That's part of it, but you're ignoring the points I made. So a few simple true or false
I'm really not, I'm just reinforcing what I said --
That’s not entirely true, QBR is calculated by looking at success on a play-by-play basis for the QB position. It’s similar to how S&P, FEI, and other advanced stats looks at drive success or efficiency or whatever.
So Book has a bad QBR because of how many times he didn’t get the job done on a play-by-play basis.
I never said you were wrong or crazy or anything like that, just that the idea that "subtract half the sacks and the INT and he has a great QBR" is not entirely true. Those plays sure as heck weren't worth 30+ points of QBR, and the primary driver of his score was him playing like butt not things outside of his control.
1) A QB with an OC who calls more screens is automatically disadvantaged (compared to a QB with an OC who calls less screens), and even with the same amount of, or even more production (pure yards and TDs) can have a lower QBR (than the QB not throwing screens).
2) A QB with higher production (pure yards and TDs) with a crap OL (giving up sacks), can have a lower QBR than a QB with less production, but has a great line (less or no sacks).
Both of the above can be true.
Point is, QBR is different from QB Rating, and has it's strengths and weaknesses. A QB like Book, can have higher production (pure yards, TDs) than others, but still look worse from a QBR perspective simply due to ND's love of screens, and a struggling OL. But, will have a higher QB Rating.
To both those points, consider this passage --
For example, Rodgers’ longest completion against the Redskins was a 34-yarder to James Jones in the second quarter, but he could have gained those yards through the air or on a short screen that was broken for a long gain. He also could have completed the pass when under duress or thrown it from a clean pocket. In all of those scenarios, Rodgers’ level of skill differs, and the credit he receives for the 34-yard gain (or in this case, plus-2.0 EPA) should differ as well.
That means on completed passes, the EPA is divided among the quarterback, his receivers and the offensive line based on how far the ball travels in the air, what percentage of the yards were gained after the catch (compared to how many yards after catch are expected) and whether the quarterback was under pressure. This division of credit is based on statistical analysis of thousands upon thousands of NFL plays. In this sense, QBR knows that Cousins was helped by his receiver, who gained fewer yards after the catch than expected given where he caught the ball, but hurt by his offensive line.
Consequently, it already tries to adjust for exactly the things you are talking about. Yes, someone throwing nothing but screens is going to get
less credit for the gains, but that's intentional. That doesn't necessarily mean they're "disadvantaged" in trying to get a good grade out of 100 over the course of the game. For example, someone throwing short passes that goes 35/40 for 300 yards & 3 TDs is likely to have a similar 90+ grade to someone who goes 20/30 for 300 yards & 3 TDs. Why? Because the player pushing the ball down the field gets more EPA per throw, but he's also being less efficient and likely missing more throws to get to those numbers. Baked in there is whether or not the OL and WRs are playing well.
So...
1. The player with a vertical passing game only has an "advantage" if it's effective on a YPA basis, and if the player doing the short passing game is inefficient (i.e. misses a fair amount of throws).
2. The opposite of this should be true, because you are supposed to get more credit for completing throws under duress.