Implied Probability Deep Dive: Turning Odds into Percentages
Once you can convert a price, the harder question is what the resulting probability means. This guide focuses on interpretation: normalization assumptions, probability error, expected value, and pushes. Use the companion conversion guide for the format-by-format arithmetic.
Keep Five Different Quantities Separate
The offered price determines the payout. Its raw implied probability q is the break-even threshold in a win/loss model. A normalized market estimate r allocates margin across the complete market. An analyst’s assumed probability p is a model input. The unknown true probability is not established by any of those calculations.
The worked conversion guide explains the formulas. Here is a cross-format reference, rounded only for display:
| American | Decimal | Fractional | Raw implied probability |
|---|---|---|---|
| -300 | 1.3333 | 1/3 | 75.00% |
| -150 | 1.6667 | 2/3 | 60.00% |
| -110 | 1.9091 | 10/11 | 52.38% |
| +100 | 2.0000 | 1/1 | 50.00% |
| +150 | 2.5000 | 3/2 | 40.00% |
| +200 | 3.0000 | 2/1 | 33.33% |
| +500 | 6.0000 | 5/1 | 16.67% |
For mutually exclusive, exhaustive outcomes, proportional normalization uses r_i = q_i / sum(q). In a -110/-110 market, each 52.38% normalizes to 50%. This imposes a proportional-margin assumption; summing to 100% does not make the estimates true.
Probability Advantage Is Not Monetary EV
Assume no fees, taxes, pushes, or voids. At +150 with a $100 stake, a win profits $150 and a loss costs $100. If an analyst assumes p = 45%, the gap above the 40% break-even threshold is 5 percentage points. Expected net profit is 0.45 × $150 - 0.55 × $100 = +$12.50.
Generally, EV = stake × (p × decimal odds - 1). The probability gap has probability units; EV has currency units. If the assumed p is wrong, the sign of EV can be wrong. A model output is not evidence of a repeatable real edge.
This is an application of the expected-value definition to the possible net outcomes.
Add Pushes Explicitly
A refunded push contributes zero net profit. Use EV = P(win) × net winnings - P(loss) × stake, with win, loss, and push probabilities summing to one.
Hypothetical $110 stake at -110: P(win) = 0.48, P(loss) = 0.42, P(push) = 0.10. EV = 0.48 × $100 - 0.42 × $110 = +$1.80. Among decisive outcomes, the assumed win rate is 0.48/0.90 = 53.33%, above the 52.38% threshold. Comparing the unconditional 48% directly with 52.38% would ignore refunded pushes.
These assumed probabilities illustrate the model; they are not historical push or win rates. Different void and settlement rules require their own outcomes.
Expected, Realized, and Long-Run Results
The +150 example realizes either +$150 or -$100, not +$12.50 each time. Repeated independent, identically distributed trials connect sample averages to expectations under the model. Changing prices, correlated selections, and uncertain probabilities require more care; one season’s profit does not validate a forecast.
Keep exposure separate from forecasting: continue to bankroll management and statistical variance.
Frequently Asked Questions
Does removing the vig reveal the true probability?
No. Proportional normalization is one way to turn a full market's raw implied probabilities into estimates summing to 100%. It assumes a proportional allocation of margin and does not reveal unknown true probabilities.
Is the difference between two probabilities expected profit?
No. At +150, an assumed 45% win probability exceeds the 40% break-even threshold by 5 percentage points. On a $100 stake, expected net profit is 0.45 × $150 - 0.55 × $100 = +$12.50, not $5.
How do pushes affect the calculation?
A refunded push has zero net profit. Use P(win) × net winnings - P(loss) × stake, with win, loss, and push probabilities summing to one. The usual 1 / decimal-odds threshold then applies among decisive outcomes, rather than to an unconditional win probability.