This article by Judge Richard Posner (7th Circuit Court of Appeals) does a fine job discussing appellate briefs and oral arguments.
"The second biggest mistake that appellate advocates make—after exaggerating how much the judges know about or are willing to devote time to learning about a given appeal—is to think that they can win by rubbing the judges’ noses in the precedents. In an argued civil case, as I have just been emphasizing, there probably is no dispositive precedent—otherwise the case would probably not have gotten to the point of an orally argued appeal. And if there is no dispositive precedent, then unless the appellate judges are very gullible, it is futile to argue the case as if there were.
In a case that is not controlled by precedent, the task of the advocate is to convince the court that the position for which he or she is contending is the more reasonable one in light of all relevant circumstances, which include but are not exhausted by the case law, the statutory text, and the other conventional materials of legal decision making. I say “reasonable” rather than “correct” to give due recognition to the ineliminable element of discretion in the decision of a case that is not ruled by precedent or other conventional sources of law."