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.
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:
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...