What Are The Odds Of Randomly Meeting Someone You Know?

I live in Chicago, along with close to three million other meat machines, 11 million if you include the proverbial Chicagoland area. I go through periods where it’s not uncommon to run into people I know, downtown and beyond. We meet at varied places like a bus stop on State Street or walking down La Salle Avenue near the Daley Center.

Usually, I don’t owe them money.

As someone in market research, I tend to chalk these encounters as synchronicity or destiny or some other esoteric fancy.

But is it really that statistically rare to randomly meet someone you know by just walking down the street?

Research experts have already weighed in on these odds. They might seem startling, at first glance, but they make sense. Casually running into someone you know today is not that improbable.

In a Huffington Post article, Red Cup Agency founder Lee Schneider delves into statistical probabilities of meeting someone you know while on a stroll. He cites the work of Psychologist Richard Wiseman that posits we all know around 300 people by first name (and hopefully one of them isn’t Leonidas).

Schneider crunches some numbers, using New York as his walkabout basecamp:

Assume that all 300 of my friends were in New York at the same time and assume 26,402.9 persons per square mile, as per US Census data. But since I am walking, you have to calculate how many people I’d meet not per square foot, but while moving in a straight line as I walked. That would be a whopping 733.4139 people per linear mile. Since I know 300 of them, divided by the 8.2 million of New York’s population, it would follow that I’d encounter .0268 friends per mile. The chance of seeing at least one of them was about 12.7%.

For Chicago, my calculations with some variables hover a bit over five percent (and living in Chicago for more than 15 years, I certainly know much more than 300 people by first name).

I agree with Schneider when he says, “Wow.”

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Essentially, walk around enough in any medium to large city, and after some miles there is a reasonable chance you will encounter a familiar face.

A statistician employing more complex formulas, this time using San Francisco, states that the chance of meeting someone you know by walking for an hour is approximately 10%!

For you math geeks, here is the Byzantine formula (or just skip it if you are not):

The population of San Francisco is about 800,000. Let’s call it 10^6. I know perhaps 100 people in the city at any given time. There are maybe 20-50 people on any given stretch of city block. Say I walk for an hour at 3 mph and that the average block is 100m long, so I walk for 50 blocks in that time and pass on the order of 10^{3} people. If we assume people are randomly distributed (this is probably pessimistic, since I know that I spend most of my time in SF in a few places and I assume my friends tend to be somewhat similar) then I have a .9999 chance of not knowing any given person I run into. If we assume that these are independent events then I have a .9999^{1000} chance of not knowing any of those people [technical note: this is really (999900/1000000) * (9998999/999999) * …, but these numbers are large enough and we’ve made enough other approximations that we can ignore this.] .9999^1000 = .90 so if I walk around the city for an hour, I have about a 1/10 chance of meeting someone I know.

If you want another but more generic formula on “randomly” meeting someone you know, this physicist provides one. It certainly can be useful if you owe money.

Sure, more variables can be applied as well as qualitative features. If you’re not looking at people at all—like looking down at your smartphone as most do in Chicago and miraculously don’t get run over—the odds will surely decline. Furthermore, if you’re actively looking for familiar faces, the odds can increase by subconscious or conscious drives.

As an example of raising the probabilities by being aware, a statistician coldly claimed that the odds of a person meeting a future girlfriend or boyfriend were 1 in 285,000. With those numbers, it would seem everyone would be single. However, the odds mercifully increase when someone is actually on the lookout or adjusting lifestyles.

Try not to find love online only, though, as convenient as it may seem. Some scientists put it at about one percent.
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These probabilities may not exactly be all good news, beyond just owing money. Take, for example, an article in BBC News that found that the odds of meeting your boss on vacation are around 1 in 1000. That may not sound bad—until you’re in Miami trying to take a needed break from work life and your CEO strolls by you on the beach in a speedo.

I’m sure many of you are asking what this has to do with market research. Simple: market research is not immune to those esoteric fancies I mentioned. We get bogged down on accepted axioms. At qSample, we have spent energy and resources providing sound data that might go against the proverbial grain. Some examples:

Trap questions are reliable for surveys
Sex sells for advertising and marketing
Long questionnaires will provide good data

In the end, we feel these insights provide better research for clients. So consider this a reminder to keep following the data (or at least stop looking at your phone while crossing Wacker Drive).

I fully understand different statistics influence variables, especially when it comes to meeting or avoiding certain people in this world. Nonetheless, entertaining this too much can lead you down a Google labyrinth or open manhole if you’re on your phone. The gods invented baseball to get obsessive over statistics.

The point is maybe it’s better to look up from your WhatsApp while heading to the train, enjoy the exercise, and don’t be that surprised to meet someone you know today.

Even if it’s your boss in a speedo.

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