Implied Probability
The probability of an outcome implied by its quoted odds. The building block of nearly every other betting calculation.
Implied probability is the win probability that a set of decimal odds implies, computed as the reciprocal of the decimal price. Because bookmakers add a margin (vig) to their prices, the sum of implied probabilities across all outcomes of a market exceeds 100%. The fair, no-vig probabilities are recovered by normalizing each implied probability against the total. Implied probability is the unit in which all other edge and value calculations are expressed.
- Every edge measurement, fair-odds calculation, and Kelly stake depends on converting prices into probabilities first.
- Comparing your model's probability to the market-implied probability is the single most common edge calculation in sports analytics.
- Stripping the vig (overround) to recover no-vig implied probabilities reveals the bookmaker's actual estimate of true odds, which is the comparison that matters for measuring real edge.
- Implied probability is the natural framing for cross-market comparison. American, decimal, and fractional odds are display conventions; implied probability is the underlying quantity.
implied_prob = 1 / decimal_oddsConvert American odds to decimal first if needed: positive American = (american / 100) + 1, negative = (100 / |american|) + 1. Then take the reciprocal. To recover no-vig probability for a two-way market, divide each implied probability by the sum across both sides.
American -110 = decimal 1.909, implied probability 1 / 1.909 = 52.4%. The opposite side at -110 also implies 52.4%, summing to 104.8%. Dividing each by 1.048 yields no-vig fair probabilities of 50.0% on each side.
- Comparing your model's probability against raw implied probability instead of no-vig implied probability. The raw figure is inflated by the bookmaker's margin and overstates the price you must beat.
- Treating implied probability as the bookmaker's estimate of true probability. Bookmakers shade prices to balance action, not to perfectly model outcomes. Sharp markets approximate true probability; soft markets can deviate.
- Adding implied probabilities for legs of a parlay. Multiplication on probabilities is correct; addition on percentages is not.
Compute it yourself.
We built a free calculator that implements the formula above. Plug in your numbers and see the math.
Open No-Vig Probability ConverterWhat is the difference between implied probability and true probability?
Implied probability is what the market price implies. True probability is the actual frequency at which the outcome occurs over a long run. Sharp markets produce implied probabilities that closely track true probability; soft markets can deviate by several percentage points. The gap between implied and true is precisely where edge lives.
Why do implied probabilities sum to more than 100%?
Because the bookmaker has built a margin into both sides of the market. The excess over 100% is the overround. The bookmaker's hold (the share of every dollar wagered they expect to keep) equals the overround divided by the total implied probability.
How accurate is the no-vig fair probability?
The proportional method (dividing each implied probability by the sum) is a reasonable first approximation and standard in industry practice. More sophisticated methods like Shin's distribution adjust for asymmetry between favorites and longshots, particularly at long odds. For most two-way markets at typical hold levels, the proportional method is accurate within a few tenths of a percent.
Why do American odds exist if implied probability is universal?
American odds are a display convention from US sportsbooks that emphasizes payout per $100 unit, which is intuitive for retail bettors. Decimal odds are dominant globally and are easier mathematically. Both encode the same implied probability; conversion is exact.