In my last post on this topic, I used linear regression to analyze my custom formula that attempts to predict each team's future success in the NFL. If you missed that, you can get caught up on it (and every post in my "Crunching the Numbers" series) by checking out this hub.

The previous article gave an overview of how linear regression works and the adjustments I made so that results will be easier to read. I won't go through that all again, but I'll sum up the highlights here:

All numbers associated with each statistic are correlation coefficients , and they quantify whether or not that statistic has any sort of relationship to winning

A positive number implies a positive relationship (for example, more points scored = more games won)

implies a (for example, points scored = games won) A negative number implies a negative relationship (for example, fewer points allowed = more games won)

implies a (for example, points allowed = games won) In order to have 95% confidence that a number is not coincidence , the value of the number must be at least 1.00

, the value of the number The maximum value a number can have is 2.8623

If you want to know more, feel free to check out the first post, but these are the big things to keep in mind when looking at the results of my analysis. I divided up offense and defense mostly because those two have different statistics that correlate with winning. There are three categories with each statistic, "2014," "Overall," and "Trend." The 2014 column simply states how that statistic correlated with winning in 2014 alone. The Overall column shows how that statistic has correlated with winning since 2013.





The Trend column is a little more in-depth. That number is the difference between the overall correlation and the 2013 correlation, which serves as "year zero" for this study. If the number is positive, that means that statistic has shown a stronger connection to winning as time progressed. On the other hand, if the number is negative, it means that statistic has shown a weaker connection to winning as time progressed. If the number is zero, that implies the statistic has shown roughly the same connection to winning; however, in a logical sense if a statistic is truly indicative of winning than the relationship to wins should get stronger as time passes. For a frame of reference, the maximum theoretical value for the trend column is 2.863.





Now that all of the background is out of the way, let's start things off with offense!





OFFENSE

Here are the results for the offensive statistics, listed in order of strongest overall correlation:

Statistic 2014 Overall Trend Points Scored/Game 2.264 2.337 0.319 Average Team Passer Rating 1.959 2.034 0.232 Turnover Margin/Game 1.980 1.993 0.116 Interception % -1.759 -1.975 0.595 Yards/Pass Attempt 1.797 1.902 0.156 Interceptions/Game -1.625 -1.827 0.295 Giveaways/Game -1.613 -1.812 0.298 QB Sacked/Game -1.656 -1.582 0.440 Rushing First Downs/Game 1.120 1.575 0.275 Rushing Attempts/Game 1.440 1.432 0.234 Completion Percentage 1.124 1.297 0.096 Incompletions/Game -0.795 -1.121 -0.426 Rushing Play % 1.115 1.060 -0.154 Passing Play % -1.115 -1.060 -0.154

A few key observations can be made right off the bat. First and foremost, points scored has far and away the strongest connection to winning, which is rather obvious. Additionally, winning is heavily skewed towards quarterback play and ball security; in fact, a rushing statistic doesn't even appear until the ninth spot on the list. This is very indicative of the modern, pass-happy NFL, and also makes sense since the quarterback is generally the only player who can turn the ball over in multiple ways.

When looking at the long-term, almost every statistic showed a meaningful improvement in its relationship to winning, with the exception of four. Completion percentage stayed somewhat steady, but incompletions per game saw a significant decrease. The ratio of run-pass play selection also saw a symmetric weakening in their connection to winning.

What does this all mean? Play selection and passer accuracy are clearly unrelated, so to me it says two things. One, the ability of the quarterback to complete a pass appears to becoming less important than his ability to avoid sacks (0.440 increase in strength) and take care of the football (0.595 increase in strength for interception percentage). Whether or not this trend continues remains to be seen, but it will certainly be something I'll be keeping an eye on as the seasons pass.

I'll save my concluding thoughts on all of this for the end. For now, let's move onto defense.

DEFENSE

Here are the results for defense, listed in order of strongest overall correlation:

Statistic 2014 Overall Trend Points Allowed/Game -2.077 -2.075 -0.106 Passing Play % 1.849 1.901 0.408 Rushing Play % -1.849 -1.897 0.412 Average Team Passer Rating -1.714 -1.796 0.020 Rushing Attempts/Game -1.885 -1.776 0.432 Incompletions/Game 1.502 1.648 0.433 Yards/Pass Attempt -1.346 -1.452 0.240 Interceptions/Game 1.093 1.243 0.131 Takeaways/Game 1.277 1.162 -0.138 Interception % 1.078 1.142 -0.161 QB Sacked/Game 0.284 0.909 -0.453

Like offense, the scoring defense has the strongest connection to winning, but after that the similarities end. Even that is putting it lightly - while play selection had the weakest connection to offensive success, it has easily the strongest connection to defensive success. After that, passer rating narrowly edges out rushing attempts per game, and incompletions per game and yards per pass attempt find themselves in the middle. Again, this is the defense's answer to modern passing: force the opponent to pass and then render the quarterback ineffective. There is nothing all that groundbreaking there.

What is interesting are the statistics that found themselves at the bottom of the list. Three of them relate to turnovers, and the basement-dweller was our favorite Cinderella story from 2014 - the pass rush! More than anything I was surprised that sacks had virtually no connection to winning in 2014, which is indicated by their paltry 0.284 correlation coefficient. For now, I'm guessing that it is a fluke, but for the time being the large drop in strength (-0.453) is impossible to neglect. I'll definitely be keeping an eye on this moving forward.

As for the turnovers, considering the enormous impact they have on the game, I was shocked to see them near the bottom of this list, with two statistics showing a slip in the correlation with winning. Even more perplexing is the strong connection turnovers has to winning on the offensive side. Why would there be such a discrepancy between the two? This question is too big to answer in this post, but I'll touch up on it in the conclusions below.

Conclusion

Unfortunately, this data seems to raise more profound questions than any answers it could possibly provide. But there are important inferences we can make from what we have. Specifically, we can make basic generalizations about the roles that the offense and defense play during a regular game of football:

The offense, in addition to scoring points, is responsible for protecting the ball, preventing sacks, getting good production from the quarterback, and having a basic commitment to the running game.

The defense, in addition to preventing offensive scores, is responsible for "setting the tone" by forcing the opposing offense into passing more, preventing good production from the quarterback, and limiting the volume of rushes by the offense.

These statements may seem trivial, but the reality is that it is anything but. As a football nerd with too much time on my hands, I have a tendency to overthink things, and the truth here is that the information above has some serious "chicken-or-egg" type ramifications and deserves its own post.

Be sure to keep an eye out for my last post on this topic, where I attempt to use the quasi-philosophical implications of this data to uncover the fundamental nature of the sport of football.