Though I don´t even pretend to be a historian, I read somewhere that one of the main goals in battle was flanking the enemy on his right side. Why? Because that´s the unprotected side, as most people are right-handed, that´s the hand where the weapon is held, while the left side is protected by the shield. Thus it makes sense to deploy the best troops on the left wing. And also to place the officer on the left side - he can protect himself with his own shield (I suppose they usually had one) while his vulnerable right is protected by the mass of his men.