How to Convert Betting Odds to Implied Probability
Implied probability expresses betting odds as a percentage. It represents the probability associated with a price before accounting for factors such as the bookmaker’s margin. It is not necessarily an objective estimate of the outcome’s true likelihood, and it does not guarantee what will happen.
What Is Implied Probability?
How to Convert American Odds to Implied Probability
American odds use positive and negative numbers to express potential returns relative to a standard stake. Positive odds show the profit on a $100 stake, while negative odds show how much must be staked to earn $100 in profit. The conversion formula differs depending on whether the odds are positive or negative.
Positive American odds
Implied probability (%) = 100 ÷ (American odds + 100) × 100
Example: +150 odds → 100 ÷ (150 + 100) × 100 = 40%
For odds of +150, divide 100 by 150 + 100, then multiply by 100. The implied probability is 40%. In other words, a price of +150 corresponds to an implied probability of 40% before accounting for the bookmaker’s margin.
Negative American odds
Implied probability (%) = |American odds| ÷ (|American odds| + 100) × 100
Example: −200 odds → 200 ÷ (200 + 100) × 100 = 66.67%
For odds of −200, divide 200 by 200 + 100, then multiply by 100. The implied probability is approximately 66.67%. This is the probability implied by the price, not a guarantee that the outcome will occur.
How to Convert Decimal Odds to Implied Probability
Decimal odds represent the total return, including the original stake, for each unit wagered. To convert decimal odds into implied probability, divide 1 by the decimal odds and multiply by 100.
Implied probability (%) = (1 ÷ decimal odds) × 100
Example: decimal odds of 2.50 → (1 ÷ 2.50) × 100 = 40%
Decimal odds of 2.50 imply a probability of 40%, because 1 divided by 2.50 equals 0.40. Decimal odds of 1.50 imply approximately 66.67%.
How to Convert Fractional Odds to Implied Probability
Fractional odds express potential profit relative to the stake. Odds of 3/1 mean a potential profit of $3 for every $1 wagered, plus the return of the original stake. To convert fractional odds into implied probability, divide the denominator by the sum of the numerator and denominator, then multiply by 100.
Implied probability (%) = denominator ÷ (numerator + denominator) × 100
For fractional odds of 3/1, the calculation is 1 ÷ (3 + 1) × 100 = 25%. Fractional odds of 1/2 imply a probability of approximately 66.67%.
Why Implied Probability Isn’t the Same as True Probability
Implied probability is calculated from the price offered, but the price may include a bookmaker’s margin. When you convert the odds for every possible outcome in a market, their implied probabilities will often add up to more than 100%. That excess is commonly called the overround, or bookmaker’s margin. It helps explain why implied probability should not automatically be treated as an unbiased estimate of an outcome’s actual likelihood.
For example, if two opposing outcomes each have odds of −110, each side implies a probability of about 52.38%. Together, they total approximately 104.76%. The amount above 100% reflects the market’s overround, although it does not necessarily equal a bookmaker’s realized profit.
Implied Probability Formulas at a Glance
- Positive American odds: 100 ÷ (odds + 100) × 100
- Negative American odds: absolute value of odds ÷ (absolute value of odds + 100) × 100
- Decimal odds: (1 ÷ decimal odds) × 100
- Fractional odds: denominator ÷ (numerator + denominator) × 100
The Bottom Line
Converting betting odds to implied probability provides a common scale for comparing prices across odds formats. It helps clarify what a price implies, but it does not establish the true probability of an outcome. For meaningful analysis, consider the available alternatives, the bookmaker’s margin, and the context behind the market.
Continue exploring our Sports & Betting Markets coverage for more analysis of betting odds, market movements, and the context behind the numbers. For broader reference material, visit Guides & Research.