Metrics

The metrics that have been implemented so far are the following:

  1. Nakamoto coefficient: The Nakamoto coefficient represents the minimum number of entities that collectively control more than 50% of all tokens in circulation at a given point in time. The output of the metric is an integer.
  2. Gini coefficient: The Gini coefficient represents the degree of inequality in token ownership. The output of the metric is a decimal number in [0,1]. 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).
  3. Entropy: Shannon entropy represents the expected amount of information in the distribution of tokens across entities. The output of the metric is a real number. Typically, a higher value of entropy indicates higher decentralization (lower predictability).
  4. HHI: 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. The output of the metric is a real number in (0, 10000]. Values close to 0 indicate low concentration (many entities hold a similar number of tokens) and values close to 10000 indicate high concentration (one entity controls most or all tokens). The U.S. Department of Justice has set the following thresholds for interpreting HHI values (in traditional markets):
    • (0, 1500): Competitive market
    • [1500, 2500]: Moderately concentrated market
    • (2500, 10000]: Highly concentrated market
  5. Theil index: The Theil index is another measure of entropy which is intended to capture the lack of diversity, or the redundancy, in a population. In practice, it is calculated as the maximum possible entropy minus the observed entropy. The output is a real number. Values close to 0 indicate equality and values towards infinity indicate inequality. Therefore, a high Theil Index suggests a population that is highly centralized.
  6. Max power ratio: The max power ratio represents the share of tokens that are owned by the most "powerful" entity, i.e. the wealthiest entity. The output of the metric is a decimal number in [0,1].
  7. Tau-decentralization index: The tau-decentralization index is a generalization of the Nakamoto coefficient. It is defined as the minimum number of entities that collectively control more than a given threshold of the total tokens in circulation. The threshold parameter is a decimal in [0, 1] (0.66 by default) and the output of the metric is an integer.