I apologize in advance for thread-hijacking. I'll quit after this. :-)
It looks at the order of scoring in the box score along with the score at the end of each quarter to estimate how much time was spent in each situation. For example in the first quarter we might have
0 0 - tied 3 minutes
3 0 - up a little 3 minutes
3 7 - down a little 3 minutes
3 14 - down a lot 3 minutes
10 14 - down a little 3 minutes
That might be wrong for a specific game, but over a large number of games, it should be reasonably accurate. play-by-play of an entire game would be far better but I don't have that data.
Now lets say we were trying to calculate attempts, we could take a bunch of games with pass attempts and the breakdown of time in each situation
5% 10% 30% 25% 30% - 26 attempts
30% 25% 30% 10% 5% - 40 attempts
etc, for a berjillion stat-lines.
Now an algorithm tries changing expected attempts in each situation and adding them up to try and make the predictions match reality as closely as possible. Using every box score from 1980 to 2008, I get
Down a lot: 38.5 att/game
Down a little: 34.5 att/game
Tied: 32.9 att/game
Up a little: 29.4 att/game
Up a lot: 26.2 att/game
In an invented game where the team scores 2 TDs in the first quarter and that's all the scoring for the game, the breakdown would be:
Down a lot: 0%
Down a little: 0%
Tied: 8.3% (5 minutes)
Up a little: 8.3% (5 minutes)
Up a lot: 83.3% (50 minutes)
The predicted pass attempts would be 26.2*.833 + 29.4*.0833 + 32.9*.0833 = 27 pass attempts. The losing side would be expected to have 37.7 pass attempts.
I also realized that guys like Alex Smith would dominate the "down by a lot" results over the course of a year, so I averaged it by team *first*. In other words, we figure out how the 49ers do when losing big, and figure out how the Titans do when losing big, and the other 30 teams, then average THOSE numbers. So the Titans play when down big would be weighted just as heavily as the 49ers play, even though they spent far less time down big.
One big issue with my approach is correlation/causation. For instance, commentators love to say team X is 7-0 when they run the ball more than 35 times, with the implication that running the ball gets them the win. It's fairly obvious though that team X goes run heavy when they've already
got the lead, which is why they end up with more rush attempts in their wins. The same applies to QB stats. I think in the final analysis, it doesn't matter so much though -- If you spend 80% of the time down big and throw 0 INTs, you did far better than an average QB in that situation.
So att/game for Favre (average)
Down a lot: 42.7 (38.5)
Down a little: 41.1 (35.4)
Tied: 36.3 (33.5)
Up a little: 33.2 (29.7)
Up a lot: 28.2 (26.6)
Favre throws the ball more than average in all situations, which leads me to think he's probably been an above-average passer for his career. (Pass attempts is fairly well correlated with quality -- 10 of the top 20 all time are hall of famers, and 2 future hall of famers, and guys like Jim Everett who would have been a shoo-in if they played for strong teams). My weird quality system also takes into account completions, yards, sacks, sack yards, TDs, Interceptions... Favre's issues with throwing interceptions when he has the lead is why he doesn't appear better in the system I made.
By flipping the stat lines, I should in theory be able to do something similar with team defenses. :-)
whew! Okay, I'm done thread hijacking. Again, my apologies.