Carl Bialik writes:
There hasn't been a single 7-3 finish in the NFL since the league adopted the two-point conversion rule in 1994 . . . "Football scores are funny," Driner wrote me [Bialik] in an email. "Did you know that teams win more often when they score 13 points than when they score 14? It's a cause-effect thing. In order to get 13, you (usually) need two field goals. And teams don't kick field goals if they're down by 20 points. So teams lose 35-14 more often than they lose 35-13. That's why scoring 13 is better correlated with winning than scoring 14 is.
And, most amazingly,
An NFL game hasn't finished with a score of 7-0 in over a quarter-century.
More boringly, the most common final score is 20-17.
I watched the Pittsburgh-San Diego game that finished 11-10 this year and found myself getting oddly excited when the announcers pointed out that such a final score had never happened in the NFL before. The Steelers had a touchdown erroneously disallowed right at the end of the game, which should have made it 17 or 18-10, and my glee at the wrong call being made was among the nerdiest things I've ever felt.
Also, that 20-17 item should make the NFL really happy -- not too much offense, not too much defense, and close at the end.
Lots of those findings come from the blog at pro-football-reference.com:
http://www.pro-football-reference.com/blog/
There was once an exhibition game between the Bears and the Packers that ended 4-2. Dick Butkus was the leading scorer.