Dear weychien:

Input ore > black box efficiency > output.

But to put numbers to the efficiency factor is not so easy. Different products react differently. Several factors influence the efficiency of ball mill grinding. The pulp density within the mill should be as high as possible consistent with ease of flow through the mill. It is essential that the balls are coated with a layer of pulp. Too dilute a pulp increases metal to metal contact - which increased steel wear and reduces efficiency.

Most do a bench test rather than relying on some theoretical model.