Gini coefficient measurement

This page illustrates the approach Rated takes in computing this metric for the Ethereum network.

The Gini coefficient (Gini) is a measure of inequality across a certain set of values. In this case, we're measuring the Gini of the validator market share of entities we have identified.

Entity groupings

We have taken the commonality by highest order such that grouping by pools takes precedence over node operators, which take precedence over deposit addresses.

Interpreting the Gini

A Gini coefficient of 0 reflects perfect equality, where all income or wealth values are the same, while a Gini coefficient of 1 (or 100%) reflects maximal inequality among values.

Gini calculation

Basing our calculation of the work by Evgeny Medvedev here, we first take the validator_count of each of the entities on the latest day and rank them in descending order accordingly. We then use the 1-2B formula for measuring the Gini, where B is the area under the Lorenz curve such that:

Gini == 1 - 2 * SUM((validator_count * (rank - 1) + validator_count / 2)) / COUNT(entities) / SUM(validator_count)

The shape of a Lorenz Curve.

Function components

validator_count * (rank — 1)

is the area of the rectangular horizontal slice under the Lorenz curve.

validator_count / 2

is the area of the triangle on the left of the rectangular slice.

SUM((validator_count * (rank — 1) + validator_count / 2)) 

is the sum of all the slices

COUNT(entities) 

normalizes the x axis to the range 0 to 1

SUM(validator_count)

normalizes the y axis to the range 0 to 1