Also, Carmichael had the luxury of calling plays last season, full-time from Game 6 through the playoffs. It would actually seem that he took the Saints offense to another level once he took over the play-calling duties.
If you were to break down the 2011 season by play-calling duties, you would only see a slight difference in effectiveness between Payton and Carmichael in play-calling.
The Week 6 game has to be omitted because that is the game that Payton went down with the injury. So, if you analyze the first 5 games in favor of Payton, and the last 10 in favor of Carmichael, you get your results.
Here are the stats: