Propensity scores are very useful because they tell you the likelihood of something happening. Confidence values for models reflect confidence in our predictions so a high degree of confidence doesn't help us determine if we're going to have a customer that's going to stay or leave a company, instead it indicates the confidence that we have in our prediction. Sometimes it's helpful to modify the confidence value so that a high confidence value means a prediction that a person is going to leave and a low confidence value indicates that a person is going to stay. Basically, we end up creating a propensity to leave score which would be helpful so that we could make interventions, different marketing efforts, and so on.
Consider this table, for example:
We have two values for Leaving and two values for Staying, each with the confidence values that we have in those predictions. In this example, let's assume that we are trying to calculate the propensity of losing a customer. We will create a propensity score; this means that when a person is predicted to leave, the propensity score is the same thing as a confidence value. So you can see that for the first person, we're predicting they are going to leave, and as we have a high degree of confidence in that prediction, therefore the propensity score is pretty high. For the second person, we're predicting they are also going to leave, but the confidence in that prediction is not quite as high, so therefore, we can see that the propensity score is not quite so high either.
While predicting the opposite, if we are predicting that a third person is going to stay but the confidence in that prediction is not very great, really what we're doing is taking 1 minus the confidence value of the opposite of what we really want, and that ends up being the propensity score. Finally, in the last example, we have a person that we're predicting is going to stay. The confidence in that prediction is extremely high, so therefore, the likelihood of that person leaving is very low.
The following figure sums up the propensity formulas:
In essence, what propensity scores do is modify confidence values so that you can see the likelihood of something happening. So, if you could put them all on some kind of spectrum it would be possible to see, for example, that there are some people for whom there is a high degree of confidence that they are going to leave, so maybe there's not much that we can do about that. We have another group of people for whom we have a high degree of confidence that they're going to stay, so the propensity of them leaving is pretty low. Again, we may not necessarily need to worry about them that much, but maybe the people we need to focus on are the people in the middle, because they're the predictions that are not quite as extreme, and so we cannot be quite as confident about those predictions. Potentially, we can do something with that group. We might be able to change their minds, or something like that, and that's how propensity scores can be used.