Ever have one of those days? You know what I’m talking about. A day when…

- You are running late to work in the morning and you have an important meeting to attend.
- An unforeseen rainstorm drenches you on your way from your car to the office.
- You just received an email from the IRS saying that you owe them thousands that must be paid immediately.
- You get a text from your kid saying that your cat has been thrown up in three rooms in the house.
- You can’t find your phone anywhere, which, of course, has implications for everything in your life.
- You can literally feel your stress levels rising above where they normally are.

Ever have a day when you just wished you’d stayed home and crawled up into a ball?

Sure, you’ve been there. We all have.

As someone who has taught courses in statistics at the college level since 1996, I’m here to tell you that there is a very powerful and important concept that is commonly used by behavioral scientists which should give you reason for hope even at life’s most difficult times.

Normal Distribution: Most scores are expected to be close to the average (AKA, “mean”)

Source: Wolfgang Kowarschick

### What Is Regression to the Mean?

Developed in the UK back in the 19th century by Sir Francis Galton, *regression to the mean* is a concept that is partly rooted in something that we call the *normal distribution*,

The normal distribution, often called a *bell-shaped curve*, is a mathematically-derived probability distribution that characterizes an extraordinary proportion of variables in the natural world. The guts of the normal distribution essentially are this:

- Most scores on some variable tend to be near average.
- There tend to be as many scores above the mean (ie, the average score) as there are scores below the mean.
- Very few scores can be expected to be much above or much below the mean.

For various reasons (as described in my and Sarah Hall’s book, *Straightforward Statistics** ^{1}, *variables across all kinds of phenomena tend to be normally distributed. Here are some examples:

**Temperature.**In the natural world, temperatures in any given region on a particular day tend to be normally distributed (eg, in upstate New York in the middle of June, you can expect high temps to probably be in the 80s, but they could easily be in the 60s, 70s, 90s, or even 100s.**Lifespan of Animals.**If you have a golden retriever, you can expect it to live about 12-14 years. But it might, unfortunately, pass away earlier. Or you might get lucky and your dog might live for nearly 20 years. But on average, you can generally expect a lifespan that is close to average.**Personality Traits.**Most personality traits tend to be normally distributed. So if you are going to meet someone new and you are not sure, for instance, how extraverted (or outgoing) they are, your best bet is that they are average on this one. The same goes for most behavioral traits. You may well be wrong in your expectations, but assuming average is usually—probabilistically speaking—a good start.

This same reasoning applies to such broad-reaching phenomena such as:

- How much snow to expect this winter.
- How much you’ll pay for a pint at a new pub.
- Your time in your next 5K race.
- Your heart rate at your next doctor’s visit.
- The price of a bag of dog food.
- Your high school GPA.
- Your salary.

The basic idea of ”regression to the mean” is that when you are dealing with normally distributed variables, because scores near the mean are highest in probability, you can generally expect that, on average, most scores on most dimensions in your world will be near the mean on those dimensions.

Of course, exceptions abound. In a normal distribution, there are, in fact, scores that are “toward the tails,” or that are relatively extreme. But given the nature of a normal distribution, such scores tend to be relatively rare.

When Galton developed the idea of ”regression to the mean,” he was specifically referring to predictions of scores. He basically said that, all things being equal, you should predict scores that tend to be near the mean of the relevant variable. And when things are not close to the mean, we can expect future scores to “regress toward the mean.” For instance, if two very tall people have a child, the expectation, statistically speaking, should be that the child’s height will likely be somewhere between the height of the parents and the average height for the relevant population.

### How Regression to the Mean Can Provide Much-Needed Perspective

The next time you’re having a bad day, think about regression to the mean. Sure, you may have been late to work today, but that is not typical, and you can expect that tomorrow you’ll arrive at your normal time. You might feel very high levels of stress today, but you can expect your stress levels to decrease toward your personal mean. And it might be raining cats and dogs today, but, simply based on the concept of regression to the mean, even before checking your weather app, you can reasonably guess that tomorrow will likely have some nice rays of sunshine for you.

Regression to the mean is a real and very powerful statistical concept that can be useful in helping us understand ourselves and the world around us in positive and profound kinds of ways.

Life is not all peaches and cream. We run into stressors of all shapes and sizes on a regular basis. Understanding the concept of regression to the mean can help. *On average, things tend to gravitate toward average*, There’s an important truth about life right there.

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Source: Joe Haupt / Wikimedia Commons

So if today is miserable, for any number of reasons, think about the classic lyric from the Broadway musical “Annie”: “The sun’ll come out, tomorrow…”

On average, by chance alone, based on the powerful statistical principle of regression to the mean, Annie is probably right. Think about that. And try to have a great day.