Implied Probability Calculator
Print PageAn Implied Probability Calculator (also known as an Odds to Probability Converter, Sportsbook Vig & Overround Calculator, No-Vig Fair Odds Utility, or Betting Market Value Analyzer) converts sports betting odds across American (Moneyline +150 / -110), Decimal (European 2.50 / 1.91), and Fractional (British 3/2 / 10/11) formats into exact mathematical implied probabilities (Pimplied). It also calculates total sportsbook overround (vigorish / bookmaker margin) and strips out the bookmaker fee using multiplicative de-overrounding to reveal true no-vig fair probabilities (Pfair).
Bookmakers never offer fair probability odds. By shading betting lines (e.g. charging -110 / -110 on a 50/50 coin flip point spread), the sportsbook creates a total market implied probability sum of 104.76% (where the extra 4.76% represents their profit margin or “vig”). An implied probability calculator strips away this hidden fee to reveal the true underlying win probability of each team.
Our free online Implied Probability Calculator provides instant odds conversions, overround margin analysis, and no-vig fair odds calculations:
- Positive American Odds (+L e.g. +150):
Pimplied = 100 ÷ (L + 100) = 100 ÷ (150 + 100) = 40.00%. - Negative American Odds (-L e.g. -110):
Pimplied = |L| ÷ (|L| + 100) = 110 ÷ 210 ≈ 52.38%. - Decimal Odds (D e.g. 2.50):
Pimplied = 1 ÷ D = 1 ÷ 2.50 = 40.00%. - Fractional Odds (A/B e.g. 3/2):
Pimplied = B ÷ (A + B) = 2 ÷ (3 + 2) = 40.00%. - Total Market Overround (S):
S = ∑ Pimplied, i;Vig Margin % = (S - 1.0) · 100%. - No-Vig True Fair Probability (Pfair):
Pfair, i = Pimplied, i ÷ S.
Master Sports Betting Odds to Implied Probability Conversion Table
The table below displays the exact mathematical conversions across American, Decimal, and Fractional odds formats, along with their raw implied probabilities and no-vig fair probabilities (assuming a standard 4.76% sportsbook margin):
| American Odds (Moneyline) | Decimal Odds (European) | Fractional Odds (UK) | Raw Implied Probability Pimplied | No-Vig Fair Probability (De-Overrounded) | Market Betting Designation |
|---|---|---|---|---|---|
| +400 | 5.00 | 4/1 | 20.00% | 19.09% | Heavy Underdog |
| +300 | 4.00 | 3/1 | 25.00% | 23.86% | Significant Underdog |
| +200 | 3.00 | 2/1 | 33.33% | 31.82% | Moderate Underdog |
| +150 | 2.50 | 3/2 | 40.00% | 38.18% | Slight Underdog |
| +100 (EVEN) | 2.00 | 1/1 | 50.00% | 47.73% | Even Money Line |
| -110 (Standard Spread Line) | 1.909 | 10/11 | 52.38% | 50.00% (50/50 True Fair Odds) | STANDARD 2-WAY SPREAD LINE |
| -150 | 1.667 | 2/3 | 60.00% | 57.27% | Moderate Favorite |
| -200 | 1.500 | 1/2 | 66.67% | 63.64% | Solid Favorite |
| -300 | 1.333 | 1/3 | 75.00% | 71.59% | Heavy Favorite |
Step-by-Step Super Bowl Moneyline (-150 Favorite vs. +130 Underdog) De-Overrounding Example
To calculate the sportsbook overround and find the true no-vig fair probabilities for a Super Bowl moneyline of Favorite -150 versus Underdog +130:
Step 1 (Calculate Favorite Implied Probability): P1 = 150 ÷ (150 + 100) = 150 ÷ 250 = 0.6000 (60.00%)
Step 2 (Calculate Underdog Implied Probability): P2 = 100 ÷ (130 + 100) = 100 ÷ 230 = 0.434783 (43.48%)
Step 3 (Calculate Total Market Overround S): S = 60.00% + 43.48% = 103.48% (3.48% Sportsbook Vig)
Step 4 (Calculate Favorite True Fair Probability): Pfair, 1 = 60.00% ÷ 1.034783 = 57.98%
Step 5 (Calculate Underdog True Fair Probability): Pfair, 2 = 43.48% ÷ 1.034783 = 42.02%
Thus, while the sportsbook odds suggest a 60.00% to 43.48% split, stripping out the 3.48% vig reveals that the Favorite has a 57.98% true probability of winning while the Underdog has a 42.02% true probability.
Understanding Sportsbook Overround & Positive Expected Value (+EV)
Below is a comparative reference chart detailing sportsbook pricing terms and handicapping principles:
| Betting Concept | Sportsbook Market Definition | How Bettors Use It to Find Value |
|---|---|---|
| Vigorish (Vig / Juice / Margin) | The house commission added to odds (Sum of probabilities > 100%). | Must be removed to find true win probability before placing value bets. |
| Positive Expected Value (+EV Bet) | When a bettor’s estimated win probability exceeds the implied probability of the sportsbook odds. | If True Fair Odds = 55% but Sportsbook Odds implied = 48%, bet carries +EV! |
History & Mathematics: 1931 Charles McNeil & The Point Spread
1931 Charles McNeil & The Invention of Point Spread Vig
In 1931, Chicago mathematician and bookmaker Charles K. McNeil invented the modern Point Spread and standardized the -110 / -110 vigorish system (charging $110 to win $100). McNeil realized that balancing money on both sides of a handicap line guaranteed a risk-free 4.76% profit margin for the house.
17th Century British Turf Clubs & Fractional Odds
In 17th-century England, horse racing turf clubs created fractional odds (e.g. 3/1 or 5/2) to allow bookmakers to quickly adjust payout ledgers as betting volume shifted on race tracks.
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Frequently Asked Questions (FAQ)
What is Implied Probability in sports betting?
Implied Probability is the percentage chance of an outcome occurring as suggested by bookmaker betting odds. It reflects both the actual probability of the event and the sportsbook’s profit margin (vig).
How do you convert -110 odds to implied probability?
For -110 American odds: P = 110 ÷ (110 + 100) = 110 ÷ 210 = 52.38%.
How do you remove the vig from betting odds?
Calculate implied probabilities for all outcomes in a market, sum them to find total overround (e.g., 104.76%), and divide each individual implied probability by total overround (e.g., 52.38% ÷ 1.0476 = 50.00%).