Implied Probability from American Odds: Understanding the True Likelihood of a Bet
Implied probability is the likelihood of an outcome as suggested by the odds. It helps bettors assess whether a wager has value by comparing the sportsbook's implied probability with their expectations.
Formula for Converting American Odds to Implied Probability
For Positive Odds (+x) (Underdog): Implied Probability = 100 / (x + 100)
- +150: 100 / (150 + 100) = 40.00%
- +250: 100 / (250 + 100) = 28.57%
- +300: 100 / (300 + 100) = 25.00%
For Negative Odds (-x) (Favorite): Implied Probability = x / (x + 100) Examples of Converting American Odds to Implied Probability
- -200: 200 / (200 + 100) = 66.67%
- -120: 120 / (120 + 100) = 54.55%
Real-World Example: NBA Game on March 2, 2025. Consider a recent NBA game between the Denver Nuggets and Boston Celtics with the following odds:
- Denver Nuggets: +154
- Boston Celtics: -184
Implied Probabilities:
- Denver Nuggets: 100 / (154 + 100) = 39.37%
- Boston Celtics: 184 / (184 + 100) = 64.94%
Total Probability: 39.37% + 64.94% = 104.31%
This indicates a 4.31% vig (house edge) from the bookmaker. Key Takeaways
- Underdog odds (positive values) require adding 100 to the odds before calculating probability.
- Favorite odds (negative values) use the odds directly in the numerator.
- If the total implied probability exceeds 100%, the excess represents the bookmaker's margin (vig).
- Understanding implied probability helps bettors evaluate whether a bet offers value compared to their own estimates.