I was told here a year before that the NFL might be trying to reproduce a long standing historic rivalry in the NFC, with the Saints and Packers. Like the Colts vs Patriots. I kind of discounted that, and said yours was a natural one that formed. Maybe I was wrong. This seems completely out of place t me.
NFL Videos: New Orleans Saints vs. Green Bay Packers movie trailer
I looked below to see what other teams the NFL chose to pair together for this marketing campaign and sure enough the vast majority were division rivals: Cowboys-Giants, Ravens-Steelers, Jets-Patriots, Redskins-Eagles. The Saints-Packers trailer was the third one listed and only non-division matchup on the first page.
The NFL markets its product by associating a star player (usually a QB) with a team; listen to in-season ads for upcoming games and it's always something like 'join us Sunday when (name of player) and the (name of team) take on (name of player) and the (name of team) in a battle of (name of division or conference) powerhouses'.
One alway popular topic of conversation is 'who is the best quarterback', and any list would include Drew Brees and Aaron Rodgers. So even though the Saints and Packers are not in the same division it does make sense for the NFL to take advantage of the amount of interest that debate draws by placing those two together, rather than the more natural rivalries of say the Packers and Bears, or to a lesser extent the Saints and Falcons.
Green Bay and New Orleans are both in a position to win several division titles over the next few years. If that does happen then the two will meet on an annual basis because of the way the NFL produces its schedule (#1 vs #1, #2 vs #2, etc.). Should that occur then a Packers-Saints rivalry could form that would be very similar, and almost duplicate the Patriots-Colts rivalry of this past decade: two good teams dominating their respective division, both with elite quarterbacks, coupled with a 'who is the better QB' debate.
