How the bookmaker margin is calculated
Decimal odds are the inverse of the probability the bookmaker prices in. Add up the probabilities of every outcome in a market and you get more than 100%: the excess is the margin.
margin = 1/o1 + 1/oX + 1/o2 − 1
To remove the margin, the calculator divides each outcome's probability by their sum (the proportional method). The fair odds are 1 divided by the margin-free probability: the price there would be if the bookmaker took no commission.
Worked example
Odds of 2.10 / 3.40 / 3.60 add up to 104.8% probability, so the bookmaker margin is 4.8%. The home win probability without the margin is 45.4%, and its fair odds are 2.20.
What it is useful for
- Comparing the margin of different bookmakers on the same match: the lower it is, the closer the odds are to fair.
- Turning odds into a probability without the margin distorting it, and comparing it with your own estimate or a model's prediction.
- Spotting value bet candidates: if your probability is higher than the margin-free market probability, the odds may be too generous.
Frequently asked questions
How do you calculate the bookmaker margin?
Add up the inverse of the odds for every outcome in the market and subtract one. For 1X2 that is 1/o1 + 1/oX + 1/o2 − 1.
How do you convert odds into probability?
Divide one by the odds: 1/2.10 ≈ 47.6%. That probability includes the margin; to remove it, divide the outcome's probability by the sum of the probabilities of all outcomes.
What counts as a low margin?
The lower the margin, the better the line for the bettor. Compare the margin of different bookmakers on the same market: it is usually lower on popular matches than in minor leagues and exotic markets.
What are fair odds?
Odds without the bookmaker margin: one divided by the margin-free probability of the outcome. They show what the price would be without the bookmaker's commission.
More on the blog
The xG.Football model calculates result, totals and both-teams-to-score probabilities for the day's matches — handy to compare with the odds.
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