When is log-loss metric appropriate for evaluating performance of a classifier? Specifically, for which model classes and under which circumstances is it reasonable to tune the classifier to optimize the log-loss rate?
 A: Log-loss is an appropriate performance measure when you're model output is the probability of a binary outcome.
The log-loss measure considers confidence of the prediction when assessing how to penalize incorrect classification. For instance consider two predictions of an outcome P(Y=1|X), where the predictions are 0.51 and 0.99 respectively. In the former case the model is only slightly confident of the class prediction (assuming a 0.5 cutoff), while in the latter it is extremely confident. Since in our case both are wrong, the penalty will be more harsh for the more confident (but incorrect) prediction by employing a log-loss penalty.
A: If you want a good probability estimate that punishes extreme values when these are wrong, then logloss can do that.
Read more on Making Sense of Logarithmic Loss.

Log Loss heavily penalises classifiers that are confident about an
  incorrect classification. For example, if for a particular
  observation, the classifier assigns a very small probability to the
  correct class then the corresponding contribution to the Log Loss will
  be very large indeed. Naturally this is going to have a significant
  impact on the overall Log Loss for the classifier. The bottom line is
  that it’s better to be somewhat wrong than emphatically wrong. Of
  course it’s always better to be completely right, but that is seldom
  achievable in practice!

