A friend of mine practices Social Security disability, and hence files quite a few appellate briefs in the U.S. District Court. A while back, Leeds came up with the heretical idea of completely omitting the statement of facts from his brief. Instead, all discussion of the facts occurs in the context of the argument as to each asserted error in the ALJ's decision.
Heretical, maybe--but effective. One of our magistrate judges recently had this to say about a brief prepared in this style:
The Court would stop to express some preference for the organization of the plaintiff's brief. It is traditional in Social Security briefs, both plaintiff and government, to make a kind of initial evidentiary dump, substantially logging the medical evidence and testimony on the front end regardless of relevance, with much less association of that evidence to relevant legal authorities and argument as briefing develops. Here, the plaintiff has more naturally included facts and medical record as they relate to the specific objections she levies against the ALJ's decision. This makes for a more accessible presentation, from the Court's perspective.
As much as I have a hard time wrapping my brain around having no statement of facts at all, I do think there is a tendency to view the Statement of Facts and Argument portions of a brief as ships that pass in the night. True, appellate courts review for errors of law. But the application of law never occurs in a vacuum--it's always in the context of the facts of the case.
So perhaps a more persuasive brief will be one with a shorter Statement of Facts, along the lines of "here's what you need to know to get started," with the detailed exposition being saved for the argument. I am guessing a brief written in this style would be shorter, too, because presenting the facts only in the context of the argument will naturally promote the omission of irrelevant facts.