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NorthCoast
05-23-2009, 09:37 AM
Jan 3, 2008
Does Defense Win Championships?

Well, of course. And so does offense. But the conventional wisdom that "defense wins championships" implies that defense is particularly more important than offense in the playoffs and the Super Bowl. This post will begin to look at whether defense really does matter more than offense in the NFL by comparing the right tails of the performance distributions of offenses and defenses--where playoff teams come from.

This time of year we are helped to the standard slew of articles declaring that defense is more important. Here is the latest example from ESPN.com. It's a good example because it suffers from some fatal flaws (itemized by Phil Birnbaum here). Typically, these articles look at past examples of NFL champions and comparing the offensive and defensive rankings of each team. I don't think this kind of analysis is necessarily very valid--

* They are anecdotal
* The sample size is usually very small, and results are probably not statistically significant--just due to chance
* If the sample size is large, it covers very distinct periods of NFL passing and blocking rules, confounding any results
* If the sample size is limited to one period of NFL rules, it can be dominated by one or two particular teams would skew the results (PIT in the 70s or NE currently, for example)
* Often, the analysis shows that defense is indeed important, but not more important than offense
* The rankings of each squad is almost always based on points scored or total yards, which are more often than not deceiving about the true performance of a squad


The biggest flaw may be using total points or total yards to compare squads. Offensive points scored is dependent on defense ability and special teams. Defenses that provide good field position allow an offense an easier time scoring. Teams with poor defenses provide poor field position, which allows their offense to gain more yards but probably fewer points scored. Additionally, teams that are winning will usually sacrifice total yards for chewing up time on the clock.

There is also an assumption that playoff football is somehow systematically different than regular season football. I'm not comfortable with that assumption--the rules are the same, the refs are the same, the field is still 100 yds long, and a touchdown is still 7 points. There are some unique things about the playoffs, but for now I'm going to set them aside and begin to look at how offenses and defenses compare in general by using regular season stats. (Using post-season stats is possible, but very problematic. About half of all playoff teams only play a single game before being eliminated, yielding very erratic and extreme team averages).

To best compare offensive and defensive performance and ability, squad efficiency--yards per play--should be used. Offensive and defensive efficiency are independent of each other. They aren't dependent on special teams or field position considerations. And perhaps most importantly, they aren't confused by the direction of causation. For example, total rushing yards correlates strongly with winning, but it's actually the winning that allows teams to inflate their rushing yards by eating the clock at the end of a winning game.

Efficiency stats are usually divided into passing and running efficiencies here at NFL Stats. But in this article we're interested in offenses and defenses as a package and not pass/run balance, so we'll use offensive efficiency (yards gained per offensive play) and defensive efficiency (yards allowed per offensive play). Data is from the 2002-2006 NFL seasons (N=160).

The graph below illustrates the actual distribution of team offensive and defensive efficiencies. The vertical axis represents the number of squads with the noted efficiency level (horizontal axis).

http://1.bp.blogspot.com/_ksxjg7CFQxA/R31DRyT6gnI/AAAAAAAAChM/pd35pnitDSY/s1600/table%2B2.PNG

Team efficiencies are expected to be distributed approximately normally. That is, there are a few really great offenses, an equally few really poor ones, and a bunch of average ones. League offensive and defensive efficiency must be balanced--there has to be equally as many yards gained as allowed. Accordingly, the average offensive efficiency and the average defensive efficiency are both 5.3 yards per play. The standard deviations are different, however. Offensive efficiency is 0.49 yds and defensive efficiency is about 20% smaller at 0.38 yds.

With enough observations, we would expect the distributions to smooth out, resembling more of a typical bell-shaped normal distribution. With the given averages and standard deviations, the theoretical efficiencies are approximated in the figure below.

http://3.bp.blogspot.com/_ksxjg7CFQxA/R31BrST6gmI/AAAAAAAAChE/VOhd7bdpB2k/s1600/table%2B1.PNG

The actual and theoretical distributions show the same tendency--offensive efficiencies are spread wider than defensive efficiencies. Notice the right tails of the distributions (below). This is where playoff and championship teams come from. (Actually, we should be comparing the right tail of the offense and the left tail of the defense. But the normal distribution is symmetrical, so rotating the defense about the league average yields the same comparison.)

http://2.bp.blogspot.com/_ksxjg7CFQxA/R31FICT6gpI/AAAAAAAAChc/zzjejuxx85g/s1600/table%2B3.PNG

This means that great offenses tend to be "better" than great defenses, and terrible offenses tend to be "worse" than terrible defenses. If my offense is 2 standard deviations (SD) above the mean and your defense is 2 SD above the mean, my offense would tend to prevail because a great offense tends to gain more yards above the NFL average than an equally great defense allows below the NFL average.

So if a great offense usually trumps a great defense, where does the perception that "defense wins championships" come from? Truly dominant defenses such as the 2000 Ravens, 2002 Buccaneers, or 1985 Bears are relatively rare, and are therefore more memorable. Also, defense has traditionally been overlooked, at least by the mainstream hype-laden media. Even football insiders seem to focus on offense, demonstrated by who is inducted in the Hall of Fame, or who the MVPs tend to be. So the phrase "defense wins championships" may really mean "defense helps win championships more than most people think they do."

One thing that this analysis does not do is focus on the specific case of great offensive vs. great defense. It considers team efficiencies as a whole. While this analysis indicates the likely outcomes of strong offenses vs. strong defenses, it is an indirect inference. A case by case study could look at playoff-type match-ups of good teams only, and tell us more.

Admittedly, there are some special qualities about the playoffs. The outdoor weather in northern cities can be extreme, and the home team is more often the better team. Weather may indeed affect the balance of offense and defense, but it likely affects the balance between running and passing games more. And weather affects both opponents in a game, so it's not clear if it really matters. Playoff weather could also be analyzed in further research.

So when looking at the NFL as a whole, offense and defense balances symmetrically. But when focusing on the right tails of performance, where playoff teams come from, we see that great offenses out-pace equally great defenses.

http://www.advancednflstats.com/2008/01/does-defense-win-championships.html