Implied probability: turning odds into a percentage
Implied probability is the chance a betting price builds in. For decimal odds D it is 1 divided by D; for American odds +A it is 100 divided by A plus 100, and for -A it is A divided by A plus 100. So +100 implies 50%, +150 implies 40.0% and -200 implies 66.7%.
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- 2 min read
- 4 sections
- 1 table
- 4 FAQ
The formulas
- Decimal odds D: probability = 1 / D.
- American plus number +A: probability = 100 / (A + 100).
- American minus number -A: probability = A / (A + 100).
Each result is a share, so multiply by 100 for a percentage.
The formula for a minus number divides the amount you must stake by that stake plus 100, which is why a bigger favourite gets a higher percentage.
A plus number works in reverse: the bigger the plus, the lower the percentage. Fractional odds a/b first convert to decimal as 1 + a/b.
Bottom line: every price can be read as a percentage, and the percentage includes the sportsbook's margin.
Three worked examples
| American odds | Working | Decimal odds | Implied probability |
|---|---|---|---|
| +100 | 100 / 200 | 2.00 | 50.0% |
| +150 | 100 / 250 | 2.50 | 40.0% |
| -200 | 200 / 300 | 1.50 | 66.7% |
Check the second row with the decimal formula: 1 / 2.50 = 0.40, or 40.0%. The same result from two formulas is a quick test of your arithmetic. Try your own price on the odds converter.
Why a market adds to more than 100%
Add the implied probabilities of every outcome in a market. If the sum is 104.76%, as in a hypothetical -110/-110 market, the extra 4.76 points is the margin. See vig and juice for that worked example.
The same logic applies to a moneyline. For several legs together, see the parlay calculation.
How we checked
The formulas and examples are derived by us from the definitions of decimal and American odds. No sportsbook price is used. More: bet types, odds and margins.
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FAQ
What is the formula for decimal odds?
Implied probability is 1 divided by the decimal odds. Decimal odds of 2.50 give 1 / 2.50, which is 40.0%.
What is the formula for American odds?
For a plus number A, divide 100 by A plus 100. For a minus number A, divide A by A plus 100. So +150 gives 40.0% and -200 gives 66.7%.
Why do the probabilities of a market add to more than 100%?
The sportsbook builds its margin into the prices. The excess over 100% is the vig, also called overround.
Does implied probability tell me the real chance of winning?
No. It is the chance the price implies, including the margin. It is not a forecast, and we do not suggest a bet is better because its implied probability looks low.