I am going to post some thoughts as a prediction so I can be on the record and see how I do. I am an engineer, not a lawyer so the Ideal Gas Law is my strength, not jurisprudence. As an engineer, I see no proof that the balls were even tampered with so in my mind, nothing else really matters. But I am an engineer and not a judge and I believe the judge, based on reported statements, is not seeing that point as definitively as me. He seems to think that the guys may have done something even if Brady did not specifically order it.
On the law side, based on what I have read, I think the judge can rule that even though the collective bargaining agreement does stipulate that Goodell can arbitrate these matters, there is still an implied requirement for the NFL to execute this role in a reasonably fair manner. I predict that the judge is going to say that the NFL abused the power granted to them in the CBA and went way overboard. If this had actually been a fair and reasonable arbitration, then the judge would be very reluctant to overturn but since the NFL turned this into a kangaroo court, it is not really arbitration and the judge should have much more latitude to overturn.
The ruling will be in favor of Brady and the NFL will be ordered to rehear the arbitration but to do so in a way that meets the standard of a real arbitration if they want it to be upheld. What happens from there, who knows. I am not sure that there is a scenario where Goodell can preside over an arbitration and have it be fair.