Divide 1 by the decimal odd and multiply by 100: an odd of 2.20 gives 45.45%. This probability is called implied because it is deduced from the displayed price — it still contains the bookmaker's margin and does not describe the true probability of the outcome.
What is an implied probability?
The implied probability is the probability deduced from a displayed odd. It answers a precise question: what chance of success would be needed for this price to be balanced? It does not answer the question "what is the probability of this outcome".
The adjective "implied" carries the whole meaning. The probability is neither measured nor estimated by a model: it is simply contained in the price, and it inherits every one of that price's flaws — the operator's margin first, then any estimation errors it may have made.
What is the implied probability formula?
With a decimal odd, the implied probability is calculated by dividing 1 by the odd, then multiplying by 100.
implied probability (%) = (1 ÷ decimal odd) × 100
An odd of 2.00 gives 50%. An odd of 1.80 gives 55.56%. An odd of 5.00 gives 20%. The higher the odd, the lower the implied probability: the two move in opposite directions, which is mechanical since one is the inverse of the other.
Convert an odd into an implied probability
Enter a decimal odd and a stake. Both the comma and the point are accepted.
Comma or dot accepted: 2,20 as well as 2.20.
Only used to illustrate the return. Nothing is stored.
Result
- Implied probability
- 45.45%
- Gross return
- €22.00
- Net profit
- €12.00
Warning:
Implied probability is derived from the displayed odds: it still contains the bookmaker margin. It does not describe the real probability of the outcome.
A table of examples
Common odds and their implied probability, with the return on a €10 stake. The gross return includes the stake; the net profit only counts what is added to the stake placed.
| Odd | Calculation | Implied probability | Gross return | Net profit |
|---|---|---|---|---|
| 1.50 | 1 ÷ 1.50 | 66.67% | €15.00 | €5.00 |
| 1.80 | 1 ÷ 1.80 | 55.56% | €18.00 | €8.00 |
| 2.00 | 1 ÷ 2.00 | 50.00% | €20.00 | €10.00 |
| 2.20 | 1 ÷ 2.20 | 45.45% | €22.00 | €12.00 |
| 3.40 | 1 ÷ 3.40 | 29.41% | €34.00 | €24.00 |
| 5.00 | 1 ÷ 5.00 | 20.00% | €50.00 | €40.00 |
Careful how you read the return. A decimal odd pays out with the stake included. An odd of 2.20 does not "double" the stake: it multiplies it by 2.2, of which 1 corresponds to the stake handed back.
How do you do the reverse calculation?
To go from a probability to an odd, you divide 1 by that probability expressed as a fraction. A probability estimated at 50% gives 1 ÷ 0.50 = 2.00. A probability estimated at 45.45% does indeed give 2.20 back.
This reverse calculation has a name when the probability comes from somewhere other than the bookmaker: it is the fair odd, covered on fair odds. The nuance is not cosmetic. Inverting the implied probability of an odd merely recovers the odd you started from; inverting an independently estimated probability produces new information, comparable with the displayed price.
What implied probability does not mean
Three false readings come up systematically.
It is not the true probability of the outcome. The implied probability is extracted from a commercial price. The true probability of a sporting event is observable neither before the match nor after it: a match played only once does not reveal the distribution it came from.
It is not a margin-corrected probability. Add up the implied probabilities of every outcome of a match: the total exceeds 100%. Each probability taken in isolation is therefore slightly overstated. To compare two bookmakers on a common basis, you first have to remove that excess — that is the purpose of margin-free odds.
It is not a value signal. An implied probability of 45.45% says nothing about whether a bet is worth taking. To talk about theoretical value you need a second estimate, independent of the odd — a subject covered on value bet.
Why does the total exceed 100%?
Because the bookmaker's margin is spread across every odd in the market. On odds of 1.80 and 2.00, the total of the implied probabilities reaches 105.56%: the 5.56 points above 100% make up the overround.
This excess explains why an implied probability is always slightly higher than the estimate it covers. The detailed calculation, the distinction between overround and theoretical margin and the reasons the margin varies from one market to another are covered on bookmaker margin.
Calculate the margin of a complete market →
What OddScore does with this conversion
OddScore continuously converts the odds of several bookmakers, then removes the margin of each one before any comparison. Comparing two raw implied probabilities would amount to comparing two prices loaded in different ways: a low-margin operator would systematically look more "cautious" than a high-margin one, without that having the slightest connection to its sporting estimate.
This conversion is the first link in the chain: what matters next is how it evolves over time and how consistent it is across operators, two readings detailed in the guide on odds movements.
The three levels. Implied probability shows what a price assumes; it allows you to estimate the gap between two prices once the margin has been removed; it does not allow you to conclude that an outcome will happen.
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
Why the sum of the implied probabilities exceeds 100%.
Understand the marginMargin-free odds: the proportional method
Redistributing the overround to compare two operators on a common basis.
Remove the marginFair odds: from an estimated probability to an odd
The reverse calculation, applied to an estimate independent of the bookmaker.
Calculate a fair oddFrequently asked questions
How do you calculate an implied probability?
Divide 1 by the decimal odd, then multiply the result by 100. An odd of 2.50 corresponds to an implied probability of 40%.
What is the implied probability of an odd of 2.20?
It is 45.45%, that is 1 divided by 2.20. The winning stake would return €22 on €10 staked, including €12 of net profit.
Is the implied probability the true probability of the outcome?
No. It is deduced from a price that contains a commercial margin. The true probability of a sporting event is observable by nobody, neither before nor after the match.
Why do the implied probabilities of a match exceed 100%?
Because each one contains a share of the bookmaker's margin. The total, called the book percentage, almost always sits above 100%; the excess is the overround.
How do you find the odd again from a probability?
The reverse calculation divides 1 by the probability expressed as a fraction. A probability of 50% gives an odd of 2.00, a probability of 40% an odd of 2.50.
Does the odds format change the implied probability?
No. 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 implied probability of 40%.
Sources & methodology
This page draws on the standard formula for converting decimal odds, on the economic research devoted to the overround and to betting-market prices, and on the odds-analysis methodology developed by OddScore.
- Convert the decimal odd into an implied probability (1 ÷ odd), with no prior margin removal.
- Calculate the gross return of a stake (odd × stake) and the net profit (gross return − stake).
- Systematically point out that the probability obtained still contains the operator's margin.