# Implied probability

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Canonical: https://novigapi.com/learn/implied-probability

Implied probability is the chance of an outcome that a set of odds suggests, and it is also the win rate you need to break even at that price.

```
decimal: q = 1 / d; American negative: q = |A| / (|A| + 100); American positive: q = 100 / (A + 100)
```

Implied probability converts a price into a percentage. Odds of +150 imply a 40% chance; odds of -200 imply 66.7%. The number answers one practical question: how often does this bet have to win for me to break even? If you think an outcome happens more often than its implied probability, the price is worth taking. If less, it is not.

## How it works

Every odds format can be turned into a probability. Decimal odds are the simplest: divide 1 by the decimal price. For American odds, a negative number tells you how much you stake to win $100, so the probability is the stake over the total return. A positive number tells you how much a $100 stake wins, so the probability is 100 over the total return. Fractional odds a/b become b / (a + b).

## Worked example

Implied probability by price

| American | Decimal | Implied probability | Novig price |
| --- | --- | --- | --- |
| -200 | 1.500 | 66.67% | 66.7% |
| -110 | 1.909 | 52.38% | 52.4% |
| +100 | 2.000 | 50.00% | 50.0% |
| +150 | 2.500 | 40.00% | 40.0% |
| +300 | 4.000 | 25.00% | 25.0% |


For -110: 110 / (110 + 100) = 0.5238. For +150: 100 / (150 + 100) = 0.40. For decimal 4.00: 1 / 4 = 0.25. The [implied probability calculator](https://novigapi.com/implied-probability-calculator) does these conversions for any format, and the [odds converter](https://novigapi.com/odds-converter) goes in the other direction.

## Implied is not fair

A sportsbook's implied probabilities include its margin. A -110/-110 market implies 52.38% on each side, 104.76% in total. To get a fair probability you have to remove that excess, which is called devigging. Implied probability tells you the break-even rate for a specific bet; the fair probability tells you what the market actually thinks.

## On Novig

Novig shows prices as percentages, so the implied probability is printed on the screen. Buying Yes at 40% costs $0.40 for every $1.00 it pays if it wins, so you break even if Yes wins 40% of the time. Two adjustments apply. The price you can buy at is the ask, which is 1 minus the best bid on the other side. And on live game markets, the taker fee of 0.06 x P x (1 - P) per contract raises your effective break-even: at 40% the fee is $0.0144 a contract, so your break-even becomes 41.44%. The [Novig odds converter](https://novigapi.com/novig-odds-converter) shows the fee-adjusted figure.

## Common mistakes

- Adding the implied probabilities of a market and expecting 100%. A sportsbook's always add to more.
- Confusing the implied probability of a parlay with the product of fair leg probabilities. The book's parlay price compounds the margin on each leg.

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