Implied Probability: Definition & How to Calculate It

DefinitionThe probability of an outcome implied by its price or odds. For a contract paying $1, the implied probability is its price in dollars; for bookmaker odds it must be converted and cleaned of the margin.

How to calculate it#

event contract: p = \frac{price}{payout}, decimal odds: p = \frac{1}{d}, American + A : p = \frac{100}{A + 100}

For an order book, use the mid between bid and ask, not the last trade. A 41/43 market implies 42%. Full conversion tables are in how to read prediction market odds.

Implied versus true probability#

An implied probability is a price, not a fact. Five things separate it from the true probability: the spread, fees (which raise the break-even probability by the fee per contract), the time value of locked collateral (a 63% event a year away is worth about 60.5¢ at 4%), the favourite–longshot bias, and the contract's resolution wording. Our pricing primer works through each.

Across outcomes#

Implied probabilities over a complete set of outcomes should sum to about 1 at the mids. Bookmaker odds sum to more (the overround); exchange asks sum to slightly more and bids to slightly less, by a band set by spreads and fees (no-arbitrage bounds).

Questions#

How do you calculate implied probability from a prediction market?

Divide the price by the payout. A contract that pays $1 and trades at 63¢ implies 63%. Use the midpoint of bid and ask.

Is implied probability the real probability?

It is an estimate. Spreads, fees, interest on collateral, systematic biases and contract wording all create gaps.