Is A Dominant Offense Enough To Win In The NFL?

If it's true that defenses win Championships, then some of the early favorites for the Super Bowl this season could be in a heap of trouble. The three teams with the best records in the league so far are all ranked in the bottom five of passing defenses - at least as measured by passing yards allowed. Here are the bottom five:

The current NFL record for passing yards allowed in a 16-game regular season is held by the 1995 Atlanta Falcons, with 4,541 yards. New England and Green Bay are on pace to surpass the Falcons' mark. Are these teams' defenses really that bad or are these numbers misleading? After the break, we look this in a little more detail and also figure out what this means for the Dallas Cowboys.

Here are some recent messages from the NFL highlighting how dominant the passing game has become in the NFL, and by extension, how passing defenses have struggled:

• There have been 106 individual 300-yard passing performances so far in 2011, the most in a single season all-time.
• Drew Brees has eleven 300-yard passing games in 2011, the most in a single season in NFL history.
• There have been 15 individual 400-yard games in 2011, the most in a single season in NFL history.
• This is the first season in NFL history with two 3,000-yard rookie passers in Andy Dalton and Cam Newton.
• There are four quarterbacks with at least 4,350 passing yards this season: Drew Brees (4,780), Tom Brady (4,593), Eli Manning (4,362) and Aaron Rodgers (4,360). Before this season, there was a total of two quarterbacks in NFL history to pass for at least 4,350 yards through the first 14 games (Rich Gannon, 4,409 in 2002 and Warren Moon, 4,401 in 1990).

While the major networks and many people who are paid to report about the NFL would have you believe that what matters is how many yards you accumulate, this is not in fact true. Volume stats do not correlate to victory. Efficiency stats do. How much someone passes or runs for can make for nice anecdotal discussions in the context of fantasy football, but has next to nothing to do with winning in the NFL.

Today, winning in the NFL is all about passing efficiency. The best offenses are those that pass the ball the most effectively, the best defenses are those that prevent their opponents from passing it effectively. The best teams in the league are those that do both most effectively.

One way to look at that is by calculating the difference between a team's passer rating on offense minus the defensive passer rating. This passer rating differential effectively tells you how much more effective a team is at passing the ball relative to its opponents and, and it can be a very strong indicator of team strength.

Here are the top ten teams so far this season by passer rating differential:

The Packers, Saints and Patriots, in that order, are the top three teams in terms offensive passer rating. Their defenses rank 8th (GB), 21st (NO) and 24th (NE) respectively in defensive passer rating. The latter two clearly have issues with their pass defenses, but their passing offense is so strong that that they're still ranked in the top five overall in passer rating differential.

You think this is all some fancy-pants stat mumbo-jumbo without any real bearing on actual game results? In statistics, there's a very simple way to show how meaningful a stat like passer rating differential is at predicting actual W/L records. To do that, we'll look at the "correlation coefficient" of a linear regression between passer rating differential and actual wins (This may sound complicated, but with a spreadsheet, a seventh-grader can do this in one minute).

In statistics, the correlation coefficient measures the relationship between two variables. This coefficient is often referred to as "r²" and is expressed as a number between 1 and -1. The closer the r² number is to 1 or -1, the stronger the relationship between the two variables. The closer it is to zero, the weaker the relationship.

R² between passer rating differential and wins so far this year is 0.81, an astonishingly high correlation. It is almost as good as scoring differential (0.84) at predicting the W/L record of an NFL team.

But now back to our original question: how much trouble are the Packers, Saints and Patriots in for all the passing yards they've given up? The short answer, none at all. The correlation between passing yards allowed and W/L record this year is 0.0064 - in other words, it's non-existent.

So those teams shouldn't be overly worried - as long as their offense keeps producing. The problem is though, that if you manage to stop their offense, their defense will likely not be able to compensate. All of which brings us to the Dallas Cowboys, ranked fifth overall in passer rating differential.

The Cowboys have the number four passing offense as measured by passer rating and the 15th ranked pass defense. This season, they combine one of the most efficient passing attacks in the league (and the most efficient in franchise history as measured by passer rating) with an average pass defense.

In an article for SI.com earlier this year, Kerry Byrne looked at the passer rating differential of teams that won it all:

Of the 71 champions since 1940, an incredible 26 of them -- 37 percent -- finished No. 1 in Passer Rating Differential; another 14 finished No. 2 in Passer Rating Differential. In other words, 56 percent of NFL champions were No. 1 or No. 2 in PRD.

That's a pretty impressive finding. So the next time you find yourself stuck in a debate about whether offenses or defenses win championships, you can lean back, smile and deliver a salomonic verdict: it's the difference between the two that really counts.

And just for fun, here are some correlations with 2011 W/L records and a collection of other stats:

*ANY/A: Adjusted net passing yards per attempt is basically passing yards minus sack yards divided by pass attempts minus sacks - with a 20 yard bonus for every touchdown and a 45 yard penalty for every interception. It provides a single, easy-to-understand number that encapsulates a team's passing performance using five different passing stats, only leaving out fumbles in terms of what a quarterback does. Here's the exact definition:

(Passing Yards + (Passing TDs)*20 - (INTs thrown)*45 - Sack Yards) / (Passing Attempts + Sacks)

*Y/A: Yards gained per pass attempt (Passing Yards / Passes Attempted).

*NY/A: Net yards gained per pass attempt, which is basically Y/A adjusted for sacks (Passing Yards - Sack Yards) / (Passes Attempted + Sacks).