Since this was a District Court decision, the appeal would go to the Court of Appeals for the Federal Circuit, which keeps statistics on reversal rates on its web site. Last I looked, the reversal rate was somewhere between 18-30%. I.e., the odds are stacked against reversal on appeal.

And you do need something specific to appeal. You can't simply say, "We lost, we'd like to appeal". Pretty much the only appeals that take that form are death penalty cases, which typically have automatic appeals.