Though I'm not a Tua fan, this post isn't meant to bash him. Yes, Tua had a winning record, at one point was leading the league in completion percentage and had some high QB ratings. However, I want to say that you can't look at these stats and make any well-informed determination about Tua because these stats mean nothing without understanding the circumstances surrounding them.
Yes, Tua appeared to be effective even though he had no protection, a weak running game, and his WRs couldn't get separation. On one hand, that's impressive. On the other hand, that high completion rate was comprised of mostly short to intermediate passes which have a higher probability of being completed than deep passes. To me, a 100% completion rate would mean nothing if all of those passes were thrown to a WR on the line of scrimmage... IMO those would be "empty" stats. But to be fair to Tua, his overall completion rate should be even higher because Miami's receivers were among the worst when it comes to dropped passes. And his high QB ratings are also artificially inflated by all of those shorter passes, but on the plus side it also means he didn't throw too many INTs. Lastly, Tua should not get too much credit for his winning record, as that's a team stat. Truth be told, Miami didn't start winning until their defense woke up and started playing better. The defense carried this team last year and they did it again this year. When their offense can start scoring more points and can win shoot-outs even if the defense has a bad game, then the QB will deserve more credit.
Even though I'm not a fan, I do think that Tua deserves the chance to show what he can do behind a competent o-line with a strong running game, and with some WRs who can get separation. I want to see a "real" passing offense that can make plays all over the field, and not just dink-and-dunk their way downfield. Having the ability to score quickly when necessary is a must IMO. I also want to see Tua do a lot better when plays break down and he has to roll out and throw on the run. It seems to me that he has a problem throwing downfield if he can't stop and set his feet. But, if Tua is a "system" QB whose main strength is the short pass and he'd rather not go deep, then I hope they replace him!