Consistency of Offensive and Defensive Efficiency Part I - Regular Season

Looking at the correlations of the stats to regular season win totals, offense seems to be more important than defense to winning. For example,

• Rush offense efficiency: 0.2052
  
• Rush defense efficiency: -0.13296
  

However, Football Outsiders did a study that showed that defense was more important to postseason success. This seems to fall in line with the 2002-6 Colts. And the same pattern can be found in baseball, where pitching metrics (especially for relievers) become the most highly correlated to playoff success (Baseball between the Numbers). But correlation does not equal causation. Why does offense suddenly drop in importance?

With the the single elimination playoffs, the better team does not always necessarily win. Teams never perform at their absolute average, which makes predicting wins through teams' average performance fairly difficult. The Jaguars by a fair share of metrics perform really well on average, but it hasn't translated to a great record because of their inconsistency. Over one game, anything can happen. So the team that gets deeper into the playoffs should be reliable and consistent.

If defense is the better predictor of postseason success, then is defense more consistent from game to game? Over a 16 game sample, if it is more consistent, then because the outcomes of games are so varied, the more consistent defensive metrics are more lowly correlated with win totals. Or an alternative hypothesis might be that because defensive performance is less consistent, that you need a very good defense, for whom rock bottom isn't that bad, to overcome the consistently excellent offenses in the playoffs. From year to year, defensive efficiency changes more than offensive efficiency (according to FO), so more week-to-week inconsistency would be reasonable to expect. Let's take a look at what the numbers have to say.

Correlation of week's performance with next week's performance, Unadjusted for opponent
Stat	Corr. Coef.
RunOff	0.08295
RunDef	0.039186
PassOff	0.17349
PassDef	0.010152
SackRateMade(Def)	0.01733
SackRateAllow(Off)	0.18595
3rdDownOff	0.071573
3rdDownDef	0.011514
IntRateGiven(Off)	-0.012781
IntRateTaken(Def)	0.01926
FumRateGiven(Off)	0.025166
FumRateTaken(Def)	0.025957

Average in-season standard deviation of metric, Unadjusted for opponent
Stat	Avg. Std. Dev.
RunOff	1.1732yds
RunDef	1.1885yds
PassOff	1.8195yds
PassDef	1.8962yds
SackRateMade(Def)	4.919%
SackRateAllow(Off)	4.6111%
3rdDownOff	13.096%
3rdDownDef	13.405%
IntRateGiven(Off)	2.9114%
IntRateTaken(Def)	2.8889%
FumRateGiven(Off)	2.7177%
FumRateTaken(Def)	2.7259%

According to these methods using the unadjusted-for-opponent stats, defensive performance is less consistent than offensive performance (except maybe with turnovers). The differences between the average std. deviations of the offensive and defensive metrics are small, but they are at least consistent in favor of offense. The differences in correlation coefficients are more significant. Surprisingly, the week-to-week correlation of defensive performance is near zero. The performance of defense one week seemingly has no bearing on performance the following week whatsoever. And momentum is, at best, a small factor on offensive performance, which apparently doesn't matter as much in the playoffs anyway. Much of this variance likely has to do with the opponents, so now is the time when we adjust for opponents.

Correlation of week's performance with next week's performance, Adjusted for opponent
Stat	Corr. Coef.
RunOff	0.095318
RunDef	0.052455
PassOff	0.13248
PassDef	0.026777
SackRateMade(Def)	0.022664
SackRateAllow(Off)	0.17386
3rdDownOff	0.071013
3rdDownDef	0.017221
IntRateGiven(Off)	-0.0048146
IntRateTaken(Def)	0.010823
FumRateGiven(Off)	0.018135
FumRateTaken(Def)	0.024204

Average in-season standard deviation of metric, Adjusted for opponent
Stat	Avg. Std. Dev.
RunOff	1.1083yds
RunDef	1.1073yds
PassOff	1.9546yds
PassDef	1.7601yds
SackRateMade(Def)	4.6508%
SackRateAllow(Off)	4.5034%
3rdDownOff	12.682%
3rdDownDef	12.788%
IntRateGiven(Off)	2.9403%
IntRateTaken(Def)	2.9135%
FumRateGiven(Off)	2.6759%
FumRateTaken(Def)	2.6853%

As it turns out, adjusting for opponents closes the gap a little, but offense is still more consistent overall. Adjusted for opponent, rush pass off. eff. have more variance than their defensive counterparts, but the week-to-week correlation is still well in favor of the offense.

Three out of the four tests I ran say that offensive performance is actually more consistent than defensive performance. So the conclusion seems to be that the defense needs to be very good so it can matchup okay with the consistently good offenses of playoff teams, even when they're not performing at their optimum. Does this reasoning make sense to anyone else? Definitely a topic for further exploration/discussion.


Addendum: Reply to bettingman's post
Do defenses adapt over the season and improve? Makes sense as they have to react to the offense. I just threw together these graphs. It's by game rather than week, so the two rates won't exactly sync up.







Rushing offense improves over the year by about .2 yards/attempt, but passing offense worsens over the year by about .2 yards/attempt. Sack rates don't trend either way, but interception rates increase by about .3%. So the passing game does indeed become less effective as the year progresses. The improvement in the rushing game might stem from defenses focusing more on the passing game. Also of note, kick and punt return averages decrease over the season but start to pick up again towards the end of the season. Clearly, special teams do a good job of adapating their return coverages. Do the return units start to adapt to the coverages as well?