With respect, I believe you're seriously mistaken here. It is my understanding that back when EA and Sega were both in the football game business the NFL/NFLPA did not get paid up front:
If this is correct (and DrJones was in a position to know since he actually worked for EA prior to "the Great Purge") that means that Sega wound up paying the NFL only a $1.99 per unit sold instead of $4.99. The notion that the NFL wouldn't care about this or the precedent it might set vis a vis their other business partners is fanciful at best.
Confident or desperate? Again according to VGChartz:
NFL 2k3 (North America) PS2 1.06 million units + XB .38 million units = 1.44 million units
ESPN NFL Football (aka NFL 2k4) PS2 .27 million units + XB .27 million total = .54 million
That's a 62% drop in sales from 2002 to 2003. Under those circumstances I can certainly understand why Sega felt they needed to roll the dice.
Perhaps. The fact that it was an licensed NFL game for a mere $20 and it was released three weeks before Madden (July 20th vs Aug 9th) may have had little something to do with those numbers as well.