.

On Betfair, back books sit just above 100% and lay books just below. That gap is competing offers, not a margin.

Worked Betfair example

A bookmaker prices a match Home 1.50, Draw 4.20, Away 7.00. On Betfair the same match shows best back prices of 1.55, 4.4, 7.6 and best lay prices of 1.56, 4.5, 7.8. Your model has the away side at 13.0%. (Illustrative prices.)

Bookmaker implied probabilities. 1 ÷ 1.50 = 66.67%, 1 ÷ 4.20 = 23.81%, 1 ÷ 7.00 = 14.29%.
Overround. 66.67% + 23.81% + 14.29% = 104.76%. The book is 4.76% over.
Proportional. Divide each by 1.0476: 63.64%, 22.73%, 13.64%. Fair odds 1.571, 4.40, 7.33.
Power. Solving for the power that makes the book add to 100% gives k = 1.0554. Fair chances 65.19%, 21.99%, 12.83%. Fair odds 1.534, 4.548, 7.797.
Shin. Solving for the informed-money share gives z = 0.0241 (about 2.4%). Fair chances 64.71%, 22.34%, 12.95%. Fair odds 1.545, 4.475, 7.724.
Check Betfair. The back book is 64.52% + 22.73% + 13.16% = 100.40%, and the lay book is 99.15%. The best back on the away side, 7.6, sits right among the bookmaker's fair odds by power and Shin.
Is 7.6 on Betfair value? Under proportional, the fair away price is 7.33, so 7.6 looks generous. Under power it's 7.80, so 7.6 is slightly short. Your model's 13.0% means fair odds of 7.69, so on your own numbers 7.6 isn't value either.

Verdict: the three methods disagree by about 1.5 points on the favourite and nearly half a point of odds on the away side. If you'd used proportional as your benchmark, you'd have backed the away side thinking it was value.

Two-way markets barely care

Over/Under 2.5 at a bookmaker: Over 1.83, Under 1.95, a book of 105.93%. Fair odds come out at 1.938 and 2.066 (proportional), 1.933 and 2.072 (power), 1.935 and 2.070 (Shin). With two close runners, the method hardly matters. It matters most when favourites and outsiders sit in the same book.

The formula

Overround

B = \sum_i \frac{1}{O_i}, \qquad \text{Overround} = B - 1

O_i is the decimal price of outcome i.
B is the book total.

In plain English: add up every outcome's implied probability. Whatever is above 100% is the margin.

Proportional

p_i = \frac{q_i}{B}

q_i is the raw implied probability, 1 ÷ O_i.
p_i is the fair probability.

In plain English: divide every percentage by the book total. Every selection gives up the same share.

Power

p_i = q_i^{\,k}, \qquad \text{with } k \text{ chosen so that } \sum_i p_i = 1

k is a power slightly above 1, found by trial and error (the tool does this for you).

In plain English: raising a small number to a power above 1 shrinks it proportionally more than a big one, so outsiders lose more of their inflated percentage.

Shin

p_i = \frac{\sqrt{z^2 + 4(1-z)\,q_i^2 / B} - z}{2(1-z)}, \qquad \text{with } z \text{ chosen so that } \sum_i p_i = 1

z is Shin's estimate of the share of money from well-informed bettors, found by trial and error.
B is the book total, as above.

In plain English: Shin works out how much insider money would explain the margin, then removes it the way a cautious bookmaker would have added it: more on the outsiders.

Fair odds

O_i^{\text{fair}} = \frac{1}{p_i}

In plain English: once you have fair probabilities, one divided by each gives the fair price.

Try it

Enter 1.50, 4.20 and 7.00, and check the overround reads 4.76% and the Shin fair odds read 1.545, 4.475 and 7.724. Then try a lopsided book like 1.20, 6.50 and 15.0 and watch how far apart the methods pull on the outsider.

Common mistakes

Comparing your model with raw bookmaker odds. A 4.76% overround hides several points of probability. Always compare with fair odds.
Using proportional by default on three-way markets. It leaves the outsider too short, which makes outsiders look like value when they aren't.
Stripping a margin from Betfair prices as if it were a bookmaker's. The small gap between back and lay books isn't a fee. For a single fair estimate, use the price the two sides meet at, or the last traded price.
Removing the margin from an incomplete book. Every outcome must be priced at the same moment. Leave one out and the maths breaks.
Treating fair odds as the truth. They're the market's view without the margin. Whether that view is right is a separate question (Lesson 2.5).

Why beating the price is the whole game: why good models still lose money.

Overround and removing the margin