If Brady wants to prove his innocence then he'll sue. If he's guilty and just covering it up (aka the Patriot way) then he'll appeal and live with the results. My guess is he's guilty and just doesn't like the consequences. So once this gets heard by Goodell he'll live with the results of arbitration.
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Once this goes to legal action all of those things he did not want to show the investigators become fair game. If he has something to hide he will never go beyond the arbitration process.
*You're absolutely fooling yourself if you think the Patriots are alone in pushing beyond the rules. They are spotlighted for a number of reasons, and their are coups (<-- not exaggerating) that try to expose them and bring them down. Every single team has their ways of pushing beyond the rules, both on the field and off.
*There are a number of reasons why this won't go all the way to the legal finish line; it won't be determined solely by Brady and his defense of his legacy or some **** like that. The NFL has a lot of reasons they don't want it to go there, too.
I'm a lifelong Pats fan with some decent connections to things, so let me just say this:
Is it probable that NE was pushing the rules with inflation of the balls? Yes. Is it probable that other teams do this, too (e.g. Green Bay)? Yes, it is EQUALLY probable.
Are there problems with the Wells Report (which I've read, btw)? Definitely. Big problems. Chief among them are (a) that there isn't any scientific evidence given for loss of psi due to worsening weather conditions and play (which certainly happened); (b) there isn't ANY direct evidence that any deflation of the footballs was meant to take the balls below the minimum level.
This all seems like a microcosm of the Spygate issue (which many teams were also doing, btw):
Spygate: The Pats get caught doing something... which results in absolute scrutiny from the league... which results in the Patriots steamrolling the entire league. Ruthlessly
Deflategate: The Pats get caught doing something... which results in scrutiny and halftime adjustments... which results in Brady absolutely murdering the **** out of the Colts in the second half.