It's not really Dak or Dez's fault for the Cowboy's dip in production.
The Cowboys run a version of Air Coryell, which puts a big emphasis on medium and deeper routes/throws. The system works great if you have a QB with an arm like prime Aikman....it can also work with a QB with a "good" arm but an extremely high-level of understanding/football IQ. Romo had above average talent but may have been one of the top 2 or 3 smartest QB's in the game. His only draw back was his gunslinger mentality and the fact that while talented, didn't quite have the cannon to make up being a gunslinger (like a young Brett Favre).
Romo made so many adjustments with play-calls and at the line that he made a very vanilla offense look fairly explosive. Romo would make d-coordinators scratch their heads. With him gone, you're left with Dak. Dakota Rayne has talent, but he's going into his 3rd year with an offense designed for Romo...and an offense that Romo knew how to adjust to the nth degree. Romo didn't start until 3.5 years in while Dak didn't have the chance to sit and learn from Bill Parcells. Dak gets to learn from Jason Garrett

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Dak tends to be a 'SITI' thrower (see-it, throw it) instead of throwing with anticipation. That said, the coaching and lack of creativity is what may doom Dak. Romo made the coaches look much better than they were and he's was an experienced veteran by the time Garrett took over. Dak will continue to look shaky until they tailor the offense to fit his strengths and scheme in a way that isn't so dependent on the QB covering for poor coaching and game planning.