Combine accuracy, precision, and recall I am working on a classification problem. Several models are produced and all have accuracy, precision and recall metrics on test data. I need to pick the best model among the alternatives.
What I can think of immediately is to combine precision and recall using F1-measure and use this as a decision metric to pick the best model.
However the requirement I am given is that accuracy should also be part of the decision metric or I should prove that combining F1-measure and accuracy will not improve the decision metric. Does anybody have any idea how to do either?

Although my manager's original request was to combine accuracy, precision and recall, I was able to sell him the idea that what we really want to do is to combine all four quadrants of the confusion matrix in a balanced way. What I mean by the balanced is that the metric should work under extreme class imbalances.
After some research, I came up with two candidate metrics: Balanced accuracy and Matthews' Correlation Coefficient (MCC). They both  work when there is class imbalance. Unlike these metrics accuracy fails whenever there is class imbalance; precision and recall fails when there are more positives than negatives(assuming that they are equally important to you).
