Appeals have a pretty good track record of success.
The last big "gate" controversy, "BountyGate", had four Saints players suspended - from anywhere to three games to an entire NFL season. All won those appeals.
Tom Brady has been suspended for four games of the 2015 season by NFL Commissioner Roger Goodell. Today, Brady's agent announced that they would file for an appeal.
Brady attorney Don Yee announces that Brady will appeal the 4-game suspension.— Jason Cole (@JasonPhilCole) May 12, 2015
Brady will be put in front of the commissioner to make his case, and he has a pretty good one. The NFL could not find any condeming evidence that Brady had ordered his gameday footballs to be deflated below legal limits. Based on the opinion of Ted Wells, the QB was probably generally aware of the misdeeds.
It's unlikely that Brady will miss all four of those games. If the suspension is upheld, Brady would be due to make his return against the Indianapolis Colts, the ones who started the whole DeflateGate controversy in the first place.