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NFL Stat Analysis: Opposition Adjusted Quarterback Rating

Published: September 25, 2009

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Opponent Adjusted Quarterback Rating: Week Two

I recently put together a regression model to determine the factors that most drive the number of points a football team scores in any given game.  It’s a work in progress, but the factors I looked at were:
  • Yards per attempt (Y/A)
  • Interception Percentage
  • Yards/Rush
  • Average Y/A yielded by opponent
  • Average points yielded by opponent
Of the variables above, Y/A was, by the far, the strongest—followed by interception percentage.  The other three were pretty close in importance.
You’ll notice that a quarterback has a direct impact on two of the five. With that in mind, I decided to create a quarterback rating system that looks primarily at the factors of Y/A and interception percentage. 
Further, because a quarterback’s performance is obviously affected by their opponent, I added an element that accounts for the quality of the opponent’s defense
The formula for the rating, which I’m going to call the Opposition Adjusted Quarterback Rating (OA Quarterback Rating) until I can think of a cooler or funnier name.
The formula was basically:
  • Y/A minus the opponent’s average Y/A yielded PLUS
  • Int percentage minus the opponent’s average Int percentage yielded
A few notes.  Because the season is only two weeks old, the “Opposition Stats”—the stats that were used for Y/A and Int percentage yielded—were from all of 2008 and the first two weeks of 2009.  So, there is a margin of error there.
Also, when calculating the “Opposition Stats”, the metrics from the game against the current quarterback was not counted.  (i.e., if Jay Cutler is playing the Raiders, the “Opposition Stats” are from all of the games in 2008 and 2009 except for the one being played against the Raiders).
By the way, this is all a work in progress.  As I get more information I will layer it in.
Below are the OA Quarterback Ratings for 2009 through Week Two.  See the 2008 rankings here.

OA Quarterback Ratings: Through Week Two 2009

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NFL Stat Analysis: Yards Per Attempt: More Important Than You Think

Published: September 25, 2009

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My goal is to get into more robust analysis than what you’re about to read. But, just to get myself started, I started looking at some data to see if there is any way to predict a team’s offensive output (in terms of points).

Before I get to that, I want to give a little background. I’m of the ever shrinking school of thought that a quarterback should not be judged by his win-loss record. Working backwards, I decided that quarterbacks have much more control over their team’s offensive output than they do over the actual game results. That’s why my first article/analysis/”journey into loser-dome” is trying to find the stats that can predict offensive output.

I started off by looking at a couple of basic stats:

  1. Yards per attempt
  2. Interception %
  3. Average points given up by opponent (with the game being analyzed backed out)

I’ll dig into more stats as I get more time, but I wanted to get moving on this.

The first thing I did was look at the correlation of each of these individual statistics with the team’s scoring output. The numbers used were the averages for the 2008 season.

The 3 graphs to the right show the correlation between each of the 3 variables above and team scoring. If there is a correlation, we’ll see a linear pattern, with the data points arranging themselves diagonally from bottom left to top right (or, if it is a negative correlation, from top left to bottom right).

The results were a little surprising to me. Basically, the correlation of team score and the quarterback’s yards per attempt is significantly stronger than the other two. Interception % ahad almost no predictive value and average defense only offered a little more.

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Applying “Model” to Game Level Yards Per Attempt
Let’s take this a step further and apply the formula from the correlation of average yards per attempt and team score (Table 1-a) and apply it to individual games in 2008. The formula was y = 3.9572x – 5.7059 (x is yards per attempt, y is team score)

The resulting graph has an R squared of 0.2746. This means that 27.46 percent of the variance can be accounted for by this one variable. While that’s not great, when you consider all of the factors that go into a 60 minute football game, being able to explain one-quarter of the variance team output with one metric is pretty surprising.
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Do We Even Have to Look At The Score?
We know that there is some predictive value to comparing a quarterback’s yards per attempt to the team’s scoring. So, what if we look at how frequently the quarterback with the higher yards per attempt wins individual games.
Teams with a favorable yards per attempt won at a 71% clip (150-61). Only the Seahawks (2-6), Rams (0-3), Chiefs (1-3), Raiders (2-4), Lions (0-1), Bengals (1-2) and Packers (5-6) had losing records in games where they had better yards per attempt. Only the Titans (5-2) had a winning record when they had an inferior yards per attempt.

All of this says to me that a player who has a better yards per attempt statistic has a better chance of leading his team to victory.
What does this all mean? Not sure.

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One Last Thing
Below is a listing of quarterbacks and their yards per attempt.

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