In ZvZ what should be the primary goal of mutalisks? Recently I have been hearing it is best to target overlords out on the map before trying to poke into your enemies bases. Logically, I am thinking it would be best to see if any damage can be done to the base, particularly the mineral line, before proceeding to systematically kill the overlords on the map and gain map control. What is the logic for professional players to go after overlords first? What is the best use of the investment?
There are two answers:
Is the opponent good? I.e. does he know mutalisks are coming?
If yes, your mutalisks won't do a lot of damage in his base since he will be prepared for them. By killing the overlords, you reduce his map vision, forcing him to play more defensive since he never knows where the next attack will come from. They give you complete map control, which is a big factor in winning the game.
Is the opponent bad? I.e. can you suprise the opponent?
If yes, your mutalisks can do a lot of damage if they suddenly appear in the opponents base so skipping overlords and going straight for the base while avoiding being spotted is the better option. Killing a whole mineral line can win the game.
Generally, it's bad to assume that your opponent is a bad player, so going for the safer path of getting map control will usually gain better results.