How it works
The implied probability of a price is 1 divided by its decimal odds. Add up the implied probabilities of every outcome in a market and a bookmaker’s total comes to more than 100%: the excess is the margin, also called the overround or the vig. Take it out and you have the fair odds, the prices the market would offer with no margin at all.
How to take it out is a modelling choice. Proportional scales every chance down by the same factor. The power and Shin methods take more of it from the long shots, which is where bookmakers tend to put more of it (the favourite-longshot bias).
The formula
- Implied probability = 1 ÷ decimal odds
- Book sum = the implied probabilities of every outcome, added up
- Margin (overround) = book sum − 1
- Fair probability (proportional) = implied probability ÷ book sum
- Fair odds = 1 ÷ fair probability
A worked football example
A match priced home 2.40, draw 3.50, away 2.90 implies 41.7%, 28.6% and 34.5%: a book of 104.7%, so the margin is 4.7%. Taken out proportionally, the fair chances are 39.8%, 27.3% and 32.9%, and the fair odds 2.51, 3.67 and 3.04.
What it does not tell you
Fair odds are the bookmakers’ own view with the margin removed. They are a good estimate of what the market believes, not of what will happen. A real edge needs an independent probability that disagrees with the market, and a reason it is right.
Common questions
What is a bookmaker’s margin?
It is how far the implied probabilities of every outcome add up past 100%. A two-way market at 1.91 on both sides adds up to 104.7%, a margin of 4.7%. It is the bookmaker’s built-in edge over a bettor who backs every outcome.
What is the difference between overround and hold?
The overround is the excess over 100%: book sum minus 1. The hold is the share of a balanced book the bookmaker keeps: 1 − 1 ÷ book sum. A 5% overround is a hold of about 4.8%.
Which method should I use to remove the margin?
Proportional is the simplest and the most common. Power and Shin take more of the margin from long shots, which tends to match how bookmakers price, so they give favourites slightly higher fair chances. On a tight market the three barely differ.
Can the implied probabilities add up to less than 100%?
Only when the prices come from different bookmakers. A total under 100% means backing every outcome in proportion returns more than the stake whatever happens: an arbitrage. The arbitrage calculator works out the stakes.
Is the implied probability the real chance?
No. It is the chance the price implies, margin included. Even the fair probability is the market’s opinion. It is often a good one, but it is not a fact about the match.