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Coincidences and the law of truly large numbers

Every so often a market produces something that feels too unlikely to be chance: a long shot wins at the last minute, a price jumps just before news breaks, or a trader seems to call event after event. Sometimes there is a real explanation. Often there is not. This SoftCta guide explains why coincidences are more common than intuition suggests and how to read them.

The law of truly large numbers

In a 1989 paper, statisticians Persi Diaconis and Frederick Mosteller described the law of truly large numbers: with a large enough sample, any outrageous thing is likely to happen. A one-in-a-million event happens to roughly 330 people a day in a country of 330 million if everyone has a daily chance. When there are many markets, traders and days, rare things will occur somewhere regularly.

The birthday problem

In a room of 23 people, the probability that at least two share a birthday is just over 50%. The result surprises people because they think about matching their own birthday, which is unlikely, rather than about the 253 possible pairs in the room. Many market coincidences work the same way: the question is not whether this specific thing would happen, but whether something striking would happen somewhere.

Look-elsewhere effects

If you scan hundreds of markets for an unusual price move, you will find some. Physicists call this the look-elsewhere effect; statisticians call it the multiple comparisons problem. Our guide on spurious correlation explains the same issue for indicators. Before treating a pattern as meaningful, ask how many places you would have looked and how many patterns would have counted as surprising.

Streaks and track records

A trader with a run of correct calls may be skilled, or may be one of many people whose lucky streaks are being noticed. Our guides on hot hand and streak fallacies and narrative fallacy cover the stories that attach to such runs. Survivorship plays a role too: the people who lost after similar calls are rarely profiled.

When a coincidence is worth checking

Some coincidences do point to something real. Price moves immediately before an official release can reflect leaks, which venues address in their integrity rules. The test is whether the pattern repeats, whether it has a plausible mechanism and whether it holds up against a base rate of similar events. One striking case is a reason to look, not a conclusion.

Pricing first-time events

The same thinking helps with events that have never happened. Something unprecedented in one market may be routine across a larger reference class. Our guide on the rule of succession explains how to price such events without assuming zero.

A reading habit

When something feels too unlikely to be chance, write down how many comparable opportunities existed, what a base rate would suggest and what further evidence would confirm a real cause. Convert prices with the implied probability tool and verify live prices on the venue before acting on a story.

Primary sources SoftCta readers open

• Diaconis and Mosteller, 'Methods for Studying Coincidences' (1989)
• Introductory probability texts on the birthday problem
• Venue market listings for counting comparable markets
• Statistical literature on multiple comparisons

Reading the quote step by step

• Read the full title and rules, including the named settlement source and the time zone.
• Convert the Yes and No prices to implied probabilities and note the gap between them.
• Subtract fees and spread to see the effective price you would actually face.
• Write your own probability range and the evidence behind it, then compare.
• Check related and near-duplicate markets on other venues for consistency.

Closing SoftCta checklist

• Re-read the venue definition in your own words before reacting to a price.
• Convert prices with fee and spread awareness; verify live cents on the operator.
• Prefer primary settlement sources over secondary headlines and social summaries.
• Treat ChanceWire hubs, movers, and tools as orientation — not order entry.
• Confirm age, location, and product eligibility; SoftCta pages will not suggest location spoofing.
• If clarity is incomplete, watching is a complete SoftCta outcome — no pick-selling urgency required.

SoftCta habits

• Write your own probability range before checking the crowd price.
• Prefer dated primary sources over social summaries.
• Compare related markets when a single book looks extreme.
• Size curiosity with fees and depth in mind; substantial risk of loss.