Why your personal coincidences are actually statistically inevitable events

The Mathematics of Coincidence - Sarah Hart · 58:26 · Video: Gresham College · Watch at the source

In short: We often mistake rare personal experiences for supernatural signs. Whether it is matching a PIN to a bathroom code or surviving multiple lightning strikes, mathematics reveals that what feels impossible for an individual is often a statistical certainty when viewed across a sufficiently large population. You are less special than you think.

Professor Sarah Hart, speaking at Gresham College on 5th March 2024, argues that our intuition regarding probability is frequently flawed. We tend to focus on the minuscule odds of a specific event happening to us personally, ignoring the vast number of opportunities for that event to occur to someone else. This cognitive bias has real-world consequences, influencing everything from scientific research to legal proceedings.

Consider the case of Roy Sullivan, known as the human lightning rod, who survived seven lightning strikes. While the mathematical probability of one person being struck seven times is infinitesimally small—roughly one in two followed by twenty-nine zeros—this calculation assumes that every person has an equal, independent chance of being hit. In reality, geography, lifestyle, and timing create massive variations in risk. Lightning is more frequent in specific regions, during summer months, and in the afternoon. Furthermore, demographic factors play a role; for instance, men account for 84% of lightning fatalities, compared to 16% for women.

The core lesson is that while any single ticket has a tiny chance of winning the lottery, the jackpot is claimed repeatedly every year. Similarly, Hart’s own experience of her bank PIN matching a café’s bathroom code seemed like a startling coincidence. However, with 141,671 residents in York and millions of annual tourists, the math dictates that hundreds of people likely share that same four-digit code. When we widen the net from the individual to the population, the improbable becomes the expected.

Understanding these mechanics is essential for avoiding the trap of seeing patterns where none exist. By applying rigorous probability, we can distinguish between genuine anomalies and the inevitable outcomes of large-scale systems. Whether in a courtroom or a laboratory, failing to account for the sheer scale of potential occurrences leads to a fundamental misunderstanding of the world around us.

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