── ── Mental model
Power-Law Distribution
A power-law distribution is a statistical distribution where probability of size x is proportional to x^(−α): large events are rare but far more probable than a Gaussian model predicts, and the largest events dominate the total — there is no "typical" case.
How it works
Step 1 — Identify the distribution: What is distributed? Preliminary hypothesis: Gaussian or power-law?
Step 2 — Check power-law indicators: Top __% accounts for __% of total. High mean-to-median ratio? Long right tail? Log-log plot roughly linear?
Step 3 — Estimate tail exponent (if data available): α < 2 → infinite variance; α < 1 → infinite mean. Practical implication:
When to use it
- user is allocating capital or resources across a portfolio and wants to know where to concentrate
- user says 'our average customer / deal / employee performs at X' and is making decisions from that average
- user is building a risk model using standard deviation or VaR
- user asks why a few customers or deals drive almost all revenue
- user is evaluating VC fund returns or startup portfolio outcomes
When not to use it
When the decision is routine and reversible, applying a formal method costs more than it returns.
Worked example
Pareto 1896, Mandelbrot 1963, and VC Return Data
Vilfredo Pareto (1848–1923) was an Italian engineer, economist, and sociologist. His 1896 observation about Italian land ownership was not an isolated curiosity — he went on to find similar distributions in England, France, Germany, and across historical data. The pattern was consistent: a stable mathematical relationship between wealth rank and wealth magnitude, following what is now called a power law.
Install this skill (free, MIT)
npx skills add deciqAI/knowledge-skills