# A Mathematical Explanation For Why Your Friends Have More Friends Than You

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Here’s a little exercise: make a list of all your friends. Then ask all your friends to do the same. Chances are, on average, your buddies’ lists are longer than your own. But don’t beat yourself up too quickly. The fault isn’t necessarily your own.Scientific American’s John Allen Paulos explains the simple mathematical explanation for one of life’s cruel truths:

We are all more likely to become friends with someone who has a lot of friends than we are to befriend someone with few friends. It’s not that we avoid those with few friends; rather it’s more probable that we will be among a popular person’s friends simply because he or she has a larger number of them.

Essentially, you’re more likely to be friends with a popular person because he or she has a lot of friends. So, If you calculate the average number of friends an individual has, it will be less than the average number of friends that individual’s friend has.

This social phenomenon was first observed in a 1991 scientific paper by sociologist Scott Feld titled, “Why Your Friends Have More Friends Than You Do.”

Psychology Today’s Satoshi Kanazawa provides a real-world example that helps to understand the friendship paradox:

There are 12 people who have a friend who has 12 friends, but there is only one person who has a friend who has only one friend. And, of course, there is no one who has a friend who doesn’t have any friend. Yet there is actually only one person who has 12 friends. So “12” gets counted only once when you compute the average number of friends that people have, but it gets counted 12 times when you compute the average number of friends that their friends have.

In other words, next time you’re feeling socially inadequate, just blame it on maths.

(h/t @counterparties)