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# 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:
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