These guys have too much time on their hands, but interesting nonetheless.
HOW CAN A 16-GAME SEASON BE SIGNIFICANT?
Football statistics can't be analyzed in the same way baseball statistics are. After all, there are only 16 games in a season. Baseball has ten times more, and even the NBA offers five times more. The more games, the more events to analyze, and the more events to analyze, the more statistical significance...
...Fans have gotten used to judging players based on how much they help fantasy teams win and lose, not how much they help real teams win and lose...
...DVOA, or Defense-adjusted Value Over Average. DVOA breaks down every single play of the NFL season to see how much success offensive players achieved in each specific situation compared to the league average in that situation, adjusted for the strength of the opponent...
...DVOA does a better job of distributing credit for scoring points and winning games. It uses a value based on both total yards and yards towards a first down, based on work done by Pete Palmer, Bob Carroll, and John Thorn in their seminal book, The Hidden Game of Football. On first down, a play is considered a success if it gains 45 percent of needed yards; on second down, a play needs to gain 60 percent of needed yards; on third or fourth down, only gaining a new first down is considered success.
We then expand upon that basic idea with a more complicated system of "success points." A successful play is worth one point, an unsuccessful play zero points. Extra points are awarded for big plays, gradually increasing to three points for 10 yards, four points for 20 yards, and five points for 40 yards or more. There are fractional points in between. (For example, eight yards on third-and-10 is worth 0.63 "success points.") Losing four yards is -1 point, losing 12 yards is -1.8 points, an interception is -6 points, and a fumble is worth anywhere from -1.70 to -3.98 points depending on how often a fumble in that situation is lost to the defense - no matter who actually recovers the fumble. Red zone plays are worth 20 percent more, and there is a bonus given for a touchdown.
...The biggest advantage of DVOA is the ability to break teams and players down to find strengths and weaknesses in a variety of situations. In the aggregate, DVOA may not be quite as accurate as some of the other, similar "power ratings" formulas based on comparing drives rather than individual plays, but, unlike those other ratings, DVOA can be separated not only by player but also by down, or by week, or by distance needed for first down. This can give us a better idea of not just which team is better but why, and what a team has to do in order to improve itself in the future...
...After dealing with DVOA for a few months, we had to deal with a strange tendency; well-regarded players, particularly those known for their durability, had DVOA ratings that came out around average...The problem is that DVOA doesn't take into account the value of a player being involved in a greater number of plays, even if his performance is league-average. A player who is involved in more plays can draw the defense's attention away from other parts of the offense. If that player is a running back, he can take time off the clock with repeated runs. And most importantly, nearly every player is a starter for a reason: he is better than the alternative...
...Special teams are an important part of football and we needed a way to add that performance to the team DVOA ranking. Our special teams metric includes five separate measurements: field goals (and extra points), net punting, punt returns, net kickoffs, and kick returns.
The foundation of most of these special teams ratings is the concept that each yard line has a different value based on how the likelihood of scoring changes with better field position...
...One exception to the use of DVOA/DPAR, and the use of "play success" instead of raw yardage, is the rating system for offensive and defensive lines. Actually, these are only measures of running plays, and of course the defensive numbers don't measure just the defensive line, but the whole front seven against the run.
One of the most difficult goals of statistical analysis in football is somehow isolating how much responsibility for a play lies with each of the 22 men on the field. Nowhere is this as obvious as the running game, where one player runs while up to nine other players -- including wideouts, tight ends, and fullback -- block in different directions. None of the statistics we use for measuring rushing -- yards, touchdowns, yards per carry -- differentiate between the contribution of the running back and the contribution of the offensive line. Neither do our advanced metrics DVOA and DPAR.
We have enough data amassed that we can try to separate the effect that the running back has on a particular play from the effect of the offensive line (and other offensive blockers) and the effect of the defense. A team might have two running backs in its stable: RB A, who averages 3.0 yards per carry, and RB B, who averages 3.5 yards per carry. Who is the better back? Imagine that RB A doesnâ€™t just average 3.0 yards per carry, but gets exactly 3 yards on every single carry, while RB B has a highly variable yardage output: sometimes 5 yards, sometimes â€“2 yards, sometimes 20 yards. The difference in variability between the runners can be exploited to not only determine the difference between the runners, but the effect the offensive line has on every running play...