### Examining the Ratio: Striking a Balance

#### by Jerome's Friend

As Andy Reid settles into his new position in Kansas City and we recover from a pass-heavy hangover (albeit with an unknown offense yet to emerge from the fog ahead), I would love nothing more than to illustrate the importance of running the ball. Unfortunately, my assumption was incorrect. Running when protecting a lead and passing when playing from behind are phenomena that do not offset each other. Therefore, the basis for my earlier conclusion that running more often may lead to more Eagles victories is not necessarily true. But after further research and analysis, it’s not entirely wrong either.

In order to better control for game context and increase statistical significance, I added two more seasons of data (2008 and 2009) and removed all fourth quarter rushing and passing attempts. I’m making another assumption here (it could be wrong and subject to many exceptions), that most rushing attempts when protecting a lead and most passing attempts when playing from behind occur during the fourth quarter. The subsequent “adjusted” run/pass and pass/run ratios include only data from the first three quarters of Eagles games during the past five years (80 games). As expected, these adjustments drastically changed the results of my previous logistic regression, making them less meaningful. Here is my prior run/pass ratio result along with the new adjusted ratio results:

The odds ratio for the adjusted run/pass ratio indicates that for every one unit increase in the run/pass ratio, the Eagles are over three times more likely to win (a big difference from 38 times more likely to win, as stated earlier). Compare this with the adjusted pass/run ration, where for every one unit increase, the Eagles are just 44% more likely to win. It seems that running attempts continue to have a greater impact on game outcomes. However, these two results have p-values greater than .05, are not statistically significant, and can be ignored. This pissed me off.

Thanks to feedback from commenters on Philly’s Inferno (mjoedgaard) and Reddit’s /r/eagles and /r/nfl pages (fourth_down_surprise) as well as some great feedback from Bleeding Green Nation and Wingheads, I did more research. In his 2007 article, Brian Burke from Advanced NFL Stats performed some linear regressions using multiple facets of the game and concluded that passing efficiency correlates more to wins than rushing. In 2003, Aaron Schatz from Football Outsiders also performed a regression analysis and concluded that teams do not necessarily need to establish the run early to win, and fourth quarter leads dictate more running plays for the winning team (and those running plays are extraordinarily effective). Burke’s and Schatz’s conclusions seem to agree with my new adjusted logistic regression results (By the way, both of these articles are great. Read them.). However, they also got me thinking more about balance. Could balance be important?

Using the same dataset (Eagles games from 2008-2012, first through third quarter only), I created a statistic, “Attempts from Balance”, which is the number of attempts (rushing or passing) needed to achieve a one-to-one run/pass ratio. I wanted to test the hypothesis that, as the attempts from balance decrease (or the closer to a balanced attack the team gets), the more likely the team can win. Here is the result:

The result of the logistic regression is statistically significant (p-value < .05) and indicates that for every one unit decrease in attempts from balance during the first three quarters (where one unit represents five attempts), the Eagles were nearly 2.5 times more likely to win. Here is a breakdown of the probabilities:

During games in which the Eagles executed a perfectly balanced attack through three quarters, they had a 78% chance of winning. When the team had between six and ten more rushing attempts than passing attempts, or passing attempts than rushing attempts, their win probability dropped to 37%. (Not included in the table are two games in which the Eagles had more than 12 passing attempts from balance. Disagreeing with this statistical model, the Eagles won both games.) This seems to illustrate that yes, balance is important and correlates with wins.

Of course, there are still many unforeseen variables at play here, and the direction of this correlation cannot be assumed. We can very easily say that game situations during the first three quarters over an 80-game span dictate balance, rather than balance dictating the result (although I think as the dataset grows, this becomes less likely). Also, this does not, on the surface, seem to agree with Burke’s and Schatz’s conclusions that passing is more important. However, their work is a result of linear regressions in which season stats are compared to aggregate numbers of wins, rather than non-linear regressions comparing single game stats and outcomes. But it’s hard to dismiss (and rather fun to accept) that this analysis does seem to jive with nearly every Eagle fan’s frustration during Andy Reid’s pass-first-answer-questions-later tenure. So maybe Chip Kelly should take note: strike with a balanced attack and pound the damn ball with ferocity.

*Click here for the detailed logistic regression file: Eagles Run Ratio – Logistic Regression*

*You can follow Philly’s Inferno on Facebook and Twitter (@JeromesFriend).*

While it seems that the ideal of finding the “golden ratio” will remain beyond our grasp due to the overarching noise in the data, this article does support the hypothesis that getting close to a balanced attack will yield beneficial results. I suspect the balanced attack is important to keep teams off guard, and any deviations from such a play should only be done under special circumstances (4th quarter deficit, having Rodgers as QB, etc…). I enjoyed the read; thanks.

Glad you enjoyed it man. I would love to see how the regression would look with more inclusive NFL team data. Unfortunately it would take way more time than I have to assemble that kind of dataset.

I have a feeling that balance, like PI(3.14…) is something that will show up in a lot of different things that we can’t fully explain why. There is such a thing as the PI phenomena or something to that effect. Basically saying that PI is a bigger player in things than we fully understand. 2nd time on your site and enjoyed both times.

Thanks Doug, I appreciate it! Keep coming back!

Man, great comment. Maybe I can look into that Pi phenomenon. You got me thinking though. How about the “golden ratio”? It’s where (1 + sqrt 5)/2 = 1.618…. It’s common in architecture and engineering and shows up in nature a lot, like tree branches and leaves, and possibly DNA. Maybe it, along with Pi, also appears in football somehow.

That is exactly how many snaps it takes for King Dunlap to commit a holding… ^^

Haha… Brilliant.

Fascinating stuff. It wouldn’t surprise me one bit. I’ve always thought that all truth/knowledge connects and can be broken down into one truth or beginning. Patterns are every where and connecting them helps expedite your understanding of how things work. Very cool stuff.

It really is. And we are one Higgs boson closer to a theory of everything.