First the easy answers. Field position? - if a team starts with good field position they can score points with less than stellar per play performance. But East Carolina finished 61st in average starting field position.
Mistake free football? - Don't turn the ball over, don't kill drives with penalties, and a team can over-perform it's per play metrics. East Carolina was slightly above average in both cases, but not enough to explain the discrepancy between yards per play and points per possession.
Maintain drives? - If you get 2.6 yards per play on every play, you'll never lose a game. A high completion percentage allowed East Carolina to maintain drives longer than the per play statistics would suggest (5.5 plays per possession).
Red zone play? - Touchdowns are worth twice as many points as field goals, and often the difference between the two is a few yards near the end zone. This is especially important for teams that move the ball by maintaining drives and not with explosive plays. And East Carolina was very good in this department, scoring more than 5 points per red zone trip. The problem with this explanation is that red zone performance is not a unique skill. The best teams in the red zone tend also to be the best teams at the 50 yard line. Was East Carolina uniquely good around the end zone? Can't say for sure.
The Statistical Review breaks down teams along a number of performance categories, everything from red zone scoring to field goal percentage, and compares that performance against the rest of the FBS. All 124 teams will be reviewed from 124 to 1 by the hybrid rankings. You can find short descriptions of the stats used in the table below.