Pass Rush & Pass Defense - Looking at the Numbers

In Matty's Friday article discussing cornerbacks, the first point he addressed was whether it is more important to have a pass rush or great corners.  Matty mentioned teams on each side of the debate- and pointed out teams with both great and mediocre pass rushes who had top tier pass defenses.  I decided to to take a look at the stats from last year and see if there really is any kind of correlation.

Just a note when you are reading these charts- you are going to see something on them called an R^2 value- for those of you not that familiar with stasitics- always helpful Wikipedia is here to explain it for us:

More simply, R2 is often interpreted as the proportion of response variation "explained" by the regressors in the model. Thus, R2 = 1 indicates that the fitted model explains all variability in y, while R2 = 0 indicates no 'linear' relationship between the response variable and regressors. An interior value such as R2 = 0.7 may be interpreted as follows: "Approximately seventy percent of the variation in the response variable can be explained by the explanatory variable. The remaining thirty percent can be explained by unknown, lurking variables or inherent variability."

A caution that applies to R2, as to other statistical descriptions of correlation and association is that "correlation does not imply causation." In other words, while correlations may provide valuable clues regarding causal relationships among variables, a high correlation between two variables does not represent adequate evidence that changing one variable has resulted, or may result, from changes of other variables.

So that is really a number you want to keep an eye on- a better R^2 value means that sacks correlate better with the pass defense stat.  As it points out- correlation does NOT necessarily imply causation.  That being said- it wouldn't be hard to come up with some logical links between a pass rush and pass defense so I think it is safe to say that they do at least affect eachother in most cases.

Now with the boring explanation of the charts out of the way- lets get on to the boring charts themselves.  I took a look at a few key measures of a pass defense- Interceptions, passing touchdowns allowed, opponents completion percentage, opponents yards per passing attempt, and opponents passing yards per game.

To represent pass rush- I chose pure sacks.  It might be more fair to include sacks + QB hurries + QB hits - but two factors came into play.  First, QB hurries aren't an official NFL stat-  F.O. tracks them in their Prospectus at the end of the season- but I don't believe it is even out yet - either way I don't have a reliable stat for them.  As far as hits, they also include hits that result in a pass interference penalty- which I don't think should really count towards a good pass rush.

First up- sacks vs. interceptions.  An interception is by far the least likely outcome of a pass play.  A completion percentage of 55% is pretty awful- but it still means a majority of a QBs passes are completions.  Next up are incompletions.   Interceptions are a very small percentage of all pass plays- but they change the game in such a big way- it is a stat that tends to draw the fans eye.  So how do sacks and INTs correlate?

Turns out- not very well at all.  That is basically no correlation at all.  I was really shocked when I saw this- but last year the number of sacks a team was able to get had virtually no bearing on the number of interceptions.  I was so taken aback- I went back and looked at the data from the last 5 years- just in case this year was a fluke.

That is a little bit better- it does show some positive correlation- but the variability is immense.  Remember this line from our friends at Wikipedia:

The remaining thirty percent can be explained by unknown, lurking variables or inherent variability.

I'd say we have some of those here.  A pass rush does influence it- but there are any number of other factors that are coming into play here.  I would say that INTs are definitely an item that is affected by the quality of the corners.  Other factors probably include scheme, actual passing attempts against the team, and probably even just plain old fashioned luck.

From here on out- I am just going to be posting the 1 year correlations as the 5 year numbers had no significant differences, but as you can see, are a bit harder to read.

Next up- passing TDs.  The number one goal of any defense is ultimately not focused on preventing yards, but preventing points and getting off the field.  How did the better pass rushers do in this regard?

Much better correlation here- with two very big outliers (if they weren't in there, the R^2 value would more than double to about .15, but unfortunately, you can't just toss out data to fit an argument).  There is a clear correlation here, but still a lot of variability.  In case you are interested, the big outliers are the Colts on the low end, and the Cardinals on the top end.

Next up, sacks versus yards per game.  While stopping TDs is the priority, it is of course much easier to stop passing touchdowns if you keep them as far away from the endzone as possible.  How did they match up?

This is an even better correlation.  It still isn't anything great- and other variables account for a majority of preventing passing yards per game ( you can have a great pass defense, but if the other team runs 50 pass plays they are still gonna produce some passing yards. . .), but there is a clear decrease in passing yards allowed as sacks go up.  That brings me to the next number.

As I said above, you can have a great passing defense but still give up a decent number of passing yards if the other team refuses to stop passing.  4 yards per attempt is an awful passing average, but if you throw the ball 60 times you are still going to put up 240 passing yards.  Lets see how sacks match up to YPA:

Once again, a clear correlation shows up.  Also once again, there is still tons of other variablity, but you can clearly make an argument that the better the pass rush, the fewer yards per attempt the other team is able to produce.

Last but not least, is how sacks match up with opponents completion percentage.  Forcing a team to keep to short passing routes is one thing, but its still not ideal if they keep completing them.  If you can limit the ability of your opponent to complete passes, you leave them with no choice but to start running the ball more or you get them off the field faster. 

This falls right into line with the previous two measures.  A clear pattern has emerged, but there is still a lot of variation in the numbers.  Better pass rushing D's force more incompletions, but there are still a LOT of other factors in play.

If you actually read this entire post- my congratulations to you.  What do you make of these correlations?  Do you think they have any validity at all?  Did it reinforce or change any of your opinions?

Me personally- I think that the correlation you see IS valid.  A great pass rush definitely influences your ability to successfuly defend the pass.  That being said- there are tons of other variables involved. 

For myself, I have to assume that the quality of the cornerbacks is one of the bigger affects.  After looking at this it really seems like the pass rush will amplify the abilities of your corners; meaning it will make an average corner look good, and a good corner look great.  You can help cover for the mistakes of talented rookies, or knowledgable but declining Vets.  But are you going to be happy with a terrible corner looking mediocre? You can amplify talent all you want- but if the guy has 0 talent, anything times 0 is still zero.

After looking at all this, you can definitely sign me up for the "draft a corner on the 1st day bandwagon", and after that is completed, put me on the "draft 2 back up corners on the 2nd day" bandwagon that will be behind it.