Implied Probability Calculator

Created by Wei Bin Loo
Reviewed by Anna Szczepanek, PhD and Steven Wooding
Last updated: Mar 07, 2023

With this implied probability calculator, we aim to help you calculate the probability of an incident happening given the odds. The implied probability helps you to understand how likely an incident is to occur if you are given the American odds for that incident.

We have written this article to help you understand what the implied probability is and how to apply the American odds to the implied probability formula to calculate the implied probability. We will also demonstrate some practical examples to help you understand the concept. You can also check out our probability calculator.

What is implied probability?

The implied probability is the likelihood of an incident happening based on a given odds. This concept is usually applied in sports betting, where the implied probability tells us the percentage of an incident occurring, given the odds shown by the bookmaker. To understand more about odds, please check out our odds calculator and moneyline odds calculator.

As the odds shown by the bookmaker usually take into account the margin that the bookmaker wishes to make, hence they might be slightly different than the true chance of the outcome. Our matched betting calculator can help you to understand more about sports betting.

How do American odds work?

American odds, also known as moneyline odds, is a type of betting odds used in sports betting. It is most commonly used in the United States and differs from decimal and fractional odds. American odds can be either positive or negative, and the number indicates how much money you need to bet in order to win a certain amount.

To calculate your winnings using American odds, if the odds are positive, you multiply your stake by the odds, and if the odds are negative, you divide your stake by the absolute value of the odds. For example, if you were to bet $100 with odds of +300, you would multiply $100 by 3 and would receive $300 in winnings. If the odds were -300, you would need to bet $300 to receive $100 in winnings.

We will talk about the calculation in detail in the next section.

How to convert American odds to implied probability?

To understand the implied probability sports betting calculation, let's take the sports bets below as an example:

  • Sport: Basketball
  • Bet: Golden State Warriors to win against Chicago Bulls
  • Odds: -150

You can calculate the implied probability of sports betting in three steps:

  1. Determine if the odds are positive or negative.

    The first step is to determine if the odds are positive or negative. In our example, the odds are -150, which is negative. This step is important as positive odds will have a different formula when compared to negative odds.

  2. Determine the odds.

    The next step is to understand the odds given. For this example, the odds is -150. An odds of -150 means that you need to bet $150 to have a chance of winning $100. If the odds if positive, let's say +200, it means by betting $100, you will have a chance to win $200.

  3. Calculate the implied probability.

    The last step is to calculate the implied probability using the American odds to implied probability formula.

    If the odds are positive, apply this formula: 100/(odds + 100).

    If the odds are negative, apply this formula: odds/(odds + 100).

    For our example, as the odds are negative, the implied probability will be 150/(150 + 100) = 60%.

    One thing to note is that even if we use the word positive / negative odds, you should always put down the odds as a positive number in the calculator. Use the dropdown menu at the top of the calculator to select between positive and negative odds.


Can implied probability be negative?

No, the implied probability cannot be negative. Probabilities can only be between 0% to 100%.

What are the positive American odds?

Positive American odds tell you how much money you would get on winning a $100 bet. For instance, if the American odds are 120, it means you will get $120 if you win the bet by putting down $100.

What does negative American odds mean?

Negative American odds tell you how much you need to bet to win $100. For example, if the American odds are -110, you will need to bet $110 to win $100.

How do I convert odds to implied probability?

You can convert odds to implied probability in four steps:

  1. Determine if the odds are positive or negative.
  2. Determine the odds.
  3. If the odds are positive, apply this formula: 100/(odds + 100)
  4. If the odds are negative, apply this formula: odds/(odds + 100)

What is the implied probability for an Americans odds of +500?

The implied probability will be 16.667%. You can calculate this using the following formula:

100 / (odds + 100)
= 100 / (500 + 100) = 0.1667 (16.667%)

Wei Bin Loo
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