It’s one of those things we all do. We’re on a friend’s Facebook wall, and we glance at their friend’s list. Six-hundred-and-Twenty-Seven? Seriously? We click through a few more friends’ walls. It’s hard not to jump to the obvious, ego-bruising conclusion: We—with our mere 212 friends—are losers. We’re social pariahs. No wonder we’re at home on-line, instead of out doing… well, whatever people with 627 friends do.
But here’s the weird mathematical fact: Almost everybody’s Facebook friends have more friends than they do.
David Hemenway, professor at the Harvard School of Public Health, highlighted a set of problems in a 1982 Mathematics Magazine article that have come to be called the “class-size paradox.” Here’s how the paradox works: A university might claim an average class size of 20 students. That is, if the enrollment numbers of all the classes are added together, then divided by the number of classes, the average turns out to be 20 students.
But, counter-intuitively, any individual student will almost certainly experience an average class size much larger than that. This is because the huge variance in class sizes leads larger classes to be disproportionately represented in the students’ experience. Some courses are assigned to small seminar rooms that hold, say, a dozen students. But other courses are assigned large auditoriums that might hold as many as 300. Those larger classes will be overrepresented in student experiences—after all, 300 students experience the class of 300, while only 12 students get to experience the class of 12.
At the risk of sounding silly, I’ll put it another way: A lot of people go to the beach on days when a lot of people go to the beach; fewer people go on days when fewer people go; and nobody’s there when nobody’s there. Because of this, most people will think the beach is, on average, much more crowded than it really is, on average.
The actual average for my friends’ number of friends turned out to be a whopping 467—or more than three and a half times what Facebook statistics would lead me to expect.
According to Facebook’s own statistics, the average user has 130 friends. I personally have 346, which should make me feel incredibly popular. But when I look at how many friends my friends have, 346 seems far below average.
So I did the math. I went through all my Facebook friends and tallied how many friends each had. Only 40 of my friends had 130 (the actual Facebook average) or fewer friends. The other 306 had more. My friends’ friend-counts ranged from Robert, who had 14, to John, who had 4,999. (Facebook allows 5,000 friends, so one of you can still jump on the John bandwagon.)
The actual average for my friends’ number of friends turned out to be a whopping 467—or more than three and a half times what Facebook statistics would lead me to expect. This is because Robert, with his 14 friends, shows up on only 14 friend lists. Whereas John shows up on 4,999 friends lists and makes all those people feel less popular. I’m 357 times more likely to be friends with John than I am with Robert. In this way, our list of friends tends to fill up with people who have more friends than we do—and we end up feeling unloved.
So take heart. You’re not the Facebook loser you think you are.
Unless, of course, you’re Robert.