Probability (Implied Probability)
Definition
Implied Probability is the market's collective estimate of how likely an outcome is, expressed through contract prices. Prices in dollars map to probabilities in percent (e.g., $0.72 ≈ 72%).
The Price-Probability Relationship
In prediction markets, the price of a binary contract directly represents the implied probability:
Price (in dollars) = Probability (as a decimal)
Price (in cents) = Probability (as a percentage)
Examples
| Contract Price | Implied Probability | Interpretation | |----------------|---------------------|----------------| | $0.10 (10¢) | 10% | Very unlikely | | $0.25 (25¢) | 25% | Unlikely | | $0.50 (50¢) | 50% | Toss-up | | $0.75 (75¢) | 75% | Likely | | $0.90 (90¢) | 90% | Very likely |
Why This Works
The relationship holds because of arbitrage:
- If a contract trading at $0.60 has a true 80% chance of occurring, traders will buy it (underpriced)
- Their buying pressure drives the price up toward $0.80
- This continues until the price reflects the collective belief
Important Considerations
Fees and Spreads
The exact price-to-probability conversion can be affected by:
- Trading fees
- Bid-ask spreads
- Market maker margins
Rounding in Categorical Markets
In markets with multiple outcomes, implied probabilities may sum to slightly more or less than 100% due to spreads and fees.