Only Alabama allowed fewer points per possession and BYU was the nation's most dominant defense by EP3 (effective points per possession, which also considers field position). They were 4th in plays, 3rd in yards, 4th in TDs and 3rd in red zone trips allowed per possession. They were 2nd in EPA per rush and got a TFL on more than a quarter of rush attempts. And they allowed 3rd down conversions on 26% of attempts (#1 nationally). They drop a couple spots in each category when you adjust for schedule, but no team did more against the schedule they faced then BYU. On defense.
The offense was a different story. In reality, they were only truly bad in three areas - they turned the ball over too often (see Boise State), the kicking game was atrocious (see Utah, Notre Dame), and they were as explosive as wet talcum powder. In retrospect, it is hard to diagnose how much of BYU's troubles were a product of a revolving quarterback situation, but that didn't help.
BYU brought back Robert Anae to coordinate the offense, and will be going up-tempo in 2013. This could be good. Taysom Hill is a unique talent at quarterback and he will have playmakers at running back and receiver to work with. The key to success for an up-tempo offense is 3rd down - getting conversions on offense and stops on defense. BYU was very good on 3rd downs on both sides of the ball in 2012.
It could be a disaster because Bronco Mendenhall is still the head coach. Bronco built a stellar defense, but he would not be the first defensive-minded coach that has built a program around a culture that is not conducive to up-tempo and/or spread offenses. There's a reason Anae "resigned" from this same post a couple years ago, and it wasn't because the offense was too good. And I'm not convinced that a season with Rich Rod is the cure.
That being said, it is not unreasonable that BYU could improve its points per possession from 2.16 to 2.66 with Hill at the helm and a real offensive philosophy. If the defense can turn in another top 10 performance, BYU's production would be in the vicinity of the 2012 versions of Ohio State or Georgia. That would not be bad at all.