How to calculate implied probability
Implied probability is the chance of an event happening as estimated by a price or a set of odds. It is the single most important calculation in prediction markets and sports trading. This guide covers every odds format you'll see, with worked examples.
Prediction market prices
On a binary prediction market — a YES/NO contract that pays $1 to the winning side at resolution — the price in dollars is the implied probability. There is no other math.
- YES at $0.42 → 42% implied probability of YES
- YES at $0.85 → 85% implied probability of YES
- YES at $0.05 → 5% implied probability of YES
Some platforms quote prices in cents (0–100) instead of dollars (0.00–1.00). The math is identical: 63 cents equals 63% implied probability.
American odds
American odds are the format used by US sportsbooks. They come in two flavors: negative odds (favorites) and positive odds (underdogs).
Negative American odds
For negative odds like -150, the formula is:
implied probability = |odds| / (|odds| + 100)
Worked example: -150 → 150 / (150 + 100) = 150 / 250 = 60%.
More: -110 → 110/210 = 52.4%. -200 → 200/300 = 66.7%. -500 → 500/600 = 83.3%.
Positive American odds
For positive odds like +200, the formula is:
implied probability = 100 / (odds + 100)
Worked example: +200 → 100 / (200 + 100) = 100 / 300 = 33.3%.
More: +110 → 100/210 = 47.6%. +150 → 100/250 = 40%. +500 → 100/600 = 16.7%.
Decimal odds
Decimal odds are common in Europe, Australia, and on most crypto sportsbooks. Implied probability is simply the reciprocal:
implied probability = 1 / decimal odds
Worked example: 2.50 → 1 / 2.50 = 40%. 1.50 → 1 / 1.50 = 66.7%. 4.00 → 25%.
Fractional odds
Fractional odds are most common in UK horse racing. For odds quoted as A/B (e.g. 5/2):
implied probability = B / (A + B)
Worked example: 5/2 → 2 / (5 + 2) = 2/7 = 28.6%. 2/1 → 1/3 = 33.3%. 1/4 → 4/5 = 80%.
Stripping the vig from a two-sided line
Sportsbooks build a profit margin into their odds. A "-110 / -110" line implies 52.4% on each side — but those two probabilities sum to 104.8%, not 100%. The 4.8% excess is the vig. To get fair (de-vigged) probabilities:
- Calculate the implied probability for both sides.
- Sum the two probabilities.
- Divide each side's probability by the sum.
Worked example: -110 / -110 → 52.4% and 52.4% → sum 104.8% → each side = 52.4 / 104.8 = 50.0%. Vig-free, the line is a coin flip.
Another: -150 / +130 → 60.0% and 43.5% → sum 103.5% → de-vigged 58.0% and 42.0%.
Why this matters for prediction market traders
Prediction markets quote a single price that already reflects the crowd's implied probability — no conversion needed and (typically) no vig. Comparing the prediction market price to the de-vigged sportsbook probability tells you which venue has the better number for the trade you want to make. Often the prediction market is cheaper to the cent and pays you the difference.
Frequently asked questions
What's the difference between implied probability and true probability?
Implied probability is what the market or the book is currently pricing. True probability is what the event will actually settle at on average. Trading edge comes from forming your own estimate of true probability and finding markets where it differs meaningfully from implied probability.
Why don't the two sides of a sportsbook line sum to 100%?
Because of vig. The book builds a margin into both sides, so the two implied probabilities sum to roughly 104–110%. Strip the vig before you compare to any other number.
Do prediction markets have vig?
Generally no. The two sides of a binary prediction market sum to approximately $1 (100%), minus a small bid-ask spread set by liquidity providers. Platforms typically charge a small per-fill fee instead of a vig.