Let's say I have a 3-class problem and I want to build a classifier that can differentiate between the classes based on a set of features. I want to evaluate the model based on its ability to differentiate the 3 classes.
From my reading, it sounds like macro F1 score is the common metric used to evaluate classifiers on multiclass problems, where the F1 score is calculated for each class then the unweighted average of those F1 scores is used as the macro F1 score.
In other literature, I've seen the balanced accuracy used on multiclass problems, where the accuracy is calculated for each class then the unweighted average of those accuracies is used as the balanced accuracy.
Why would the macro F1 score be favored over balanced accuracy?
Isn't the balanced accuracy more interpretable, in the sense that a balance accuracy of < 0.5 tells us that the model performs worse than chance?
How do we interpret F1 score in the same way as balanced accuracy -- what threshold indicates that the classifier is doing better/worse than chance?