Implied Probability: From Market Prices and Odds to a Forecast
What implied probability means
Implied probability is the probability that is embedded in a quoted price or odd.
In prediction markets, the price is often already a probability like 0.62. In sportsbooks, odds must be converted, and you must usually remove the margin (vig).
Prediction market prices
Many binary prediction markets quote contracts in dollars from 0.00 to 1.00.
• price 0.62 means an implied probability of about 62%
• price 0.10 means about 10%
Important: in thin markets, the last traded price can be misleading. Prefer a defined market consensus like mid price or VWAP in a documented window.
American odds to implied probability
Positive odds (+X)
p = 100 / (X + 100)
Example: +150
• p = 100 / (150 + 100) = 0.40
Negative odds (-X)
p = X / (X + 100)
Example: -150
• p = 150 / (150 + 100) = 0.60
Decimal odds to implied probability
p = 1 / decimal_odds
Example: 2.50
• p = 1 / 2.50 = 0.40
The margin problem: probabilities do not sum to 1
Sportsbook odds usually include vig, so implied probabilities across outcomes sum to more than 1.
That extra amount is the overround.
Two outcome example
Suppose a two way market has:
• Team A implied p = 0.55
• Team B implied p = 0.50
Sum = 1.05, so overround is 5%.
Removing the vig: simple normalization
A practical default method is to normalize:
p_fair_i = p_i / sum(p_all)
In the example:
• Team A fair p = 0.55 / 1.05 = 0.5238
• Team B fair p = 0.50 / 1.05 = 0.4762
This gives probabilities that sum to 1 and are usable for benchmarking and scorecards.
How to use implied probability in a scorecard
Implied probability is useful as a benchmark.
Two common approaches:
• Use base rate as your default benchmark and also report skill versus market consensus when market data is reliable.
• Compute Brier skill score versus the implied probability baseline on the same questions.
Common pitfalls
Using last trade: last traded price can be stale or one small print. Define consensus with mid or VWAP and a window.
Ignoring vig: using raw sportsbook implied probabilities will bias your benchmark.
Timestamp mismatch: if you benchmark against a later price snapshot, you introduce look ahead bias. Use a fixed evaluation checkpoint.
Takeaway
Implied probability converts prices or odds into a probability forecast. In prediction markets it is often the price itself, but in sportsbooks you must convert odds and remove vig. When used as a benchmark, define consensus cleanly and align timestamps to avoid look ahead bias.
Related
• Vig
• Choosing a Baseline: 50 50 vs Base Rate vs Market Consensus