Divide each implied probability by the sum of the market: the total returns to 100% and each outcome receives a normalised probability. On a 1X2 market priced at 2.10 / 3.40 / 3.60, the estimated margin-free odds are 2.20 / 3.56 / 3.77. That result depends on the spreading method — other methods give other figures on the same odds.
What is a margin-free odd?
A margin-free odd is the odd that would remain if the excess built into the prices of a market were redistributed across its outcomes. It serves as a basis for comparison: two operators do not apply the same margin, so their raw odds are not directly comparable.
The vocabulary hesitates between several terms — margin-free odd, no-vig odd, de-vigged price. They all describe the same operation: bringing the sum of the market's implied probabilities back to exactly 100%.
What is the calculation method?
The method used here is proportional normalisation: each implied probability is divided by the sum of the probabilities in the market.
normalised probability = implied probability ÷ sum of the implied probabilities
margin-free odd = 1 ÷ normalised probability
This method spreads the excess in proportion to each probability: an outcome weighing twice as much as another absorbs twice as much margin. It is the simplest choice to explain and to check — and it is the one applied by this site's calculators, including the bookmaker margin calculator.
A full 1X2 example
Let us take a three-outcome market priced at 2.10 / 3.40 / 3.60, the same odds as those used on the page devoted to the margin.
| Outcome | Displayed odd | Implied probability | Normalised probability | Margin-free odd |
|---|---|---|---|---|
| Home win | 2.10 | 47.62% | 45.43% | 2.20 |
| Draw | 3.40 | 29.41% | 28.06% | 3.56 |
| Away win | 3.60 | 27.78% | 26.50% | 3.77 |
| Total | — | 104.81% | 100.00% | — |
The book percentage is 104.81%, an overround of 4.81 points. After normalisation, each probability loses the same proportion of its value and the total comes back to 100%. Margin-free odds are systematically higher than the displayed odds: that is expected, since removing the margin amounts to removing what made them less generous.
Key point. A margin-free odd is not an odd available anywhere. No operator offers 2.20 on this outcome: it is a benchmark for comparison, not an offer.
What are the limits of the proportional method?
Proportional normalisation assumes that the margin is spread evenly across the outcomes. That assumption is convenient, not demonstrated.
The literature on betting markets documents a recurring bias, known as the favourite-longshot bias: big odds tend to be proportionally more loaded than short ones. If that bias is present on a given market, the proportional method underestimates the favourite's probability and overestimates the longshot's — all the more so as the gap between the odds is wide.
Four families of alternative methods exist, none of them commanding consensus:
- the power method, which raises the probabilities to a calibrated exponent rather than dividing them by a common factor;
- the logarithmic method, which spreads the excess on a logarithmic scale;
- the Shin model, which reads part of the margin as protection against better-informed punters;
- empirical corrections for the favourite-longshot bias, calibrated on historical results.
On a tight market, these methods give very similar results. On an unbalanced market — a favourite at 1.15 against a longshot at 15.00 — the gap becomes significant. Choosing a method is therefore a modelling decision, to be owned explicitly, not an implementation detail.
How OddScore removes the margin
OddScore removes the margin of each bookmaker before any comparison between operators, and documents the method used rather than presenting it as an objective result. The principle is the one described here: bringing every market back to 100% so that the gap observed between two operators reflects their estimate, and not their commercial policy.
What the platform produces remains an estimate of margin-free prices, recalculated at each snapshot. It is there to compare and to track an evolution — not to point to a bet to play.
Analyse a complete market with the calculator →
Margin-free probability, true probability: the distinction
A margin-free probability remains a reading of prices. A true probability would be a property of the event. The two do not live in the same place.
A margin-free probability is deduced from observed odds: it inherits everything the market has understood — and everything it has missed. If every operator underrates a team, the margin-free probability will underrate it in exactly the same way, without any margin removal correcting anything at all.
The true probability, for its part, is observable by nobody. A match is played only once: its result does not reveal the distribution it came from. That is why this page talks about an estimate, and never about a probability that would be the right one: the expression would have no verifiable referent.
To obtain a point of comparison that does not come from market prices, you need an estimate produced elsewhere: that is the subject of fair odds, and the prerequisite for any value bet calculation.
The three levels. Margin removal shows how a market splits up once brought back to 100%; it allows you to estimate the difference of appraisal between two operators; it does not allow you to conclude that an outcome is more likely than a price indicates.
Dig into the market
Odds movements are only part of the story. Here are the next topics to read.
Odds and probability: the complete guide
The full journey, from the displayed odd to the closing line.
Read the guideBookmaker margin: definition and calculation
Book percentage, overround and theoretical margin: what the excess measures.
Understand the marginImplied probability: converting it from an odd
The step that comes before: going from an odd to a percentage.
Convert an oddFair odds: from an estimated probability to an odd
The other way of getting a reference odd, starting from an estimate.
Calculate a fair oddFrequently asked questions
What is a margin-free odd?
It is the odd obtained after redistributing a market's overround across its outcomes. It corresponds to the inverse of the normalised probability of an outcome.
How do you remove the margin from a market?
The most common method divides each implied probability by the sum of all the probabilities in the market. The total obtained is then exactly 100%.
Does a margin-free odd give the true probability of the outcome?
No. It provides a normalised estimate based on the available prices. The result depends on the observed odds and on the spreading method used.
What are the other margin-removal methods?
The main alternatives are the power method, the logarithmic method, the Shin model and corrections for the favourite-longshot bias. They spread the excess differently, especially on big longshots.
Why does comparing two bookmakers require removing the margin?
Because two operators do not apply the same margin. Without removing it first, the gap observed between their odds mixes a difference of estimate with a difference of commercial policy.
What is the difference between a margin-free probability and a true probability?
A margin-free probability is deduced from market prices, after the excess has been redistributed. The true probability of a sporting event is observable by nobody and cannot be deduced from any price.
Sources & methodology
This page draws on the usual methods for normalising probabilities derived from odds, on the economic literature devoted to the overround and to the favourite-longshot bias, and on the odds-analysis methodology developed by OddScore.
- Convert each decimal odd in the market into an implied probability (1 ÷ odd).
- Divide each implied probability by the sum of the market: this is proportional normalisation, the method used here and implemented in the site's calculators.
- Invert each normalised probability to obtain the estimated margin-free odd.
- Describe the result as an estimate, never as a true probability: other spreading methods produce other values on the same odds.