If you have found your way into my little corner of the interwebs, then you are looking to understand analytics better. Understandably, you would prefer not to become a data scientist to achieve that understanding. However, there is one concept you must understand that causes most people to break out in a cold sweat. That’s why, in this article, I’ll be giving you a mostly harmless introduction to probability.

Events and Trials in Probability

Two key ideas you need to make sense of probabilities are trials and events.

Trials are the things that happen and whose outcomes you are interested in. For example, if 1,000 people visit an e-commerce website, there are 1,000 trials for purchases.

Events are the actual outcomes you observe resulting from a trial. In our e-commerce example, the outcomes for each visitor are either purchase or no purchase.

Note that in every trial, there is always an event (i.e., and outcome). The potential outcomes of a trial should be mutually exclusive, meaning each trial results in only one event (e.g., purchase or no purchase).

Understanding the concepts of trials and events, you’re ready to tackle an introduction to probability.

What is Probability?

Many people have an intuitive idea of what probability is. This is true even if they use terms like chance, likelihood, or odds.

To be as clear as possible, probability is a measure of certainty. Specifically, you want to know how certain a specific event is over multiple trials.

How often do you expect to see that event?

The probability of an event is simply the total number of events that happened divided by the number of trials performed.

On our e-commerce site, if 100 people make purchases out of 1,000 people who visit the site, then the probability of a purchase is:

Strictly speaking, probabilities are shown as proportions ranging between 0.0 and 1.0. However, it is often easier for us to think about them as percentages from 0% to 100%.

In the example above, the probability of a purchase is 10%.

If you are looking for a simple way to interpret a probability, consider it to be the percentage of times you expect to get a certain outcome event.

One of the most common uses for probability is in marketing and sales. The e-commerce example above represents a simple conversion rate in e-commerce.

Probability and Odds

Knowing the basic form and interpretation of a probability, you are now prepared to understand odds.

Odds compare the probability of an outcome event happening to the probability of that same outcome event not happening.

Continuing our e-commerce example, the probability of a purchase is 10%, while the probability of no purchase is (900/1,000) = 90%, or (1-P) = (1 – 0.10) = 0.90.

The odds of a purchase is therefore (10%/90%) = 0.11. You could also say the odds are 1 to 9 against a purchase.

Odds that are below 1 indicate the outcome event (i.e., purchase) is less likely than some other outcome event. Odds greater than 1 indicate that the outcome event is more likely than others.

The most important aspect of odds to note is that while probabilities fall between 0 and 1, odds can be any positive value. This is an important feature that makes analyzing probabilities computationally easier.

The most common place people see odds is in sports betting. If the odds are 3-2 for a team to win a game, then betting $10 will provide you a profit of (3/2) x $10 = $15, plus your original $10 back (if they do indeed win).

Probability in Practice

You might still be wondering, “Why does any of this matter, Rob?”

The answer is that in analytics, the interpretation of your results will frequently hinge on the interpretation of a probability. Additionally, there will be occasions when results will be expressed as odds or odds ratios.

For example, statistical tests are reported with a probability indicating how certain you are that the findings from your data are different from zero.

Additionally, if your analysts work with binary outcomes, the results may be expressed as changes in the odds of an event occurring (not the change in probability).

For these reasons, understanding the concepts of probability and odds is fundamental for moving forward.

Conclusion

There is your mostly harmless introduction to probability. My goal was to introduce the concept in practical terms. And we’re avoiding a more technical (i.e., mathematical) treatment of probability theory. After all, who cares how many blue marbles there are in the bag anyway?

You may want to bookmark this article. As you learn more about analytics, you may need a quick reminder on how to read probabilities and odds. This will be a good quick reference for you.