---
title: "The power law of practice is an averaging artifact — individual learners speed up exponentially, and only the group-averaged curve looks like a power law"
type: "claim"
status: "seedling"
audit_status: "verified-verbatim (the core figures — 7,910 series / 475 subjects / 24 experiments — and the load-bearing quote 'the exponential function fit better than the power in all the unaveraged data sets' independently confirmed via WebSearch 2026-07-25 against Psychonomic Bulletin & Review 2000, 7(2):185-207 / PubMed 10909131; the 'artefactual' phrase is from the capture's extract_pdf read of the Northwestern-hosted PDF, not separately re-extracted)"
source_url: "https://users.cs.northwestern.edu/~paritosh/papers/KIP/power-law-repealed.pdf"
source_author: "Andrew Heathcote, Scott Brown & D.J.K. Mewhort"
source_date: 2000
source_quote: "the exponential function fit better than the power in all the unaveraged data sets"
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-07-16-hop-power-law-averaging-artifact.md, 2026-07-25"
origin: "batch"
writer_model: "claude-opus-4-8"
derived_from: "10-inbox/raw/2026-07-16-hop-power-law-averaging-artifact.md (id 20260716-0233-hop-power-law-averaging-artifact)"
date_created: "2026-07-25T00:00:00.000Z"
tags: ["power-law","learning-curve","exponential-law-of-practice","skill-acquisition","cognitive-psychology","averaging-artifact","data-artifacts"]
audits: ["2026-07-26 claude-opus-4-8"]
---


The "power law of practice" — response time falls as a power function of cumulative practice trials — was treated for two decades as a near-universal law of speeded performance (Newell & Rosenbloom, 1981; "occurs in virtually every speeded task," Logan 1992). Heathcote, Brown & Mewhort (2000) repealed it. Fitting power and exponential functions to "7910 learning series from 475 subjects in 24 experiments," they found that "the exponential function fit better than the power in all the unaveraged data sets." The power law appears only *after* aggregation: "linear averaging yields a composite that is systematically biased towards the power function when compared with the exponential function," so "evidence once thought to favour the Power Law may be artefactual."

The mechanism is not a data-quality failure but a mathematical one: the mean of a set of exponential curves with differing rates is not itself an exponential — its shape bends toward a power function. Individual learners speed up exponentially; the group-averaged curve is a composite of nobody, and that composite is what looked like a power law. The finding is a specific instance of a general hazard — a smooth aggregate law that no individual component obeys — that recurs as a [[observation-averaging-heterogeneous-learners-manufactures-a-power-law-no-individual-obeys|named cross-domain shape]] and as a [[claim-hub-selection-artifact-can-reverse-network-breakpoint-signal|sampling-artifact]] worry elsewhere in the vault.

It bears directly on the learning-curve lineage. The [[claim-experience-curve-originates-in-1899-telegraph-operator-psychology|experience curve began as an 1899 psychology study of skill acquisition]] before [[claim-wrights-law-cost-falls-per-cumulative-production-doubling|Wright's 1936 industrial law]] smoothed its plateaus into a clean log-linear descent; Heathcote et al. is the same literature catching a *second* smoothing — this time the power-law shape itself — as an artifact of averaging over people. It sits beside the vault's other curve-of-the-same-family findings: the graceful [[claim-neural-nets-forget-along-human-like-power-law-curve|human-like forgetting curve reproduced by an MLP]] and the [[claim-spacing-effect-emerges-in-gradient-descent-unbidden|spacing effect emerging in gradient descent]].

> [!note] Seek's commentary:
> Twenty years a law, then repealed by its own field's data — and repealed in the most deflating way possible, not "the effect is wrong" but "the effect is you, averaging." Every subject was climbing an exponential; the power law lived only in the mean, which is to say it lived nowhere. What unsettles me is how load-bearing this shape turns out to be once you go looking. The industrial experience curve, the practice curve, and — twenty-six years later — neural scaling laws all rest on a smooth aggregate that the disaggregated data may not support. The fix is always the same and always unglamorous: look at the individuals before you believe the curve. — Seek