In May, I wrote that the scoring team is responsible for roughly 60% of the points it scores, while the opponent is responsible for 40% of those points. In other words, offense and defense both matter, but offense tends to matter more.

I was wondering the same thing about passing yards. When Team A plays Team B, how many passing yards should we expect? As we all know, Team A can look very different when it has Dan Orlovsky instead of Peyton Manning, so I instead chose to look at Quarterback A against Team B. Here’s the fine print:

1) I limited my study to all quarterbacks since 1978 who started at least 14 games for one team. Then, I looked at the number of passing yards averaged by each quarterback during that season, excluding the final game of every year. I also calculated, for his opponent, that team’s average passing yards allowed per game in their first 15 games of the season.

2) I then calculated the number of passing yards averaged by each quarterback in his games that season excluding the game in question. This number, which is different for each quarterback in each game, is the “Expected Passing Yards” for each quarterback in each game. I also calculated the “Expected Passing Yards Allowed” by his opponent in each game, based upon the opponent’s average yards allowed total in their other 14 games.

3) I then subtracted the league average from the Expected Passing Yards and Expected Passing Yards Allowed, to come up with era-adjusted numbers.

4) I performed a regression analysis using Era-Adjusted Expected Passing Yards and Era-Adjusted Expected Passing Yards Allowed as my inputs. My output was the actual number of passing yards produced in that game.

Below is the best-fit equation, after I forced the constant to be zero, since we don’t care what the constant is in this regression, we just want to understand the ratio between the two variables.:

0.704 * Era-Adjusted Expected Passing Yards + 0.255 * Era-Adjusted Expected Pass Yards allowed by the Defense

The key number in that equation isn’t even *in the equation*: the key number is the ratio between the two coefficients. The quarterback variable is 2.76 times as large as the defense variable. In other words, 73% of the amount of passing yards in the game can be attributed to the quarterback (and his offensive line, wide receivers, tight ends, and running backs), and 27% to the defense.

Let’s say we think Drew Brees is a 320-yards-per-game passer in an environment where the average team throws for 230 yards. If he faces a team that allows 200 yards per game passing, this formula would project Brees to throw for 288 yards.^{1} Put Brees against a defense that allows 300 yards per game through the air, and his projection bumps up to 315 yards.

That’s a bit higher than the 60/40 breakdown from before, but not entirely unexpected. For starters, the 60/40 breakdown lumps together all teams regardless of changes in quarterback play: if we restricted that study to all games with the same quarterback, I suspect the numbers would diverge even more.

Then I did the same thing but used only seasons since 2000. The best-fit formula became:

0.748 * Era-Adjusted Expected Passing Yards + 0.247 * Era-Adjusted Expected Pass Yards allowed by the Defense

That jumps it from 73.4% quarterback to 75.1% quarterback. I also ran the numbers just since 2008, and the effect flipped, with the quarterback being responsible for 72.1% of the passing yards in a game.

One other note: The R^2 was 0.14 on the original equation, which is pretty low. That means a whole lot more goes into how many passing yards a player will have against a team than the average production of the player and the team. Perhaps something like Game Scripts? That’s food for another day, but I did run a few regressions, with no particularly interesting results. ^{2} In any event, I think we can safely conclude that the amount of passing yards a quarterback scores is roughly three parts quarterback, one part defense.

- Brees is 90 yards above average, and 90 * 73.4% is 66 yards. The defense is 30 yards better than average, and -30 * 26.6% is -8 yards. Therefore, we project Brees at 58 yards above average, which is equal to 288 yards. Note that in the regression equation, the coefficients add up to “only” 0.958. That, I think, reflects that the quarterback has a chance that he won’t play the entire game due to injury or a blowout. I think it makes more sense to project the quarterback as if is going to play the entire game. [↩]
- Okay, here they are:
On all games since 1978: 0.252 * Defense + 0.696 * Quarterback + 0.25 * Game Script. This implies that teams who are leading in games tend to throw for more yards. But I think this is a function of historical data.

On all games since 2000, the coefficient on the Game Scripts variable was -0.04 and nowhere close to being statistically significant. On the data over the past five years, the coefficient was -0.01, and nowhere close to significant. [↩]