#Definition
Implied probability is the market's estimated likelihood of an outcome, derived directly from contract prices. In binary markets, the price in dollars equals the probability as a decimal: a Yes contract trading at $0.65 implies the market believes there's a 65% chance the event will occur.
This price-to-probability relationship is the foundation of prediction market interpretation. Rather than simply trading contracts, participants are effectively trading probabilities, and the market price represents the crowd's aggregated estimate of the true likelihood.
#Why It Matters in Prediction Markets
Implied probability is central to how prediction markets function:
Universal interpretation
A price of $0.72 means the same thing regardless of the event: a 72% implied probability. This standardization allows comparison across different types of markets.
Trading signal
If your estimated probability differs from implied probability, you have a potential trade. Believe something is 80% likely when the market says 65%? Buy Yes. The gap between your estimate and the implied probability is your expected edge.
Implied probabilities represent collective intelligence. Thousands of traders, each with partial information, buy and sell until the price reflects their aggregated beliefs.
Forecasting tool
Beyond trading, implied probabilities serve as forecasts. Researchers, journalists, and decision-makers use prediction market prices as probability estimates for uncertain events.
#How It Works
#The Price-Probability Relationship
For standard prediction markets where winning contracts pay $1:
Implied Probability = Contract Price / $1
If Yes trades at $0.70:
Implied Probability = $0.70 / $1 = 70%
#Derivation from Arbitrage
Why does this relationship hold? Because any deviation creates arbitrage:
If Yes at $0.60 implied less than 60% probability:
- Arbitrageurs buy Yes at $0.60
- If true probability is higher, they profit on average
- Buying pressure pushes price up toward true probability
If Yes at $0.60 implied more than 60% probability:
- Arbitrageurs sell Yes at $0.60
- If true probability is lower, they profit on average
- Selling pressure pushes price down toward true probability
The price stabilizes where it reflects collective probability beliefs.
#Numerical Examples
| Contract Price | Implied Probability | Interpretation |
|---|---|---|
| $0.05 | 5% | Very unlikely |
| $0.20 | 20% | Unlikely |
| $0.50 | 50% | Coin flip |
| $0.75 | 75% | Likely |
| $0.95 | 95% | Very likely |
#Conversion Formulas
From price to probability:
Probability = Price × 100%
From probability to fair price:
Fair Price = Probability / 100
Your edge (when you believe probability differs from market):
Edge = Your Estimated Probability - Implied Probability
A positive edge on Yes means the market is underpriced; you should buy.
#Adjusting for Fees and Spreads
In practice, the clean relationship has friction:
Effective Implied Probability = Contract Price + Expected Fees
If Yes costs 0.02 in fees, effective cost is $0.67, implying you need 67% true probability to break even, not 65%.
#Examples
#Example 1: Election Market
A presidential election market shows:
- Candidate A Yes: $0.58
- Candidate A No: $0.42
Interpretation: The market implies Candidate A has a 58% chance of winning. The probabilities sum to 100% in an efficient market (they may differ slightly due to spreads).
#Example 2: Economic Indicator
A market asks whether unemployment will fall below 4%:
- Yes price: $0.35
Interpretation: The market implies a 35% probability that unemployment falls below 4%. A trader who believes the probability is actually 50% sees a 15 percentage point edge.
#Example 3: Sports Outcome
A market on a championship game shows:
- Team A wins: $0.62
- Team B wins: $0.38
Interpretation: 62% implied probability for Team A. Bookmakers or other forecasters offering different odds might be wrong, or they might have information the market lacks.
#Example 4: Multi-Outcome Market
A market on election winner with three candidates:
- Candidate A: $0.55
- Candidate B: $0.35
- Candidate C: $0.12
Interpretation: The implied probabilities are 55%, 35%, and 12%. They sum to 102% due to the spread; this overround represents the market maker's take.
#Risks, Pitfalls, and Misunderstandings
Confusing price with probability in illiquid markets
In thin markets, prices may not reflect true probability; they may reflect the last random trade. Only trust implied probability in reasonably liquid markets.
Ignoring the spread
The bid-ask spread means buying Yes costs more than the midpoint. If bid is 0.65, the implied probabilities differ depending on which side you take.
Assuming implied probability equals true probability
Implied probability is the market's estimate, not ground truth. Markets can be wrong, especially when few people trade or when participants share biases.
Forgetting fees
Platform fees reduce your realized payout. A 0.95 after fees (5% fee on winnings) has different breakeven probability than one paying $1.00.
#The Formula
Example:
- Price of YES share: $0.60
- Payout if YES wins: $1.00
- Implied Probability: 1.00 = 0.60 (60%)
If the payout is different (e.g., UK odds), the math changes, but for standard binary prediction markets ($1 payout), the price is the probability.
Probability vs. expected value confusion
Implied probability tells you likelihood, not whether a trade is good. A 20% probability event at 0.25 has negative expected value.
#Practical Tips for Traders
-
Form your estimate before checking the market: Anchor bias is real. Decide what probability you believe, then compare to implied probability
-
Track the spread-adjusted probability: For buying Yes, use the ask price; for buying No, use the bid on No (or 1 minus the ask on Yes)
-
Calculate your required edge: If fees and spreads cost 3%, you need the true probability to exceed implied by more than 3% to profit
-
Compare across markets: The same event may trade at different implied probabilities on different platforms; arbitrage opportunities exist
-
Use implied probability for forecasting: Even if you don't trade, prediction market prices are often the best available forecasts for uncertain events
-
Watch for convergence at extremes: Prices near 1 may not move linearly with probability. A move from 0.97 doesn't necessarily mean probability increased by 2 percentage points.
#Related Terms
#FAQ
#Why do Yes and No prices sometimes not add to $1?
The gap represents the spread. Market makers and liquidity providers capture this difference as compensation. A Yes at 0.50 sums to $1.02; the 2 cents is the round-trip cost.
#Can implied probability be wrong?
Absolutely. Implied probability is the market's estimate, which aggregates available information but isn't infallible. Markets can be wrong due to limited participation, shared biases, or missing information. However, across many predictions, market-implied probabilities tend to be well-calibrated.
#How do I interpret prices in multi-outcome markets?
Each outcome's price represents its implied probability. Prices typically sum to slightly more than 100% due to spreads. To get true probabilities, you can normalize: divide each price by the sum of all prices.
#What's a "fair" price?
A fair price is one where implied probability equals true probability. If an event truly has a 60% chance of occurring, the fair price for Yes is $0.60. Of course, no one knows the true probability; that's why people trade.
#Does implied probability account for time?
Not directly. A market at 0.70 one day before both imply 70% probability. However, the earlier price reflects more uncertainty; it could change significantly, while the later price is nearly final.