You're Not As Unpopular As You Thought, Says Math


Dr. Katie Spalding


Dr. Katie Spalding

Freelance Writer

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory.

Freelance Writer

Using math, researchers take the friendship paradox out of the statistical averages and into the real world. Image credit: Dean Drobot/

With a few notable exceptions, math isn’t known for its ability to make us feel good. Not only is it sometimes taught in a way that makes us feel like we'll never get it, but it then has the gall to tell us things like “gambling on 50/50 odds will lead to you losing everything you have” and “life is meaningless and the universe is uncaring”.

As if that wasn’t bad enough, math has for a long time been telling everybody we’re uncool. And not just in the “nobody likes a math nerd” way that your seventh-grade bully meant it – in the “you’re unpopular and here’s a peer-reviewed paper to prove it” way that sociologist Scott Feld indicated in his famous 1991 paper "Why Your Friends Have More Friends Than You Do".


But according to a recent paper published in the Journal of Complex Networks, you might not be as much of a social pariah as previously thought. Although it’s true that Feld and subsequent scientists found that on average our friends are more popular, better looking, and richer than us – dubbed the "friendship paradox" – real-life turns out to be a bit more nuanced.

"Standard analyses are concerned with average behavior, but … average results [could] be skewed by a few outliers," lead author George Cantwell explained. "To get a fuller picture, we studied the full distribution describing how people compare to their friends – not simply the average."

The friendship paradox, or the idea that your friends have more friends than you do, isn’t actually much of a paradox at all. Basically, it comes down to the fact that you’re more likely to be friends with a popular person than an unpopular person. That’s not because they’re nicer, or cooler, or have a pool in their back yard – it’s just because you have more opportunity to be one of 50 friends than one of two.

So, for instance, in this diagram, using data from Feld’s original 1991 paper, you can see that five of the seven people in the friendship network have fewer friends than their friends do on average. Just two people – the super-popular Sue and Alice – have more.

Number of friends is given outside of parentheses, average number of friends of friends is given in parentheses. Image credit: Data from Feld, 1991, The American Journal of Sociology, graphic by IFLScience

So that’s why it works in theory. But in the real world, the team found that things work a little differently. Popular people, for instance, tend to hang out with other popular people. Loners are more likely to be friends with other loners. And in the age of social media, some people have friendship groups that number in the hundreds.

"This has a tendency to magnify the effect," Cantwell explained. "While there are surely other effects at play, around 95% of the variation within social networks can be explained by just these two."

We should "be wary of impressions we get about our success and social status from looking at the people around us because we get a distorted view," he continued. "In the offline social world, the bias is partially mitigated by the fact we tend to end up around similar others. On online social media, however, the effect can be exacerbated—there's virtually no limit on the number of people who can follow someone online and no reason to only look at 'similar' people."

So we don’t need to worry about being unpopular after all – the math says we’re probably not. Or, at least, we might be, but at least our friends are too.

 This Week in IFLScience

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