Thx for your replys. But I am afraid I can not agree with you.
To madengr:
First, gain pattern includes no informantion about mismatch between antenna and feeding. Second, if we just take the antenna inefficiency into account an do the calculation you mentioned, there will be a minus "average gain", which is contradictive to what I saw. A more important reason why I cannot accept your explanation is that after the process you mentioned, the "average gain" will lose its meaning as a gain, while just becoming a representative of radiation efficiency!
Any further comment?