I have a challenge for you. I was on a plane from Denver, my home, to Nashville to visit a college friend. She and I were roommates at a college in Nashville.
I was born in TN and moved to CO at age 23. I was in the center seat on the plane with a man next to me. We did not speak and were caught up in our books/computers/earbuds.
As we were descending into Nashville, we were told that we had to divert due to a weather event. The atmosphere in the cabin changed to something more relaxed, as so often happens when a diversion occurs from what is expected. At this point, this fellow and I began a conversation. I will stress here that if we had landed, said conversation would have never taken place.
The guy was from a city further west from Denver and had made a connection there. He was, at it turns out, flying into Nashville as his final destination, as I was. As we spoke, he told me that he was attending a funeral in a town not too far from Nashville. When asked which town (remember, I am from West TN), he told me the funeral was to be in a tiny town called Selmer. Selmer is actually about a 2 hour drive from Nashville.
I turned to him, astonished. I have an aunt, uncle and cousins who have basically lived in Selmer their whole lives. Wow, what a coincidence! But it gets better.
As we talked, he mentioned that he would be taking the ashes of the deceased to be scattered at a lake nearby, about an hour’s drive from Selmer. When I asked where this would be, I was floored by his answer. The lake and town to which he would be traveling with the ashes was Savannah, TN and Yellow Creek, a dammed area of the Tennessee River.
I graduated high school at Central High School in Savannah in 1981 (i only lived in Savannah for 4 years, mind you) and my extended family owned a small vacation home on Yellow Creek.
Okay, Skepticality, what are the odds?
Below are the extended notes provided by statistician and podcaster Kyle Polich for use in Skepticality Episode 272. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.
(Kyle studied computer science followed by artificial intelligence in grad school with a focus in probabilistic reasoning and planning. His general interests range from obvious areas like statistics, machine learning, data viz, and optimization to data provenance, data governance, econometrics, and metrology. He enjoys exploring the intersection of statistics and skepticism and sharing related insights with others including through his podcast Data Skeptic. Visit Kyle’s blog Data Skeptic, and give the podcast a listen.)
Christie’s new acquaintance from the flight happens to mention his destination is the town of Selmer, two hours drive from their landing city of Nashville. He goes on to reference two other small towns, also within two hours of Nashville, to which Christie also has a connection.
Determining just how crazy these odds might be requires an understanding of how connected we are as people. I, for example, live in Los Angeles, California. I know people who live in Santa Monica, Culver City, Hollywood, Monterey Park, La Habra, Studio City, Pacific Palisades… I don’t know anybody from Malibu… anyway, what percentage of towns within two hours drive of me do I have a connection to?
I wrote a program that looks up that list of cities for any input. I generated a list of cities near a few of my friend’s homes and I asked them to tell me which municipalities they had some connection to. From this, I could come up with the frequency that people I know have a connection to cities near them.
To my surprise, I got extremely varied results. Some people had a connection to as few as 5% of nearby cities, while my highest scoring participant claimed to be connected to 70% of nearby municipalities.
Given my wide variety of results, I want to turn the tables on you, the listener. Guess for yourself, what percentage of municipalities within two hours of your home do you have a connection to? 10%? 50%? Think about it, and come up with a percent. Once you’ve got it, imagine you have a coin. But this coin is a weighted trick coin which comes up heads as often as your percent. So if you have few connections to nearby cities, say 1%, then on average, only 1 toss out of 100 is expected to be heads. Hang on to your imaginary coin, we’re going to be flipping that in a minute.
As far as we know, the gentleman in our story called out three cities in a row that Christie had a connection to. This is the equivalent of getting three heads in a row on your imaginary coin. That being the case, we can apply some basic binomial probability to this situation.
If you are connected to only 1% of nearby cities, than your odds are exactly one in a million. But I think that’s extreme. Most people are connected to more cities than that, especially in areas they grew up in. I have a connection to 40% of the cities within 2 hours of where I grew up near Chicago, so for me, the odds of 3 hits in a row are exactly 6.4%. And for anyone connected to only 10% of nearby cities, the odds drop to 0.1%.
So the exact degree of craziness in these odds relies entirely on how connected we are to people in cities that are around us. The less connected we are, the more surprising. I think assuming people are connected to 10% of the places within 2 hours of them sounds conservative and reasonable, so by that frequency, the chances are a bit small at 0.1%, or one chance in a thousand.