Implied probability, explained
The price is the forecast. Reading it is arithmetic; trusting it is not.
Implied probability is the chance a price implies. On a prediction market it needs no conversion at all — a contract that pays $1 and trades at 42¢ is the market saying 42%. Everywhere else it is the same idea buried under a format.
The conversions
- Prediction-market pricePrice in cents is the probability. 42¢ = 42%. Nothing to convert.
- Decimal oddsProbability = 1 ÷ decimal. 2.38 → 42%.
- American, negativeProbability = odds ÷ (odds + 100), using the absolute value. −150 → 150/250 → 60%.
- American, positiveProbability = 100 ÷ (odds + 100). +240 → 100/340 → 29.4%.
- FractionalProbability = denominator ÷ (numerator + denominator). 7/5 → 5/12 → 41.7%.
The converter does all five at once, in your browser.
Where the raw number lies
First, it contains the margin. Add both sides of a real two-way market and you will get more than 100%. Two sides at −110 imply 52.38% each, 104.76% together. Neither side is really 52.38% — the extra 4.76 points are the cost of being allowed to trade. Divide each side by the total and you get the market’s actual view: 50/50. That is what the no-vig calculator is for.
Second, it is a price, and prices contain more than beliefs. A thin book, a large stale order, a trader closing a position for reasons that have nothing to do with the question — all of it moves the implied probability without anyone changing their mind about anything. On a market with $300 of depth, the implied probability is a rumour with a decimal point.
What it is still good for
Comparison. If your own estimate is 45% and the fair price is 38%, you have found a disagreement, and a disagreement is the only thing that can ever pay. Whether it pays enough to cover the fee and the wait is the next two questions — the fee calculator and the time-value calculator handle those.
Questions
What does implied probability mean?
The probability that a price implies. On a contract paying $1, the price in cents is the implied probability directly.
How do you calculate implied probability from decimal odds?
Divide one by the decimal odds. Decimal 2.38 implies 1/2.38 = 42%.
Why do both sides add up to more than 100%?
Because the venue's margin is baked into both prices. The excess over 100% is the overround; removing it proportionally gives the no-vig fair price.