The effectiveness of how NO runs the ball is not what I'm talking about. It's how often they decide to run the ball. NO ranked 2nd in pass attempts last year, 19th in rushing.
They spent the off season letting go of their top 2 receiving options, resigning their top RB, signing Spiller and drafting heavy on the defensive side of the ball. They spent the 13 pick in a T, then 31 and 44 on LBs.
You assume the vacated targets of Graham and Stills just get distributed back and the most logical influx goes to Cooks. I don't think it's that simple. Cooks is certainly in line for a larger role but that doesn't have to mean NO remains pass happy.
I don't think Sean Payton would decide to dramatically increase the rushing attempts of his offense at the expense of his passing attack without looking into how effective the rushing attack was in comparison to the passing game. I'm sure he would go with what works best and if you look at the top rushing teams they have a durable big power RB in addition to a solid offensive lines along with a top defense.
I think anyone would take into consideration how effective the rushing attack was in comparison to the passing attack before looking at the Saints and the offensive history Sean Payton has adopted over his long career.
New Orleans let go of their top two targeted receiving threats and they must have some strategy. We know that last year they moved-up to draft a WR in the first round and this year made no attempts to add any major receiving threats. We know that Cooks is back healthy and all reports are positive and he is no longer a rookie and Payton has tried at least two roles for him and is sure to have plotted a strategy of how to use Cooks.
I do not assume the targets lost with Graham and Stills or the addition of CJ Spiller or drafted an OT in the first round indicate the offense will shift to emphasizing the backfield where you seem to see a heavy increase in production to the RBs. I don't assume that because the Saints rushing attack was targeted highly and was not as effective as their receivers with the ball.
I do like CJ Spiller, he is a great threat when healthy but he's only played all sixteen games in his second and third of his five seasons in the league. In those five years Spiller has been placed on the Injury list 19 times for various injuries to his, hamstring, shoulder, knee, quad, and ankle.
http://www.kffl.com/player/22484/nfl/injury_history/c.j.-spiller
CJ Spiller has missed 10 games in five years and parts of at least five other games due to injuries. Mark Ingram has played four years and missed 11 games. Kiry Robinson has only played two years and missed 10 games. I don't see a big durable back to build a power running game around. I don't see a huge increase in the 193 targets that the Saint RBs/FBs got last year.
I don't think its simple but I don't think its that complicated either. I think WR Brandin Cooks is poised for a huge increase in targets and production.