Power Law Lab

A practical toolkit to detect, test, and reason about power-law environments.

This repo helps answer one question:

Are my outcomes governed by a power law, or do they just look that way?

It is designed for founders, investors, and researchers who care about asymmetric payoffs, winner-take-most dynamics, and convex bets.

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What this tool does

Power Law Lab has two core parts:

1. Outcome analysis

Given a dataset of outcomes (profits, views, ROI, returns, etc.), it:

• Measures concentration (top 1%, top 10%, Gini, Herfindahl)
• Fits tail models:
  • Power law
  • Lognormal
  • Exponential
• Automatically finds a tail cutoff (xmin)
• Produces visual diagnostics (log-log CCDF)
• Outputs a clear verdict:
  • powerlaw_tail_likely
  • heavy_tail_likely
  • heavy_tail_likely_ambiguous
  • unknown

This tells you what kind of world you are operating in.

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2. Synthetic data generator

A companion script lets you create controlled datasets:

• Pure power law
• Lognormal
• Normal (thin tail)
• Exponential
• Blended systems (e.g. 70% lognormal + 30% power law)

This is useful for:

• Learning how tails behave
• Testing false positives
• Stress-testing intuition
• Teaching others

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File structure

.
├── powerlaw_lab.py          # Main analysis + bet scoring tool
├── make_synthetic_input.py  # Synthetic data generator
├── README.md
└── LICENSE

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Installation

Python 3.9+

pip install -r requirements-excel.txt

Optional (for Excel support):

pip install openpyxl

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Input format

Default expected format

CSV or Excel file with:

unit_id,outcome
1,3.24
2,0.91
3,145.7
...

• unit_id can be anything (client, post, deal, strategy)
• outcome must be numeric and positive

Column names can be overridden via CLI flags.

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Analyze real or synthetic data

Basic usage

python powerlaw_lab.py analyze data.csv --auto_xmin

Outputs:

• summary.json
• ccdf_loglog.png
• hist_logx.png

With explicit columns

python powerlaw_lab.py analyze data.xlsx \
  --sheet Sheet1 \
  --value_col profit \
  --unit_col deal_id \
  --auto_xmin

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Interpreting results

Key signals that indicate a power-law environment:

• Top 1% contributes 20–40%+ of total outcome
• Gini coefficient > ~0.5
• Power law beats exponential clearly
• Tail size is large and stable across runs
• CCDF looks linear on log-log axes above xmin

This is not proof. It is a decision tool.

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Generate synthetic datasets

Pure power law

python make_synthetic_input.py generate \
  --dist powerlaw \
  --n 20000 \
  --params xmin=1,alpha=2.2 \
  --out synthetic_powerlaw.csv

Pure lognormal

python make_synthetic_input.py generate \
  --dist lognormal \
  --params mu=0,sigma=1.0 \
  --out synthetic_lognormal.csv

Blend systems (shift slider)

python make_synthetic_input.py blend \
  --dist_a lognormal --params_a mu=0,sigma=0.8 \
  --dist_b powerlaw  --params_b xmin=1,alpha=2.2 \
  --w 0.7 \
  --out synthetic_shift.csv

w controls the mix:

• w = 1.0 → pure A
• w = 0.0 → pure B

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Bet scoring (optional)

There is also an interactive bet scoring tool:

python powerlaw_lab.py score_bets

You score ideas 0–2 on:

• Upside ceiling
• Downside cap
• Leverage
• Feedback speed
• Distribution edge

Output is a ranked CSV.

This helps you allocate attention to convex bets.

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What this tool is NOT

• It does not prove universal laws.
• It does not predict individual outcomes.
• It does not replace judgment.

It helps you avoid the biggest mistake:

Treating a lognormal or normal world like a power-law world.

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When to use this

This tool is useful if you are working on:

• Startups
• Content distribution
• Investing
• Trading strategies
• Product usage
• Deal sourcing
• Any system with rare big wins

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License

MIT License (recommended)

• Free to use
• Free to modify
• Free for commercial use
• Attribution required
• No warranty

See LICENSE file.

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Philosophy

Power laws change how you allocate time, capital, and risk.

This tool exists to make that visible.

Use it to take fewer bets, but bigger ones.

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