Coincidences and Miracles

Statistically improbable events are not just possible but expected when the sample size is large enough. With 7 billion people on earth, million-to-one coincidences happen thousands of times daily. We notice and remember the hits (the friend you were just thinking about calls) and forget the misses (the thousands of times you thought of someone who didn't call). Bevelin emphasizes that our intuition about probability is fundamentally miscalibrated for large numbers—what feels miraculous is often mathematically inevitable.

When to use it

When a coincidence seems meaningful or supernatural; when 'miraculous' events are cited as evidence for a claim; when evaluating streaks, clusters, or patterns that seem too unlikely to be random; when tempted to find causal explanations for what may be statistical inevitability.

How it can help

When something seems like an extraordinary coincidence, ask: given the number of opportunities for this to happen, how likely was it that it would happen to SOMEONE? The birthday paradox is the classic example: in a group of just 23 people, there's a 50% chance two share a birthday—because there are 253 possible pairs. Before attributing meaning to coincidences—in business, markets, or personal life—calculate whether they're actually unlikely given the sample size.