Context
The Lift should show how a machine learning model performs better than randomness. Thus, a curve representing the ratio between the predicted class of a model vs the absence of that model using a random choice is shown.
Question
Mentioning ratio, this is what bugs me: The randomness is "always" (at least every source I looked at) represented as straight line over all deciles.
Wouldn't this imply that a perfectly balanced dataset has to be provided allowing each picked item to have a random chance of 50% to get picked?
In other words: Wouldn't the actual randomness have to be calculated on the ratio of the classes?
For simplicity take a binary case:
We have 60 Apples and 40 Bananas and would want to classify on the size and weight as features (let aside the usefulness of this) the fruits. The random choice now should have a 60% chance of hitting an apple and only a 40% chance of a banana. Wouldn't we have to compare that ratio as "randomness" with the model output instead of the 50:50 chance?
But maybe my missunderstand lies within the calculation...
