These graphs represent the historical decentralisation of token ownership for various blockchain systems. Each metric is calculated based on the distribution of tokens across the addresses / entities that held them in each time period. Read more ...

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The Nakamoto coefficient represents the minimum number of entities that collectively control more than 50% of the resources (in this case, the majority of circulating tokens at a given point in time).

The Gini coefficient represents the degree of inequality in a distribution. Values close to 0 indicate equality (all entities in the system control the same amount of assets) and values close to 1 indicate inequality (one entity holds most or all tokens).

Shannon entropy (also known as information entropy) represents the expected amount of information in a distribution . Typically, a higher value of entropy indicates higher decentralization (lower predictability).

The Herfindahl-Hirschman Index (HHI) is a measure of market concentration. It is defined as the sum of the squares of the market shares (as whole numbers, e.g. 40 for 40%) of the entities in the system. Values close to 0 indicate low concentration (many entities hold a similar number of tokens) and values close to 10,000 indicate high concentration (one entity controls most or all tokens).

The Theil index captures the lack of diversity, or the redundancy, in a population. In practice, it is calculated as the maximum possible entropy minus the observed entropy. Values close to 0 indicate equality and values towards infinity indicate inequality.

The max power ratio represents the share of tokens that are owned by the most "powerful" entity, i.e. the wealthiest entity.

The τ-decentralization index is a generalization of the Nakamoto coefficient. It is defined as the minimum number of entities that collectively control more than a fraction τ of the total resources (in this case more than 66% of the total tokens in circulation).