While I understand how these metrics are calculated, I am having a hard time understanding the trade-offs between them and which is good for what exactly.
When it comes to ROC-AUC vs Precision-Recall, this thread discusses how ROC-AUC-maximization can be seen as using a loss optimization criteria that penalizes "ranking a true negative at least as large as a true positive" (assuming that higher scores correspond to positives). Also, this other thread also provides a helpful discussion of ROC-AUC in contrast to Precision-Recall metrics.
However, for what type of problems would log loss be preferred over, say, ROC-AUC, AveP or the Hinge loss? Most importantly, what types of questions should one ask about the problem when choosing between these loss functions for binary classification?