What it is
Reading about concentration is abstract; moving stake and watching the coefficient collapse is education. This simulator renders a validator set as draggable bars — drag any bar taller to concentrate stake, shorter to spread it — and the Nakamoto Coefficient (33% and 51%) recomputes live with every pixel. Presets load Bitcoin-like, healthy-PoS-like, and exchange-dominated distributions so you can feel the difference between structures.
Ten minutes here builds more intuition than ten articles: you will physically experience how little it takes — a few tall bars — to drag a respectable coefficient into the danger zone.
Why decentralization matters
Stake distribution is usually presented as a finished number, hiding how fragile it is. A coefficient of 12 sounds fine until you drag two bars up and watch it become 4 — which is exactly what happens in real life when an exchange grows or a liquid-staking pool absorbs share. This lab makes concentration dynamic in your mind: decentralization isn’t a score, it’s a live battle between spreading and pooling forces, and pooling usually wins unless someone pushes back.
How the formula works
Identical math to the Nakamoto Coefficient calculator: sort shares descending, accumulate until crossing 33% then 51%; counts are the coefficients. Bars represent the top 20 entities (normalized to 100% for the demo); dragging rescales proportionally. Presets: Balanced (20 equal shares → coefficient 7/11 area), Realistic PoS (decaying shares), Exchange-dominated (3 giants + tail). All computation client-side on canvas, no data anywhere.
Calculator
Risks
A twenty-bar toy flatters reality: real networks have thousands of entities, hidden operator overlaps, and exchange-custodied stake that no chart labels honestly. Use the intuition here to interrogate real distributions (who runs the top validators? who custodies delegated stake?), not as a substitute for that homework.
Worked example
Load the Realistic PoS preset and note both coefficients. Now drag the tallest bar to double height: watch the 33% number fall first — liveness fails before safety does, which is why halts precede rewrites in real incidents. Then flatten everything toward equal and watch both numbers climb past the preset’s start: you’ve just simulated what delegating away from the top three pools accomplishes network-wide. The visceral lesson: concentration is a few drags away at all times, in both directions.
Key numbers to remember
Thresholds that matter: 33% halts BFT finality, 51% rewrites history. Healthy networks measure coefficients in double digits; single digits demand investigation; 1–3 is centralized infrastructure with extra steps. Preset anchors: balanced twenty-way split ≈ 7/11, realistic PoS ≈ 4–6/8–10, exchange-dominated ≈ 2–3/3–5. Memorize the shape of danger, then go measure reality. Revisit quarterly — distributions drift faster than reputations. And when a chain’s marketing cites node counts, mentally redraw its bars: the number that matters is concentrated power, never raw participation. Revisit quarterly — distributions drift faster than reputations.
Common mistakes
Treating the toy as measurement (it’s intuition training; real distributions need the calculator and real data). Forgetting hidden concentration (exchanges, custodians, overlapping operators) that no bar chart labels. Assuming static distributions — stake migrates constantly, so today’s healthy shape is not tomorrow’s. And concluding small networks are hopeless rather than early; trajectory matters as much as snapshots.
FAQ
Why only 20 bars? Readability. Real sets are larger but the dynamic is identical — the top of the distribution dominates the math regardless of tail length.
Do the presets match real chains? Shapes, not figures: balanced like an ideal, realistic like a mid-size PoS, dominated like an exchange-heavy network. Plug real distributions into the calculator tool for exact numbers.
Can I save my distribution? Screenshot it — no accounts, no storage, nothing leaves the page by design.
Related
- Nakamoto Coefficient · Validator · Decentralization
- Reading the Nakamoto Coefficient · Lab: Score a Chain
- Polkadot audit — the most diffuse validator set measured.