A decimal odd converts into an implied probability with 1 ÷ odd. The sum of these probabilities exceeds 100%: the excess is the margin. Removing it produces margin-free probabilities and margin-free odds — estimates, not truths. Comparing an odd with a probability estimated elsewhere gives a theoretical value; comparing the odd you took with the final price gives the closing line value.
The essentials in a few seconds
An odd is a price. Converting it into a probability, removing the margin it contains, then comparing it with an independent estimate or with the final price: that is the whole journey. Each step answers a different question and none of them says who is going to win.
Seven concepts, in the order in which they are used:
- the odd: the price displayed for an outcome;
- the implied probability:
1 ÷ odd, what that price assumes; - the margin: the excess that pushes the sum of the probabilities above 100%;
- the margin-free probability: the same reading once the excess has been redistributed;
- the fair odd: the odd matching a probability estimated elsewhere;
- the theoretical value: the gap between that estimate and the price offered;
- the closing line value: the gap between the price taken and the market's last price.
Key point. These seven concepts describe a price and how it evolves. None of them turns an odd into a tip, and none of them makes a bet "safe".
What is an odd?
An odd is the price at which an operator agrees to exchange a risk. It shows how much a winning stake returns, stake included in the decimal format: an odd of 2.20 returns €22 on €10 staked, that is €12 of net profit.
This price is not a neutral reading of the sport. It aggregates three distinct things: the bookmaker's estimate, the margin it wants to keep, and the adjustments linked to exposure — that is, to how the stakes already received are distributed. Two operators can display two different prices for the same event without either of them being "wrong": they have neither the same estimate, nor the same exposure, nor the same commercial policy. Odds movements are precisely the story of those adjustments.
| Concept | What it measures |
|---|---|
| Odd | The price displayed for an outcome |
| Implied probability | What that price assumes, margin included |
| Book percentage | The sum of the implied probabilities of a market |
| Overround | The part of the book percentage above 100% |
| Margin-free probability | The implied probability after the overround has been redistributed |
| Fair odd | The odd matching an estimated probability |
| Closing line value | The gap between the odd taken and the closing line |
How do you convert an odd into a probability?
The implied probability of a decimal odd is calculated with (1 ÷ odd) × 100. An odd of 2.00 corresponds to 50%, an odd of 1.80 to 55.56%, an odd of 2.20 to 45.45%.
This conversion is mechanical: it needs no sporting data, only the odd. That is both its strength and its limit. It faithfully translates what the price assumes, but it corrects nothing — neither the margin, nor any estimation error made by the operator.
The way the odd is written changes nothing about that probability. An odd of 2.50 is written 3/2 in fractional format and +150 in American format: all three notations describe the same price, therefore the same 40%. The three notations are covered in detail on the odds formats page.
| Decimal | Fractional | American | Implied probability |
|---|---|---|---|
| 1.50 | 1/2 | −200 | 66.67% |
| 1.80 | 4/5 | −125 | 55.56% |
| 2.00 | 1/1 | +100 | 50.00% |
| 2.20 | 6/5 | +120 | 45.45% |
| 2.50 | 3/2 | +150 | 40.00% |
| 3.40 | 12/5 | +240 | 29.41% |
| 5.00 | 4/1 | +400 | 20.00% |
For the full formula, a table of examples and a calculator, the dedicated page is implied probability.
Why does the total exceed 100%?
Because odds include a margin. Add up the implied probabilities of every outcome in a market: the total, called the book percentage, is almost always above 100%. The excess is the overround.
On a two-outcome market priced at 1.80 and 2.00:
1 ÷ 1.80 = 55.56%;1 ÷ 2.00 = 50.00%;- total = 105.56%, an overround of 5.56 points.
That 5.56 is not a profit. It describes the excess contained in the prices at a given moment. What the operator actually keeps depends on the stakes received, how they are spread across the outcomes, the results and its costs. The detailed calculation, the distinction between overround and theoretical margin and the reasons why the margin varies from one market to another are covered on the page devoted to bookmaker margin.
How do you remove the margin from a market?
The most common method is to divide each implied probability by the sum of the market. The total then comes back to exactly 100%, and each outcome receives what is called a margin-free probability.
On a 1X2 market priced at 2.10 / 3.40 / 3.60, the implied probabilities are 47.62%, 29.41% and 27.78%, a total of 104.81%. After proportional normalisation: 45.43%, 28.06% and 26.50%. The corresponding margin-free odds are 2.20, 3.56 and 3.77.
This method spreads the excess in proportion to each probability. Other approaches exist — power, logarithmic, Shin, favourite-longshot bias corrections — and produce different results on the same odds, particularly on big longshots. A margin-free probability is therefore never "the" probability of the event: it is an estimate, dependent on the observed prices and on the method used. The full method and its limits are detailed on margin-free odds.
What is a fair odd?
A fair odd is the odd that would exactly match an estimated probability: fair odd = 1 ÷ estimated probability. A probability estimated at 50% gives a fair odd of 2.00.
The difference with a margin-free odd matters and is often blurred. A margin-free odd is derived from one operator's prices, once its overround has been removed. A fair odd is derived from a probability that comes from somewhere else: a model, a consensus of several sources, your own analysis. The two can coincide, but they do not answer the same question. The fair odds page covers the conversion in all three formats and the case where a fair odd is simply wrong.
What is theoretical value?
A theoretical value appears when the estimated probability of an outcome exceeds the probability needed to justify the odd offered. With an odd of 2.20 and a probability estimated at 50%, the theoretical gap is 2.20 × 0.50 − 1 = +10%.
This calculation requires two ingredients, never just one: an odd, and an estimate that is independent of that odd. A theoretical value cannot be derived from the bookmaker's odd alone — the calculation would amount to comparing a price with itself. And since the result depends entirely on the quality of the estimate, a positive gap may be nothing more than the reflection of an over-optimistic estimate. The value bet page details where that estimate comes from, why it can be wrong and what the calculation does not prove.
What is closing line value?
Closing line value compares the price obtained with the last price displayed before the start of the match. An odd taken at 2.20 for a close at 2.00 gives 2.20 ÷ 2.00 − 1 = +10%.
The interest of the closing line lies in its status as the last available price: it is the price that incorporates the most information. That does not make it an exact price — a closing market is still a market, with its margin, its liquidity and its errors. A positive CLV therefore describes a price taken above the final price, nothing more. It guarantees neither a profit on the bet concerned, nor profitability over time. The closing line value page covers the two calculation methods and how to choose the closing line to use.
What OddScore does with these concepts
OddScore applies this journey continuously, across several bookmakers and across successive snapshots. The platform converts odds into probabilities, removes each operator's margin before any comparison, then tracks how these prices evolve until kickoff.
The point of automating it is not to do the maths better — the formulas above fit in three lines — but to repeat it: across dozens of operators, thousands of markets and at regular intervals, which no manual reading allows. What the platform produces remains a reading of prices: it does not provide tips and does not point to a bet to play.
Where to start
If odds themselves are still new territory, take a step back first: sports betting for beginners covers the market, the stake and the settlement, which the calculations below all assume you already know.
Five steps, in this order, to work through the cluster without getting lost:
- Convert a price. Start with implied probability: it is the one indispensable calculation, everything else hangs off it.
- Measure the margin. Move on to bookmaker margin to understand why the total exceeds 100% and what the overround really measures.
- Remove the margin. Continue with margin-free odds to compare two operators on a common basis.
- Estimate a fair price. Carry on with fair odds, then value bet if you have an independent estimate.
- Check the price obtained. Finish with closing line value, which compares your price with the market's last price.
Two tools support this journey, with no account and no sign-up: the odds converter to switch from one format to another, and the bookmaker margin calculator to analyse a complete market.
For the practical use of these probabilities in a match analysis, see odds and predictions.
The three levels, worth keeping in mind on every page. These calculations show what a price assumes; they allow you to estimate a gap between two prices or between a price and an estimate; they do not allow you to conclude that an outcome is going to happen.
Dig into the market
Odds movements are only part of the story. Here are the next topics to read.
Implied probability: converting it from an odd
The formula, a table of examples and a calculator to go from an odd to its implied probability.
Convert an oddMargin-free odds: the proportional method
How to redistribute the overround across the outcomes, and what the result does not tell you.
Remove the marginFair odds: from an estimated probability to an odd
Going from an estimated probability to a fair odd, in all three formats.
Calculate a fair oddBookmaker margin: definition and calculation
Book percentage, overround, theoretical margin: the measures of the excess built into prices.
Understand the marginFrequently asked questions
Is an odd a prediction?
No. An odd is a price offered by an operator. It reflects a commercial estimate of the market, adjusted for the stakes received and the risk accepted, not an announcement of the result.
How do you turn an odd into a probability?
With a decimal odd, you divide 1 by the odd and then multiply by 100. An odd of 2.00 corresponds to 50%, an odd of 2.20 to 45.45%.
Why does the sum of the probabilities exceed 100%?
Because odds include a margin. The total of the implied probabilities, called the book percentage, sits above 100%; the excess part is the overround.
What is a margin-free odd?
It is the odd obtained after redistributing the margin across the outcomes, most often through proportional normalisation. The result remains an estimate that depends on the method used.
What is the difference between a margin-free odd and a fair odd?
A margin-free odd is derived from the prices displayed by one operator. A fair odd is derived from an estimated probability, which may come from a model, a consensus or your own analysis.
Does a positive theoretical value guarantee a profit?
No. It indicates a gap between an odd and an estimated probability. If the estimate is wrong, so is the gap, and a bet with a positive theoretical value can perfectly well lose.
What is the closing line used for?
It serves as a benchmark: it shows where the market ended up placing the price. Comparing the odd you took with that final price measures the quality of the price obtained, not the profitability of a strategy.
Sources & methodology
This page draws on the standard formulas for converting decimal odds, on the economic research devoted to the overround and to price formation in betting markets, on the usual methods for normalising probabilities, and on the odds-analysis methodology developed by OddScore.
- Convert each decimal odd into an implied probability (1 ÷ odd).
- Add these probabilities to get the book percentage, then subtract 100% for the overround.
- Normalise the probabilities proportionally to estimate a margin-free market, keeping in mind that the result depends on the spreading method.
- Compare an odd with an independently estimated probability to obtain a theoretical value, and with the closing line to measure the quality of the price obtained.