Here are the basic lessons learned by Football Outsiders from statistically studying NFL football for a half-dozen years. This post by Aaron Schatz provides the discussion behind each one-liner:
You run when you win, not win when you run.
A great defense against the run is nothing without a good pass defense.
Running on third-and-short is more likely to convert than passing on third-and-short.
Standard team rankings based on total yardage are inherently flawed.
A team will score more when playing a bad defense, and will give up more points when playing a good offense.
If their overall yards per carry are equal, a running back who consistently gains yardage on every play is more valuable than a boom-and-bust running back who is frequently stuffed at the line but occasionally breaks a long highlight-worthy run.
Rushing is more dependent on the offensive line than people realize, but pass protection is more dependent on the quarterback himself than people realize.
Shotgun formations are generally more efficient than formations with the quarterback under center.
A running back with 370 or more carries during the regular season will usually suffer either a major injury or a loss of effectiveness the following year, unless he is named Eric Dickerson.
Wide receivers must be judged on both complete and incomplete passes.
The total quality of an NFL team is three parts offense, three parts defense, and one part special teams.
Teams with more offensive penalties generally lose more games, but there is no correlation between defensive penalties and losses.
Field-goal percentage is almost entirely random from season to season, while kickoff distance is one of the most consistent statistics in football.
Recovery of a fumble, despite being the product of hard work, is almost entirely random.
Field position is fluid.
The red zone is the most important place on the field to play well, but performance in the red zone from year to year is much less consistent than overall performance.
Defenses which are weak on first and second down, but strong on third down, will tend to decline the following year. This trend also applied to offenses through 2005, but may or may not still apply today.
Injuries regress to the mean on the seasonal level, and teams that avoid injuries in a given season tend to win more games.
By and large, a team built on depth is better than a team built on stars and scrubs.
Running backs usually decline after age 28, tight ends after age 29, wide receivers after age 30, and quarterbacks after age 32.
The future NFL success of quarterbacks chosen in the first two rounds of the draft can be projected with a high degree of accuracy by using just two statistics from college: games started and completion percentage.
Highly-drafted wide receivers without many college touchdowns are likely to bust.
Championship teams are generally defined by their ability to dominate inferior opponents, not their ability to win close games.
Read the whole thing there.