How to Calculate Odds (Definition and a Step-By-Step Guide)

By Indeed Editorial Team

Published May 16, 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Determining odds is a statistical technique you can use for forecasting and data analysis. In epidemiology, odds are a mathematical calculation that allows you to determine the likelihood and degree to which a disease may spread. Learning to calculate odds can help you understand more about the spread of disease, which can inform health policy decisions. In this article, we define odds, explain why they're important, discuss how to calculate them, and examine the differences between probability and odds.

What are odds?

Odds are a numerical representation of the probability of a specific outcome. You can measure them as the ratio of occurrences that result in the desired outcome to those that do not. In gaming and statistics, odds are usually necessary. Calculating odds is a mathematical concept that is similar to, but distinct from, calculating probability. Odds quantify the likelihood of an event resulting in a positive or negative outcome. You can express this number as a ratio (1:4), fraction (1/4), decimal (0.25), or percentage (25%).

Determining odds also involves considering other aspects of a situation, such as the total number of possible outcomes and the method by which you can determine them. When calculating odds, it's important to consider as much information as possible, since this leads to more precise findings. In medicine and disease prevention, it's critical to understand the relative frequency of recurrence of an event, such as a disease, in comparison to another variable, such as medical history or an individual health trait.

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How to calculate odds

Here are steps you can take to calculate odds:

1. Decide the number of favourable outcomes in a given circumstance

The first step is to decide what your favourable outcome is and determine how many possibilities it may have. For example, in the case of rolling a six-sided die, you can wager what number the die may show after you roll it. Assuming you bet that you may roll a three or four, there are two possibilities where you win. If the die shows a three, you win, and if it shows a four, you also win. In this example, there are two favourable outcomes.

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2. Decide the number of undesirable outcomes

In any game of probabilities, there may always be a chance that you won't win. Determine the number of outcomes that can cause you to lose. In the dice example, if you wager that you may roll a three or a four, you lose if you get a one, two, five, or six. Given that there are four possible ways for you to lose, there are four unfavourable outcomes.

Another way to understand this is the sum of all possible outcomes minus the sum of all possible favourable outcomes. There are a total of six potential outcomes when rolling a die, one for each number. In the case of the die, we can then deduct two (the number of desirable outcomes) from six. Six minus two is four, the number of unfavourable outcomes. Likewise, you can calculate the number of favourable results by subtracting the number of unfavourable outcomes from the total number of outcomes.

3. Express the odds in numbers

You can express odds as the ratio of favourable to unfavourable events by separating both numbers with a colon. In our scenario, the odds of success are 2:4, with two possibilities of winning vs. four chances of losing. As with fractions, you may reduce this to 1:2 by multiplying both terms with the common multiple of two. You can verbally express this ratio as "one to two odds."

You may decide to express this ratio numerically. In this instance, our odds are 2/4 or 1/2. Note that these odds do not indicate we have a 50% probability of winning. There is a one-third probability of winning. When expressing odds, keep in mind that they represent a ratio of favourable to unfavourable outcomes, not a numerical assessment of the likelihood to win.

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4. Learn how to calculate odds against an occurrence taking place

The 1:2 odds you calculated in the example are an expression of the probability of you winning. To find the odds against you, simply reverse the ratio; 1:2 becomes 2:1.

When you compute the odds as a fraction, the chances against winning are 2/1. As previously stated, this is not an indication of your risk of losing, but rather the ratio of undesirable to desirable events. If it were an expression of your probability of losing, you would have a 200% probability of losing, which isn't possible. Two chances to lose and one chance to win equals two losses divided by three possible outcomes, which is 0.66 or 66%, so in actuality, you have a 66% probability of losing.

Formula for calculating odds

One major sector where calculating odds is vital is the medical sector. Medical professionals use their knowledge of odds ratios to ascertain if a certain exposure results in an increase in risk factors for other outcomes. In these variables, exposure refers to the period during which an individual is at risk of contracting a disease or ailment. They can use the following formulas to determine the probability of occurrence of a certain event, such as a disease or disorder:

N = A+B+C+D

OR = (AD) / (BC)

Where:

  • N is the total number of participants in the study, sometimes referred to as the sample size.

  • OR denotes the probability of a specific event occurring.

  • A denotes the total number of instances exposed.

  • D denotes the total number of unexposed non-cases

  • B is the total number of non-cases exposed.

  • C denotes the total number of cases that remain undiscovered.

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When is it important to calculate odds?

When scientists investigate viruses and other infectious diseases, such as the common cold or influenza, it's critical for them to calculate probability. This enables them to educate the public about the risks of diseases, establish strategies to resist their spread, and protect themselves. Calculating the probability of contracting an ailment also assists specialists in preparing for future situations in which a disease becomes common and the public seeks advice from health professionals.

Additionally, determining odds ratios for reoccurring illnesses enables researchers to create ideas for disease prevention. Scientists can also compute the odds ratio to account for the transmission of particular diseases across vaccinated and unvaccinated populations. This information enables researchers to give helpful counsel in times of rapid disease transmission. For example, experts studying the influenza virus can categorize the likelihood of catching the illness into four groups, which assists them in planning for future iterations of the disease:

  • Individuals that came into contact with the virus and contracted it

  • Individuals who came into contact with the virus but didn't contract it

  • Individuals who avoided contact with the virus and didn't contract it

  • Individuals who were not in direct contact with the virus but contracted it

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Probability vs. odds

You can distinguish between probability and odds in a variety of ways. Probability, for example, commonly appears as a percentage, while odds may appear as a fraction or ratio. Another distinction is that probability employs a range that is limited to the integers zero and one, whereas odds employ an infinite range. Probability and odds also need different types of data, since probability considers all possible outcomes of an event, whereas odds require comparing the number of favourable outcomes against the number of probable unfavourable outcomes.

Example of odds

Here is an example of how to use odds:

"Nadia works in an environment where she and her coworkers share a common workspace. She observes that many of her coworkers are exhibiting cold-like symptoms this month and taking sick days to recover. While Nadia has not yet experienced a cold, she is curious about the likelihood of contracting one based on how many of her coworkers have taken sick days in the last month.

Nadia's office has a total of 50 employees, and she observes that 13 of her coworkers have displayed symptoms of a cold and taken a sick day in the last month. Nadia may use the odds method to determine her chances of acquiring a cold, which looks like this: O = 13 / (50 - 13). Consequently, Nadia determines that her odds of contracting a cold are 13/37 or 13:37, depending on the number of her colleagues who have contracted it."

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