── ── 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.
Run Power-Law Distribution on a real problem
Bring something you're actually deciding — free, in the browser.
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
AI and Venture Returns Concentration (2023–2026)
Between 2023 and early 2026, the economic value created by the generative-AI wave concentrated into an extraordinarily thin tail: a handful of frontier model labs (most prominently OpenAI and Anthropic) plus the dominant AI-compute supplier, Nvidia, captured a wildly disproportionate share of the value, funding, and market-cap gains. This is a textbook power-law distribution unfolding in real time — and it is exactly the kind of domain where averaging ("the average AI startup," "the average enterprise-software return") produces systematically wrong decisions. Below the case is…
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