I am in a scenario where I have two groups of possible clients. Each group is 50% of the total (imagine that the total amount of candidate clients is 1000), so I have 500 people in group_1 and 500 in group_2.
I also know that in group 1 I expect to find 80% of the real client (it is not an observed value, it is more generically an expectation), because the segmentation between the two groups is not random.
In order to obtain contact all the 1000 candidate clients, I decided to assign them to two groups of operators: operator 1 and operator 2, each one of the same size. I know that the operator 1 group is better than the other, in fact, usually, it transforms 30% more of the candidate clients into real clients. Considering this fact, I decided to assign 75% of the group 1 clients (the one with the higher expected conversion rate) to the operator 1 group, in order to maximize the number of real clients.
Using this approach I am able to obtain 100 real customers from the 1000 candidates (10% CR).
The problem is to estimate the number of clients that I could obtain without applying any strategies.
In order to so, I apply the following schema:
INPUT DATA
- n_candidate = 1000
- percentage_split_contact = 50%
- number of top operator = 15
- number of bad operator = 15
- percentage top client assign top operator = 60%
- expected number of real client in first group = 70% (if it is equal to percentage_split_contact it means random)
How should I obtain the amount of true clients obtained without applying any strategy?