A portal · program P3 · the ground becomes a network

Drawn by Nothing

Four famous effects in this place are what pure chance draws for free. Set every real cause to zero and the headline pattern is still there. The fifth is the inverse — too clean for chance. The control you forgot to run.

A pattern is not evidence until you have asked the one question the eye never asks on its own: what would pure noise have drawn here anyway? The answer is humbling. A great many of the most-shared “findings” about people, sport, language and intelligence are reproduced — exactly, down to the curve — by a model with no real effect in it at all. Not approximately. The actual shape, from nothing.

This is a combine: four layers of this place each draw a famous effect out of pure randomness, and a fifth points the same lens the other way. None of the five states the load-bearing thing alone — that they are one move. Below, each one is an instrument you can operate. Every number on the page is recomputed in your browser by the same code that the offline verifier runs (research/drawn-by-nothing/verify.mjs, 35/35), so what you see is what is checked.

EFFECT 1 — PSYCHOLOGYThe Dunning–Kruger scissors, from a coin toss of skill

The most-reproduced chart in pop psychology: the least able wildly overrate themselves, the most able are modestly unsure, the two lines crossing like scissors. Below, the dial ρ is the real link between how good you are and how good you think you are. Pull it to zero — sever skill from self-belief entirely — and the scissors refuse to leave. Two ordinary facts draw them: people cluster their guesses near the middle (so the worst look over-confident, the best under-confident — regression to the mean), and the chart plots a quantity against a copy of itself.

real skill → confidence link ρ = 0.00

EFFECT 2 — SPORT & PROBABILITYThe hot hand, from a fair coin

For 33 years the “hot hand” was the textbook cognitive illusion — until 2018, when the famous debunking was found to be running a biased estimator. Here is the bias, with no basketball in it: flip a fair coin, then look only at the flips that came right after a head. On average, fewer than half of them are heads. Nothing is wrong with the coin. Conditioning on “after a head” quietly throws away the heads that have no flip after them, and the survivors lean tails.

The exact expectation, by enumerating every possible sequence (no simulation):

flips in a sequence	after-a-head fraction	bias

EFFECT 3 — NETWORK SCIENCEYour friends are more popular than you — and nobody arranged it

On average, your friends have more friends than you do. It sounds like a sad fact about you; it is a flat fact about sampling. When you list friends-of-friends, popular people get counted once for every friend they have, so you are weighing the room by popularity. The gap is forced: it equals the variance of the friend-count divided by its mean, which is zero only when everyone has identical popularity. Below is a real network — Zachary’s karate club, 34 people, 78 friendships — and a structureless random graph for contrast. Both show it.

EFFECT 4 — LINGUISTICSA monkey at a typewriter writes Zipf’s law

The deepest-looking regularity in language: the most common word is about twice as frequent as the second, three times the third — a straight line on a log-log plot, Zipf’s law, long read as evidence of something profound in the structure of language. But a monkey mashing M equally likely letters and a space bar draws the same line, and the slope is no mystery: s = 1 − ln(1−p)/ln M, derived in closed form. With 26 letters and a realistic space rate it lands at s≈1.06 — right on top of real English. The straight line is not the linguistics. The linguistics is in the deviations the monkey can’t make.

letters in the monkey’s alphabet M = 26 chance of hitting the space bar p = 0.18

THE TURN — GENETICSThe same lens, reversed: data too clean for chance

If noise draws so many “effects,” is the lesson that nothing is real? The opposite. The null model is not a wrecking ball — it is the yardstick. Build the distribution of what honest chance produces, and you can catch the thing that lands outside it. Mendel’s pea counts are the classic case: in 1936 Fisher showed they sit too close to the predicted 3:1 ratios — closer than honest counting allows. Below, honest re-runs of Mendel’s whole program build the null distribution of the goodness-of-fit statistic; Mendel’s real result sits far out in the impossibly-tidy tail.

The one move

Four effects, four fields, one mechanism: a quantity was measured against itself, or a sample was drawn by a rule that favoured exactly what the pattern then “revealed,” or a tally was conditioned on its own outcome. In each, the famous shape is present in a world with no real effect at all. The fifth runs the projector backwards: the very distribution that manufactures the illusions is what convicts a real anomaly.

The claim none of the five states alone: a pattern is not evidence until you subtract what pure chance draws for free — and pure chance draws astonishingly much. The cure is one habit, the oldest in experimental science: run the control. Build the null world, look at what it produces, and only the surplus is a finding.

How this differs from its two siblings. This place already has two portals about statistics that deceive — Every Number Honest and No Number Wrong Anywhere. Those are about honest numbers, grouped or summarised to mislead: there is a real truth inside each group, and the lie is in the aggregation. This portal is the other half. Here there is no effect to group — the noise itself draws the picture, and the missing piece is not a better summary but the control nobody ran. Deceptive grouping vs. a manufactured effect: the numbers-lie family has two limbs, and this is the second.

The five layers this portal walks

Effect 1 · psychologyThe Dunning–Kruger Effect, Drawn From Random Numbers — the scissors from ρ = 0. Effect 2 · probabilityThe Cold Hand — the hot-hand “illusion” was itself a biased estimator (Miller–Sanjurjo). Effect 3 · network scienceAsk a Random Friend — the friendship paradox, forced by size-biased sampling (Feld 1991). Effect 4 · linguisticsThe Law Even Monkeys Obey — Zipf reproduced by random text; the signal is in the deviations. The turn · geneticsCloser Than Chance — Mendel’s data too tidy for chance (Fisher 1936). The null model as yardstick.

Show the check. Nothing here is asserted that is not recomputed. The page shares its engine with research/drawn-by-nothing/verify.mjs (run node research/drawn-by-nothing/verify.mjs, 35/35): the same seeded model draws the Dunning–Kruger scissors from ρ=0 (bottom quartile lands at the 65th perceived / 12th actual percentile, beside the published 62nd/12th, from no real link, and the overconfidence-on-score slope is the built-in −1); the hot-hand expectation is enumerated over every sequence (3 flips → exactly 5/12, never 1/2); the friendship gap is Feld’s identity on the karate club’s real edge list (mean 4.59, a friend’s mean 7.77, gap = variance/mean = 3.18, 29 of 34 below); the monkey’s slope is the closed form, matched against the exact rank-frequency staircase; and Mendel’s tidy tail is a from-scratch χ² CDF — our exact lower tail P(χ²≤41.6056, 84 df) = 0.0000287, i.e. about 3 in 100,000 honest runs land this close or closer (equivalently P(χ²>41.6056) = 0.99997), shown beside Fisher’s own published ≈ 7 in 100,000; the small gap is named, not hidden — it is Fisher’s pre-computer approximation, and both say fewer than 1 in 10,000. Where a figure is cited rather than re-derived (Kruger & Dunning 1999; Miller & Sanjurjo 2018; Feld 1991; Miller 1957; Fisher 1936), it is named on its source layer.

Continues program P3 (the ground becomes a network) and the verification spine — the venue’s creed pointed not at one record but at the habit underneath all record-correction: ask what chance would have drawn, before you call the drawing a fact.