If teams were just to guess run or pass based on whether or not Dallas was in the shotgun, they'd be pretty successful based on that alone.
Prior to today and spanning the previous month, here's the breakdown. This covers Denver, Washington, Philadelphia and Detroit. 2-2 over that time, and Dallas has shown both the best offense they can put out as well as some rather uninspired offensive performances.
Under Center: 72.6% Run / 27.4% Pass (61 Runs / 23 Passes)
Shotgun: 13.5% Run / 86.5% Pass (20 Runs / 128 Passes)
Without even taking into account the down, the distance, the score, time on the clock, field position or anything else that's what teams start with.
So, just using that basic framework what would happen if teams played the run every time Dallas was under center and played the pass every time Dallas was in the shotgun and didn't even factor in all the other stuff?
Under Center: 61 of 84 plays correctly identified.
Shotgun: 128 of 148 plays correctly identified.
Total: 189 of 232 plays correctly identified.
That's 81.4% of all the plays run that teams would be lining up expecting a run or pass and being correct. Who knows how high that percentage could be if teams actually started looking at trends based on distance to go or what down it is.