Statistics, Probability, Randomness, Surprise: Why the Long Run Is "True" and the Short Run Is Random

In 30 seconds: James uses logic to dissect four investing words. Statistics yields only two kinds of result: a unique result = a falsifiable “true proposition”; multiple possibilities = a “probability distribution.” “Hold the US market index 20+ years and you won’t lose” is a true proposition (falsifiable, true so far); “the next 20 years might not profit” is a false proposition (unfalsifiable). And return is a probability distribution — you can only expect the distribution of however long you hold. Demanding the 20-year expectation from 5 years is a mismatch.¹

True vs. false propositions (can it be falsified?)

A proposition that a counterexample can overturn is a true proposition (believed true until falsified):¹

• “All humans need oxygen” — true (unless we find someone who lives without it).
• “All swans are white” — true until a black swan is found; one black swan falsifies it.
• “Hold the US market index 20+ years and you won’t lose” — a true proposition: go look for a counterexample (a 20+ year loss); find one and it’s falsified. So far, true.

Conversely, what cannot be falsified is a false proposition:

• “The next 20 years of the US market might not profit” — you can’t verify a claim about a non-existent future, so it’s a false proposition.
• In debate, watch whether the other side is stating a logically valid true proposition; those who argue only with false propositions “simply don’t understand logic — just walk away.”

Probability distribution: expect the distribution of your holding period

When outcomes vary, statistics gives a probability distribution — the longer the time and the more samples, the closer to the historical distribution:¹

Holding period	Annualized return distribution
25 years	7.94% – 17.24%
5 years	−5.58% – +28.76%

The common mismatch: many invest only 3–5 years yet expect a 25-year return and no losses. If you hold 5 years, use the 5-year distribution as your expectation — a 5-year loss is within the distribution; you can’t demand the 20/25-year expectation from it. This is why CLEC keeps stressing your time horizon.

Randomness and surprise

• Randomness: with insufficient samples (too short a time is insufficient sampling), events are unpredictable and orderless. High-probability events don’t necessarily happen first or keep happening; the very first draw could be the least-likely event (outside the confidence interval). Short-term market moves are random.¹
• Surprise: making a confident prediction about a random event, then getting an outcome outside it. “It will definitely rain tomorrow” and it doesn’t = surprise; “the market will definitely fall tomorrow” and it rises = surprise. But “35% chance of rain tomorrow” is a probability statement (may or may not happen), not a confident prediction.

💡 This is the logic beneath A Crash Is Your Friend and “don’t ask when it rises or falls”: the short run is random and unpredictable; the long run is a falsifiable-but-so-far-true probability distribution. Discipline isn’t gambling on luck — it’s standing on the right side of probability and lengthening time.

⚠️ Probability distributions are historical statistics and can be falsified in future (black swans). Summarized from a CLEC post for education only — not investment advice. Figures are ranges given in the source.

Footnotes

1. CLEC channel, post “Statistics, Probability, Randomness, and Surprise: logical true/false propositions and investing” (Part 1), 2026-07-10; and the “94th” essay of the same name. Sources: raw/docs/X及YouTube的貼文/0030… and raw/docs/教學資料/九十四…. ↩ ↩² ↩³ ↩⁴