Gini And Gains Curve
Let’s understand Gini coefficient with the help of a fictitious story. Consider a situation where there are four brothers and all of them have been working very hard splitting wood entire day. As the day ends, all of them start feeling hungry and decided to go back home to have sumptuous food cooked by their mother. The mother, realizing that her sons toiled hard in forests, prepared their favourite chocolate cake.

Now, she asks you to share the cake amongst the four brothers. What will you do now?

What are the various possibilities that can arise?

1) You might distribute cake equally among them, thus each receiving 25% of the cake.
2) Or you might distribute the cake on the basis of the output produced by each of them. So, the brother who split the maximum quantity of woods will get the lion’s share of the chocolate pie and the rest will be given lesser share of the chocolate cake etc.
3) It may also happen that one of the brother gives his share to his elder, hungrier brother.

Hence, it is quite evident that in most probability, there will be an unequal distribution of cake amongst brothers.
On the same lines, in analytics, you can use Gini Coefficient, if you want to know:

1) The inequality among the values of a frequency distribution.
2) Or you want to know whether the inequality has increased or decreased over a period of time to determine how the distribution has changed.
3) It is useful as a measure of dispersion in a population.

For example you have country wise data for sales of GM cars all over the world. After careful study, you have observed gross inequalities in the sales across regions (Asian, African, Australian etc). Your aim is to have an idea of the inequality in sales distribution across different continents .This will help you to prepare a report (to be submitted to its sales department) on the grey areas GM needs to focus upon in order to magnify sales revenue from those regions.

Here comes the use of Gini Coefficient which will tell you the level of inequality in sales across different regions of the world.
Gini Coefficient
A Gini Coefficient measures the inequality amongst the values of a frequency distribution. If the Gini Coefficient is 0, it implies presence of perfect equality i.e when all the values of the distribution are same. However, a gini coefficient of 1 (100%) means maximal inequality among the values.

This coefficient was originally proposed by Gini as a measure of income or wealth inequality. The limitation of Gini is that is a relative measure and not an absolute one. The same value of Gini Coefficient may result from different distribution curves.
Gains Chart
A Gains chart is a commonly used performance measure used to summarize a model’s performance. It is a visual representation for comparing a model to the ‘no model’ case or average performance.

Gains chart are sometimes called as “banana charts” because of their banana like shape. The larger is the distance between the model and no model lines (i.e the fatter the banana), the more powerful the model is.

Below screenshot captures the Gains Chart:
Gains Chart
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