How to Read Prediction Market Odds: Convert Odds to Implied Probability

AbstractA prediction market quotes prices in cents, which are already probabilities. Bookmakers quote odds, which must be converted and then cleaned of their built-in margin. We give the conversion formulas for every common format, a conversion table, two methods for removing the overround (proportional and Shin), and the rules for reading an order book: use the mid, not the last trade, and check the spread before trusting either.

Prediction market prices are probabilities already#

A contract quoted at 63¢ pays $1 if the event happens, so the implied probability is simply $63/100 = 63%$ . The only care needed is in choosing which price:

Ask (lowest offer): what you pay to buy now.
Bid (highest bid): what you receive to sell now.
Mid = (bid + ask)/2: the best single estimate of the probability.
Last trade: whatever someone last paid. In a thin market it can be minutes or hours stale.

In a 41/43 market the implied probability is 42%, not 43% (what a buyer pays) or 41%. When the spread is wide (say 30/45), the honest answer is "somewhere between 30% and 45%", and the mid is not much better than a guess. For thin books, a size-weighted mid is more informative: see the microprice formula in our pricing primer.

Converting bookmaker odds#

Decimal odds $d$ (total return per unit staked, stake included):

p_{implied} = \frac{1}{d}

(1)

American (moneyline) odds $A$ :

p_{implied} = ⎩ ⎨ ⎧ \frac{100}{A + 100} \frac{- A}{- A + 100} A > 0 A < 0

(2)

Fractional odds $a / b$ (profit $a$ per $b$ staked):

p_{implied} = \frac{b}{a + b}

(3)

Table 1. Common odds and their implied probabilities, before removing any margin.
American	Decimal	Fractional	Implied probability	Equivalent contract price
-400	1.25	1/4	80.0%	80.0¢
-200	1.50	1/2	66.7%	66.7¢
-150	1.67	2/3	60.0%	60.0¢
-110	1.91	10/11	52.4%	52.4¢
+100	2.00	1/1	50.0%	50.0¢
+150	2.50	3/2	40.0%	40.0¢
+200	3.00	2/1	33.3%	33.3¢
+400	5.00	4/1	20.0%	20.0¢
+900	10.00	9/1	10.0%	10.0¢

Removing the bookmaker's margin#

Bookmaker odds include a margin, so implied probabilities across all outcomes sum to more than 100%. A two-way market at −110/−110 implies 52.38% for each side, 104.76% in total: an overround of 4.76 points. The bookmaker's expected hold on a balanced book is 4.55% of stakes.

Proportional method. Divide each implied probability by the total:

p^_{i} = \frac{π _{i}}{\sum _{j} π _{j}}

(4)

It is simple and fine for two-way markets with similar prices. It spreads the margin evenly, which is wrong when the margin is concentrated on longshots, as the favourite–longshot bias suggests it usually is.

Shin's method. Shin (1993) models the bookmaker as setting odds to protect against a fraction $z$ of insiders. The implied true probabilities solve

π_{i} = z p^_{i} + (1 - z) p^_{i}^{2} / \sum_{j} z p^_{j} + (1 - z) p^_{j}^{2}

(5)

for the $z$ that makes the $p^_{i}$ sum to one. In practice it removes more margin from longshots than from favourites, which better matches observed outcomes in multi-runner markets.

Exchange prices have no overround in this sense: Yes and No sum to 100¢ at the mid. Their equivalent is the spread plus fees, which is why prediction market prices are often a cleaner probability signal than bookmaker odds (see prediction markets vs sports betting).

Multi-outcome markets#

Markets with many outcomes (who wins a nomination, which bucket inflation lands in) list one contract per outcome. Before costs the mids should sum to about 100¢. In practice:

Asks typically sum above 100¢ and bids below. Each spread adds a little.
A sum of mids far from 100¢ means some prices are stale or thin. Normalise only after checking.
Small outcomes are where the favourite–longshot bias concentrates. Five longshots at 3¢ each are 15¢ of probability the market may not really believe.

The exact bands within which these sums can drift without creating an arbitrage, given fees, are worked out in no-arbitrage bounds for event contracts.

Questions#

How do you convert American odds to implied probability?

For positive odds +A, probability = 100/(A + 100). For negative odds −A, probability = A/(A + 100). So +200 is 33.3% and −150 is 60%.

What does 70 cents mean on a prediction market?

A contract priced at 70¢ pays $1 if the event happens, so the market implies roughly a 70% probability. Use the midpoint of bid and ask rather than the last trade.

What is the overround?

The amount by which a bookmaker's implied probabilities across all outcomes exceed 100%. It is the bookmaker's margin. At −110/−110 it is 4.76 points.

References#

Shin, H. S. (1993). Measuring the incidence of insider trading in a market for state-contingent claims. The Economic Journal, 103(420), 1141–1153.

DisclosureThis note is research and education. It is not investment advice or an offer to trade, and nothing in it describes the firm's own results.