The Problem and Promise of Probability

Probability Density Function for the normal curve

Many people believe that randomness , chance and probability provide the best explanations for coincidences. Their belief is strongly supported by an almost unassailable axiom: In Large Populations Low Probability Events Must Happen.

In his book The Improbability Principle, statistician David Hand explains that “with a large enough number of opportunities, any outrageous thing is likely to happen. No mysteries are required to explain [coincidences]—no superstitions, no god. All that’s needed are the basic laws of probability.”

Another way of saying this: the reason we witness so many low probability events is that we are involved with an unimaginably large number of events.

Our statistician is performing a sleight of Hand.

By definition, coincidences are unlikely, low probability events.   Unlikeliness characterizes meaningful coincidences. Hand is trying to tell us that a defining characteristic of coincidences, low probability, explains their occurrence. That is like saying that I am a human being and I have a body. My body fully explains my behavior.

Statisticians could begin with categorizing coincidences by degrees of probability. Some coincidence groups are just more improbable than others.  According to data from the Weird Coincidence survey thinking of someone and receiving a text message, email or phone call from that person is one of the most common coincidences. Why? Because we send so many texts and emails, and make many phone calls. And we often think about people. Two lines—the communication lines and the thoughts-about-people lines will sometimes intersect at the same person.

The frequency of messaging and the frequency of thinking about other people are base rates—the basic rate of occurrence of the event.  The higher the base rate, the more likely a coincidence involving that line of life will happen. People are pretty good at intuitively estimating the probability of a coincidence.  Hopefully, we can elicit the help of statisticians in determining the varying probabilities of different classes of coincidences. The ones with very low or indeterminate base rates further raise the possibility of exploring other explanations for their occurrence.

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