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.

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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.

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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.

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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_count2)COUNT(entities)×SUM(validator_count)1 - 2 \times \frac{\text{SUM}(\text{validator\_count} \times (\text{rank} - 1) + \frac{\text{validator\_count}}{2})}{\text{COUNT}(\text{entities}) \times \text{SUM}(\text{validator\_count})}

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The shape of a Lorenz Curve.

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Function components

validator_count×(rank−1)\text{validator\_count} \times (\text{rank} - 1)
is the area of the rectangular horizontal slice under the Lorenz curve.
validator_count/2\text{validator\_count} / 2
is the area of the triangle on the left of the rectangular slice.
SUM(validator_count×(rank−1)+validator_count2)\text{SUM}(\text{validator\_count} \times (\text{rank} - 1) + \frac{\text{validator\_count}}{2})
is the sum of all the slices
COUNT(entities)\text{COUNT}(\text{entities})
normalizes the x axis to the range 0 to 1
SUM(validator_count)\text{SUM}(\text{validator\_count})
normalizes the y axis to the range 0 to 1