Implied Probability and the Bookmaker’s Margin

The short answer

Implied probability is the percentage chance represented by a price. Add the implied probabilities for every outcome in a complete market and you get its book percentage, also called the overround. If that total exceeds 100%, the excess expresses a margin built into the prices. It is a theoretical pricing measure, not a guarantee of bookmaker profit or a prediction of the result.

How implied probability and margin work

Odds give you a way to express the price of an outcome as a percentage. For decimal odds, divide 100 by the odds:

Implied probability = 100 ÷ decimal odds

For fractional odds, divide the second number by the sum of both numbers, then multiply by 100:

Implied probability = second number ÷ (first number + second number) × 100

For example, fractional odds of 2/1 imply 1 ÷ (2 + 1) × 100 = approximately 33.3%. That percentage comes from the price; it does not independently establish the outcome’s actual chance.

To examine a whole market, follow these steps:

1. Identify all the outcomes covered by the market and check its settlement rules.
2. Convert each price into an implied probability.
3. Add those percentages to get the book percentage, or overround.
4. Subtract 100% to find the excess above 100%, expressed in percentage points.

The simple calculation works most clearly when the outcomes cover every possibility and exactly one can win. If there is a draw among the possible outcomes, include it. If the market can settle in other ways, such as a void, check the terms before relying on a simple total.

The distinction between the total and the excess is useful: a book percentage of 106%, for example, is 6 percentage points above 100% because 106% − 100% = 6 percentage points. Both figures describe the prices, not the bookmaker’s realised profit.

Worked example: a two-outcome market

Example: Imagine a market with exactly two possible outcomes, A and B. Assume exactly one must win, with no draw or other outcome to include. The prices are hypothetical and are not a recommendation.

Using the rounded figures, the book percentage is 101.01%. Its excess above 100% is 101.01% − 100% = 1.01 percentage points. The actual probabilities of two mutually exclusive outcomes that cover every possibility must add up to 100%; these price-derived figures add up to more.

Comparison example: If the same two outcomes were each priced at 2.00, each implied probability would be 100 ÷ 2.00 = 50%. The book percentage would be 50% + 50% = 100%, with an excess of 100% − 100% = 0 percentage points.

The comparison shows how changing prices changes the total. It does not establish the actual likelihood of A or B in either example. Rounding can also affect the last displayed decimal place, so keep more digits during your calculation if precision matters.

Bookmaker rules and what to check

The market name alone may not tell you everything needed for a fair comparison. Before betting or calculating a book percentage, read the applicable terms and check:

• Which outcomes count: establish whether the listed selections cover every possible result under the market rules.
• When the result is determined: check the specified period of play and whether any additional period is included.
• Void and settlement conditions: look for situations where a bet may not settle as a straightforward win or loss.
• The prices you are comparing: use prices from the same market at the same point in time.

Bookmakers may adjust odds after releasing them, including during an event for in-play betting. A calculation made from prices collected at different times may therefore describe a combination that was not available together. The applicable rules and prices should be checked with the bookmaker; this guide does not confirm any particular bookmaker’s current terms.

Common misunderstandings

The excess is not guaranteed profit

A positive excess shows that the prices add up to more than 100%; it does not show what the bookmaker will actually earn. The theoretical margin depends on attracting stakes in particular proportions. The overround alone does not reveal how much has been staked on each selection or the financial outcome when the market settles.

Implied chance is not necessarily true chance

The conversion tells you what a price implies, not an independently verified probability. Nor does the book percentage alone prove whether a particular selection’s price is good value: it summarises the set of prices rather than establishing the true chance of each outcome.

An incomplete total can mislead

Leaving out a possible winning outcome makes the sum incomplete. Likewise, combining prices from markets with different settlement conditions can make the result misleading. If your total is below 100%, first check that every relevant outcome is included and that the prices refer to the same market and time.

Related guides to read next

Practise the two price formats in Fractional and Decimal Odds: Reading and Converting Both. For more on settlement, see Singles, Doubles and Accumulators: How Multiples Settle, or explore In-Play and Cash Out for more on betting during an event. The Betting Glossary is a place to look up unfamiliar terms.