Tyger's diary got me thinking... What if Griese was named the starter in the preseason? Tyger went through each game, trying to figure out how Grossman contributed to each win and loss. There's a more quantitative way to do this using Football Outsider's DPAR QB ratings.
DPAR stands for "Defense-adjusted Points Above Replacement" and represents the extra points we would lose (or, in some cases, gain) by replacing Rex Grossman with a backup QB. Weekly game DPAR's are posted at foxsports.com by Aaron Schatz, so i went through his archives to find out Grossman's game-by-game DPAR values. Here are those numbers, along with the Bears margin of victory (negative numbers represent a loss), and the margin of victory if the Bears used your run-of-the-mill replacement QB (RMoV):
According to this method, if you were to replace Grossman with a standard backup QB, the Bears record would still be 10-2, as they would have beaten New England last week, but would have lost at Minnesota in week 2.
We can also look at the effect Grossman's high variance has had on the club. If his performances showed no variance, he'd score his average 0.9 DPAR every game and the Bears would be 11-1. They would have beaten New England and still would have beaten Minnesota on the road.
Another way to examine the effect of Grossman's high variance is to assume his performances are random. We can do this by taking each RMoV and adding Grossman's single game DPAR for each of his games, independent of the Bears MoV. For example, in week 1, it didn't matter if "Good Rex" or "Bad Rex" showed up, as even Rex's worst performance of the season still would have allowed the Bears to win. This gives us 144 "games" to sample from, and the Bears record in those games would be 126-18. That .875 win rate is equivalent to a 10.5-1.5 record over 12 games, and a 14-2 season record.
Basically, it seems that replacing Grossman with a replacement-level player would make the team slightly worse, both in terms of production from the QB position, and in terms of their W-L record.
However, that leaves the question of whether or not the team would be better with Griese as the starting QB. The reason this question is yet unanswered is that all the above numbers assume an average replacement QB, and we have to account for the fact that Griese is widely considered one of the better backups in the league. Unfortunately, the answer to that question is as dependent on which Griese shows up as it is dependent on which Grossman shows up. Here are Griese's DPAR/game averages for each year of his career for which DPAR is reported (given as year/DPAR/Games Started/DPAR per game):
Griese's career has been up and down, but he's been consistently better than your average replacement QB (2003 excepting). If we take Griese's career DPAR/G and apply it to this season's Bears team, it would give them a boost of ~2.0 points per game over Grossman, and 2.9 points per game over a replacement player. That 2.9 points would have been enough to beat New England and Minnesota, but not Miami. Thus, if we had a career-average Brian Griese for every single game this year (with no variance), you'd expect the team to be 11-1.
I don't have game-by-game reports of Griese's DPAR, but we can get a zeroth-order fudging of it by using his different season DPAR/G values. Certainly his single game variance will be higher than his seasonal variance, but this is a start. If we indepdnently apply each of Griese's season DPAR/G value to the Bear's DMoV, that gives us 72 "games" to analyze, over which the Bears would have a record of 64-8. Over 144 games, that would be a record of 128-16. Thus, even when using a method i'd expect to underestimate Griese's game-to-game variance, the improvement of Griese over Grossman is moderate: 2 games over a 144 game (9 season) "sample".
In other words, substituting Grossman's 12 games with 2 sets of Griese's 6 seasonal averages would have gotten the Bears two more wins... if you extrapolate these results over the course of 9 full NFL seasons. Given Grossman's youth, his higher ceiling (which i think will be necessary to win the super bowl), the overall youth of the team, and the fact that Grossman's skillset fits the offense better, and the moderate advantages replacing him would gain, i'd go with Grossman... well, at least for another week.