These four terms describe different parts of a price comparison. Model probability is an estimate. Implied probability is a conversion of a price. Edge compares probabilities. Expected value combines the estimated chance with the payout. Keeping them separate makes a matchup and a calculator much easier to interpret.
Model probability: an estimate of the event
If a model assigns an event a 55% chance, that is a forecast under its inputs and assumptions. It does not mean that 55% has been verified as the true chance, and it does not guarantee the next result. A useful forecast must be assessed over an appropriate set of observations and against a suitable comparison.
Implied probability: what the price requires
For decimal odds d, the simple break-even probability is 1 ÷ d in a win-or-lose market. Decimal odds include the returned stake. For American odds:
- Positive odds +A: implied probability = 100 ÷ (A + 100). At +150, it is 40%.
- Negative odds −A, using the positive magnitude of A: implied probability = A ÷ (A + 100). At −150, it is 60%.
These are price conversions, not objective estimates of the event. Quoted prices across all outcomes usually contain a margin. If both sides of a two-way market are −110, each has a raw implied probability of about 52.38%, for a total of about 104.76%.
No-vig probability: a market comparison after removing a margin
A simple proportional adjustment divides each raw implied probability by their sum. Two equally priced −110 sides then become 50% each. This assumes the outcomes are mutually exclusive and cover the complete market. Using prices from different events, different times, or an incomplete market invalidates the comparison.
Proportional normalization is one convention; it does not reveal a hidden true probability. Other margin-removal methods can allocate the adjustment differently, especially when prices are uneven.
Edge: state which reference you are using
With a 55% model estimate at −110, the edge against the raw break-even probability is about 2.62 percentage points: 55% minus 52.38%. Against a normalized 50% market estimate, it is 5 percentage points. Both calculations are understandable, but they answer different questions.
Write “percentage points” for the subtraction. A 5-percentage-point probability advantage is not automatically a 5% expected return. It is also unrelated to a spread edge expressed in points scored.
Expected value: combine chance and payoff
For a one-unit stake in a win-or-lose market, with model probability p and decimal odds d:
EV per unit = p × (d − 1) − (1 − p) = p × d − 1.
At −110, the decimal price is about 1.9091. Using a 55% model estimate gives 0.55 × 1.9091 − 1 = 0.05, or +5% expected return per unit staked. On a hypothetical $100 stake, that is an expected net value of $5 under the assumptions. The individual result is still about +$90.91 for a win or −$100 for a loss, not a payment of $5.
| Measure | Value | Interpretation |
|---|---|---|
| Model probability | 55% | Estimated chance of the selected outcome |
| Raw implied probability at −110 | 52.38% | Win-or-lose break-even threshold |
| Edge vs raw implied probability | +2.62 percentage points | Probability difference |
| Expected return at −110 | +5% | Model-based average net value per unit at that price |
Pushes, ties, and voids change the formula
If a push returns the stake, use separate win, loss, and push probabilities. For decimal odds d, net EV per unit is p(win) × (d − 1) − p(loss); a fully refunded push contributes zero net profit. Do not count a push as a loss or mix a conditional win probability with an unconditional loss probability.
Markets with partial settlements, dead heats, commissions, or special rules need calculations that reflect those rules. A basic two-outcome calculator does not automatically cover them.
Why a positive number may not be a usable advantage
The EV calculation can be arithmetically correct even when the model probability is inaccurate. Small estimation errors, stale quotes, unavailable prices, or different settlement terms can erase an apparent advantage. Use the calculators to understand sensitivity: hold the probability fixed and change the price, then hold the price fixed and vary the probability.
These examples teach the arithmetic. They do not establish an OddsRX performance record or recommend a wager.