After taking a look at the stats, there are definitely a lot of interesting things to compare. In the five games that Payton was the lone play-caller, the offense attempted a total of 134 rushes.
That comes out to be around 27%. In the 10 games Carmichael was the primary play-caller, the Saints ran it 265 times. This is also around 27% of the time. Break it down a little further and you still get eerily similar numbers: (Payton) 26.8% – (Carmichael) 26.5%.
Both Carmichael and Payton seem to be of the same offensive mind, or they trust Drew Brees to call the shots. Whatever the answer may be, the offense was very similar in play-calling in terms of Run vs. Pass.
Where things start to look different is in play effectiveness. Under Payton for the first five games, the Saints gained 577 yards on the ground (115.4 per game). In 10 games under Carmichael, the total was 1,607 (160.7 per game). That is a huge difference!
Now it seems like the question lies in whether the Saints choose to run less, the same, or more than they did a season ago. One would think that it may be more, as the team has a great backfield with tons of depth.
Even if the play-calling stays around the same, the Saints look like they are in good hands with Carmichael calling the shots.
If you look at passing stats, it is hard to notice a huge difference in terms of overall production. The number of passing attempts per game actually dropped with Carmichael calling plays (46 with Payton, 42 with Carmichael).