Login
Start Free

Implied Probability in Betting: Formula, Examples + How to Find Value

Free calculator: Skip the math — open the Implied Probability Calculator to convert any American (+/−), decimal, or fractional odds to a win% instantly.

Implied probability is the win rate that a betting odds line says is “fair.” For positive American odds (+150), implied probability = 100 ÷ (odds + 100) = 40%. For negative odds (−150), implied probability = odds ÷ (odds + 100) = 60%. When your true projected probability is higher than the implied probability, the bet has positive expected value and is worth taking.

← Back to Sports Betting Glossary

What Is Implied Probability?

Every set of betting odds carries an embedded “fair” probability that the bet wins. Convert the odds into a percentage and you’ve found the implied probability — the win rate the sportsbook is pricing in. Beat that implied probability with your own model, and you have an edge.

The key insight: implied probability is the inverse of the odds you receive. If a team is +200 (decimal 3.00), the book is saying they’ll win roughly 1 time in 3 attempts. Bet on them only if you believe they’ll win more often than that.

How to Calculate Implied Probability from American Odds

Positive odds (underdog)

Formula: 100 ÷ (odds + 100)

Negative odds (favorite)

Formula: odds ÷ (odds + 100) (using absolute value of odds)

Decimal odds

For decimal odds: implied probability = 1 ÷ decimal odds

Use PropsBot’s Odds Converter to translate between American, decimal, fractional, and implied probability instantly.

Implied Probability, Vig, and the Sportsbook’s Edge

Here’s a critical detail many bettors miss: the sum of implied probabilities across all outcomes of an event is always greater than 100%. That excess is the sportsbook’s vig (also called juice or hold).

Example: A coin-flip market priced as −110 / −110:

That extra 4.8% is the sportsbook’s house edge. To find the “true” no-vig fair probability, divide each implied probability by the total. In this example: 52.4% ÷ 104.8% = 50.0% — the actual fair probability of heads.

When you compare your model’s projection to a book’s price, always remove the vig first. PropsBot’s Odds Converter handles this automatically.

Using Implied Probability to Find Value

The single most useful application of implied probability is finding +EV bets. Three steps:

  1. Calculate the implied probability of the line offered.
  2. Remove the vig to get the fair implied probability.
  3. Compare to your model’s true probability. If your projected probability is higher than the no-vig implied probability, the bet has positive expected value.

Worked example for an NFL player prop:

This is exactly how PropsBot’s AI scores every prop on every slate — convert the line to no-vig implied probability, compare to model projection, flag positive-edge bets. Read more about positive expected value and closing line value as complementary signals.

Convert Implied Probability Back to Odds

Need to go the other direction — your model says 55% true probability, what’s the fair line?

Decimal odds: 1 ÷ probability → 1 ÷ 0.55 = 1.818

American odds (when prob > 50%): −(probability × 100) ÷ (1 − probability) → −(0.55 × 100) ÷ 0.45 = −122

American odds (when prob < 50%): (1 − probability) × 100 ÷ probability → e.g., 45% → 0.55 × 100 ÷ 0.45 = +122

If a book offers you better than your fair line (e.g., they’re at −115 and your fair is −122), the bet is +EV.

Frequently Asked Questions

What is implied probability in betting?

Implied probability is the win rate the betting odds suggest is “fair.” Convert American odds with: for positive odds, 100 ÷ (odds + 100); for negative odds, odds ÷ (odds + 100). For decimal odds, divide 1 by the decimal. Implied probability greater than your model’s true probability means the bet is negative EV.

How do you calculate implied probability from American odds?

For positive American odds (+150): 100 ÷ (150 + 100) = 40%. For negative American odds (−150): 150 ÷ (150 + 100) = 60%. Always include 100 in the denominator — that’s the standard formula.

Why does total implied probability exceed 100%?

The excess above 100% is the sportsbook’s vig (also called juice or hold). On a typical −110/−110 market, total implied probability is 104.8%, meaning the book takes a 4.8% house edge. To find true fair probability, divide each side by the total.

What is the difference between implied probability and true probability?

Implied probability is what the book’s odds imply. True probability is your independent estimate (from a model, projections, or analysis) of the bet’s actual win rate. When your true probability is higher than the no-vig implied probability, you have positive expected value.

How do I convert implied probability to American odds?

For probabilities greater than 50%, American odds = −(probability × 100) ÷ (1 − probability). For probabilities less than 50%, American odds = (1 − probability) × 100 ÷ probability. A 60% probability translates to −150; a 40% probability translates to +150.

Does PropsBot use implied probability to find bets?

Yes. PropsBot’s AI converts every prop line to no-vig implied probability, compares it to the model’s projected true probability, and ranks bets by edge. Across 218,000+ graded props the audited high-confidence ROI is 27.8%, validating the implied-probability vs. model-projection method as a profitable approach to player prop betting.

← Back to Sports Betting Glossary

Related Glossary Terms