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Herfindahl-Hirschman Index (HHI) for Token Distribution

The Herfindahl-Hirschman Index (HHI) is a measure of concentration that can be applied to token distribution across wallets. When used for cryptocurrencies, it helps quantify how concentrated or distributed token ownership is across the holder base.

Definition

For token distribution analysis, HHI is calculated by squaring the percentage of total supply held by each wallet and then summing these squares:

HHI = W₁² + W₂² + W₃² + ... + Wₙ²

Where Wᵢ represents the percentage of total token supply held by wallet i.

Interpretation for Token Distribution

When applied to token holdings, the HHI scale typically produces lower values than in traditional industry analysis due to the higher number of holders:

  • HHI < 100: Highly distributed token (very decentralized)
  • 100 ≤ HHI ≤ 500: Moderately distributed token
  • 500 ≤ HHI ≤ 1,500: Moderately concentrated token
  • HHI > 1,500: Highly concentrated token distribution

Example Calculation

Consider a token with holdings distributed across thousands of wallets, where the top 5 wallets hold: - Wallet A: 8% - Wallet B: 5% - Wallet C: 3% - Wallet D: 2% - Wallet E: 1% - All other wallets: 81% (with individual holdings < 1%)

The HHI calculation focuses on significant holders: HHI ≈ 8² + 5² + 3² + 2² + 1² + (many small contributions) = 64 + 25 + 9 + 4 + 1 + ... ≈ 103 + (contributions from smaller wallets)

This indicates a relatively distributed token with moderate concentration among top holders.

Applications in Token Analysis

  • Centralization Risk Assessment: Identifies tokens with high ownership concentration
  • Governance Evaluation: Helps understand voting power distribution in DAO structures
  • Liquidity Risk Analysis: Concentrated holdings may indicate higher volatility risk
  • Project Maturity Indicators: Distribution typically becomes less concentrated as projects mature

Considerations for Crypto Applications

  • Exchange wallets may represent many individual holders but appear as single large holders
  • Contract addresses (staking, liquidity pools) should be interpreted differently than individual holders
  • The index should be recalculated periodically to track distribution changes over time
  • Very low HHI values may be difficult to maintain for newer projects

Limitations

  • Does not distinguish between different types of holders (founders, investors, users)
  • May not account for related wallets controlled by the same entity
  • Smart contract addresses require special consideration in the calculation In such cases, consider using the HHI Index Adjusted for a more accurate representation.