I am reading Applied Predictive Modeling by Max Khun. I chapter 16 he discusses using alternate cutoffs as a remedy for class imbalance.
Suppose our model predicts the most likely outcome of 2 events, e1 and e2. We have e1 occurring with a predicted probability 0.52 and e2 with a predicted probability 0.48. Using the standard 0.5 for e1 cutoff we would predict e1, but using an alternative cutoff of 0.56 for e1 we would predict e2 because we only predict e1 when p(e1) > 0.56.
My question is, does it make sense to also readjust the probabilities when using alternate cutoffs. For example, in my previous example using 0.56 cutoff of e1.
p(e1) = 0.52; p(e2) = 0.48
Then we apply an adjustment of 0.56 - 0.5 = 0.06.
p_adj(e1) = 0.52 - 0.06 = 0.46; p_adj(e2) = 0.48 + 0.06 = 0.54
Basically we shift the probabilities so that they predict e1 when p_adj(e1) > 0.5.
I apologize if there is something obviously flawed with my logic but it feels intuitively wrong to me to predict e2 when p(e1) > p(e2). Which probabilities would be more in line with the real-world probabilities?