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For more from Chase and Jason, check out their work at Football Perspective and The Big Lead.
ShareThisThrough six weeks: rearview adjusted yards per attempt
Two months ago, I blogged on one of my favorite statistics: rearview adjusted yards per attempt. Adjusted yards per attempt is a statistic most of us are familiar with by now -- its calculated by simply adding 10 "yards" for every touchdown pass, and subtracting 45 "yards" for every interception. Then you divide passing "yards" by pass attempts, so it's basically a more precise version of yards per attempt. Quarterbacks that throw for a lot of yards per attempt with a good number of interceptions get rightly penalized (think Ben Roethlisberger last year), while quarterbacks that don't throw any interceptions get a nice boost even if they have a low yards per attempt ratio (think David Garrard this season).
So what does "rearview" add to the equation? It adjusts the performance for strength of schedule. This is particularly important to do when we're looking at mid-season numbers, which are more heavily susceptible to radically different strength of schedule numbers. When you combine the rearview adjustment with the change by adjusting the yards per attempt, you've got rearview adjusted yards per attempt.
So who are the leaders in that category this year?
For starters, all NFL QBs averaging 5.97 adjusted yards per attempt, so that should be considered our baseline for good performance. I've subtracted that number from every QB's results, so you can get a better sense of who is doing better and worse than average. Here are the results for all QBs with a minimum of 40 pass attempts this season:
Player RAY/A AY/A SOS
Tom Brady 3.13 3.30 -0.16
David Garrard 3.10 2.33 0.77
Jeff Garcia 2.63 2.63 0.01
Peyton Manning 2.23 2.08 0.15
Kurt Warner 2.15 2.42 -0.27
Jon Kitna 1.97 0.83 1.14
Derek Anderson 1.67 0.96 0.71
Tony Romo 1.63 1.29 0.34
Jake Delhomme 1.59 1.61 -0.03
Donovan McNabb 1.58 0.99 0.58
Matt Schaub 1.30 1.39 -0.09
Jay Cutler 0.84 0.13 0.71
Brett Favre 0.80 0.24 0.56
Philip Rivers 0.79 0.02 0.77
Jason Campbell 0.57 0.40 0.16
Ben Roethlisberger 0.54 1.42 -0.88
Kelly Holcomb 0.52 -0.18 0.70
Eli Manning 0.43 -0.21 0.64
Joey Harrington 0.31 -0.13 0.44
Trent Green 0.18 -0.85 1.03
Chad Pennington 0.12 -0.73 0.85
Carson Palmer -0.10 0.19 -0.29
Matt Hasselbeck -0.24 0.97 -1.22
Damon Huard -0.39 -0.09 -0.30
Daunte Culpepper -0.78 -0.21 -0.57
Trent Edwards -0.89 -1.14 0.25
Brian Griese -0.89 -0.39 -0.50
J.P. Losman -0.95 -1.50 0.56
Alex Smith -1.33 -0.90 -0.43
Drew Brees -1.74 -2.22 0.48
Steve McNair -1.80 -0.55 -1.26
Marc Bulger -1.88 -1.42 -0.46
Kyle Boller -1.96 -1.02 -0.94
Kellen Clemens -2.06 -1.40 -0.66
Josh McCown -2.33 -1.43 -0.90
Cleo Lemon -2.37 -1.80 -0.57
Vince Young -2.53 -1.91 -0.62
David Carr -2.65 -1.78 -0.87
Matt Leinart -2.73 -1.62 -1.11
Rex Grossman -2.74 -3.28 0.53
Tarvaris Jackson -3.55 -2.68 -0.87
Trent Dilfer -4.92 -3.49 -1.43
Gus Frerotte -5.45 -3.98 -1.47
What's that mean exactly? Let's take Mr. Brady as an example. He's thrown for 1771 yards, 21 TDs and 2 INTs, a total of 1891 adjusted yards. He's thrown 204 passes, giving him an average of 9.27 AY/A. Since the league average QB is at 5.97 adjusted yards per attempt, Brady's 3.30 adjusted yards per attempt better, represented in the middle column. Tom has had a slightly easier than average schedule, though, as shown by the -0.16 number in the right column. Therefore, his rearview adjusted yards per attempt is 3.13 AY/A better than the league average.
Notes
- Wow is David Garrard having an incredible season. On top of his zero interceptions, he's doing it against a pretty difficult schedule. In fact, he's only a hair behind Brady despite having significantly inferior wide receivers.
- We haven't heard a lot about it, but Carson Palmer is having a very down year. Sure he lit up the Browns, but he's thrown two interceptions in each of the past four games, all Bengals losses.
- Jon Kitna, Trent Green and Chad Pennington have faced the three toughest schedules in the league. Gus Frerotte, Trent Dilfer, Steve McNair, Matt Hasselbeck and Matt Leinart have faced the five easiest.
- Brian Griese has played a lot better than Grossman, but he has faced a much easier schedule. As bad as Steve McNair has looked, Kyle Boller hasn't been any better Warner was way better than Leinart this year, despite facing a tougher (but still easier than average) schedule.
Below are the rankings for the defenses, using rearview adjusted yards per attempt allowed:
Team RAY/A AY/A SOS
Washington Redskins 3.00 2.02 0.98
Tennessee Titans 2.42 1.45 0.97
Oakland Raiders 2.07 0.87 1.20
New England Patriots 1.82 1.28 0.54
Buffalo Bills 1.19 0.00 1.20
Philadelphia Eagles 1.19 0.25 0.94
Indianapolis Colts 1.17 1.35 -0.19
Kansas City Chiefs 1.01 0.70 0.32
Pittsburgh Steelers 0.88 1.20 -0.32
New York Giants 0.71 -0.05 0.76
Dallas Cowboys 0.60 0.73 -0.14
Green Bay Packers 0.47 0.05 0.42
Houston Texans 0.43 -0.43 0.86
Denver Broncos 0.11 -0.67 0.78
Tampa Bay Buccaneers 0.03 1.19 -1.15
Carolina Panthers -0.08 0.37 -0.44
Cincinnati Bengals -0.21 -0.54 0.34
Minnesota Vikings -0.21 -0.25 0.04
San Diego Chargers -0.27 -0.57 0.30
St. Louis Rams -0.40 -0.98 0.58
Atlanta Falcons -0.50 -0.50 -0.01
Chicago Bears -0.73 -1.05 0.32
Miami Dolphins -0.76 -1.73 0.97
Jacksonville Jaguars -0.95 -0.63 -0.32
Cleveland Browns -1.20 -0.73 -0.47
Detroit Lions -1.22 -0.09 -1.13
New York Jets -1.26 -1.61 0.36
Baltimore Ravens -1.33 0.60 -1.93
Seattle Seahawks -1.48 -0.22 -1.27
San Francisco 49ers -1.77 -0.37 -1.40
Arizona Cardinals -1.88 0.05 -1.93
New Orleans Saints -3.15 -3.03 -0.12
Washington actually leads the league in adjusted yards per attempt allowed, with 2.02 fewer yards per pass against them than the league average. But they're doing it while facing the third toughest slate of passers in the league! As a result, we can conclude that Washington's pass D has been simply outstanding this year. And the Titans aren't too far behind, facing a similarly tough schedule.
Notes
- Look how far down the Ravens defense is. They've faced some terrible passers, which has really inflated their numbers. And the Saints pass defense has just been pathetic so far this year.
- Five toughest schedules? Oakland, Buffalo, Washington, Tennessee and Miami. And the Redskins and Dolphins still have more games left with Brady and Romo. Five easiest? Arizona and Baltimore in a landslide, followed by San Fran, Seattle and Tampa Bay.
This entry was posted on Thursday, October 18th, 2007 at 5:59 am and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.
Another great post by Chase. I have a few thoughts, some of which may be questions:
1. Is it safe to assume that the SOS adjustment is based on teams played against thus far and does not include teams later on the schedule?
2. How did you arrive at adjustments of 10 yards and 45 yards? They seem to work quite well. At first glance, who would think 10 extra yards makes that big of a difference, but it does bolster the average per attempt.
3. A humorous aside about SOS: It seems ironic that while everybody expects the Patriots to win 15 or 16 games this year, 5 or 6 would probably win them the division.
4. A serious aside about SOS: Some teams seem to get screwed by a tough schedule most years (such as the Bills, I whine), while others seem to have a easy one year after year (the Colts come to mind, the Rams when they were good, etc.) As long as the league remains split into conferences and divisions, this will happen. I'd love to see the league be one big pool of teams who all play a random schedule each year with no opponent more than once. I realize I'm in the minority, but it's my pipe dream.
5. Back to the main point: Looking at the defensive chart in your post, there doesn't seem to be a big correlation between a team's AY/A allowed and how good they are (just by quick visual inspection). However, the quarterbacks' list seems a bit more like I'd expect.
I can field a couple of those questions, Bill M.
1. Yes.
2. The 10 and 45 --- in fact, the entire AYPA stat --- comes from a book called The Hidden Game of Football. [Aside: if you like this blog, you'd like The Hidden Game. It literally changed the way I watch football.] They have reasons for using 10 and 45, but I don't want to do those reasons the injustice of trying to summarize them in the amount of time I have now.
4. This seems like a good idea for a future blog post. Thanks.
1. That's correct, Bill M.
2. They're from the Hidden Game of Football -- Doug talked about it here: http://www.pro-football-reference.com/blog/wordpress/?p=95
3. Yes, the Pats should clinch about as soon as any team will ever clinch their division. Crazy.
4. I agree, although for the most part team strengths change from year to year. But it does seem like teams in the current NFC West have it pretty nice.
Why would you add 10 yds for a TD pass? For the depth of the endzone? I would buy that.
But I would hesitate to add any bonus just because TDs are the final play of a scoring drive that probably required successful rushing. Passers on teams with strong defenses would also unfairly benefit from a TD bonus.
One advantage of the TD bonus is that it keeps us from unfairly punishing QBs for passing the ball in a goal-to-go situation, where it's impossible to get many yards. If there was no TD bonus, then each play from inside the opponent's 5 would be guaranteed to have negative value.
Here's a neat site: http://www.the506.com/nflmaps
I have no affiliation to it, but I find it useful. It shows what games are on TV every Sunday across the United States.
That's a good point about the goal line passes. But I wonder what percentage of TD passes are like that? I'd guess about half.
I don't think the 10 yards "bonus" is valid. Keep these measures simple and logical.
Re: Post # 8 from James.
I tend to agree with James that giving any type of bonus for a TD pass, whether it be 10 yards or 20 yards, makes little sense. Afterall, the QB already receives substantial credit in the four areas of passer rating---TD pass percentage, yards per attempt, lack of an interception, and a completion percentage increase. Why does he need additional credit?
One argument that has been made for a bonus is that many TD passes are of short lenght, but, in reality the aveage lenght of a TD pass in recent years has been about 18.3 yards. That's a pretty hefty yardage total for just one pass.
Another argument that has been made is that it is harder to score the nearer you get to the opponant's goal line. This argument is been put into chart form by David Roper who suggests that from 16 yards in---it becomes harder to score. Is Roper right? Well, yes and no. For one thing, if the aveage lenght of a TD pass is 18.3 yards, that total is obviously outside Roper's 16 yard figure. To me, that suggests that the aveage TD pass is not influenced by Roper's model at all.
In Pete Palmer's, et als, book The Hidden Game of Football, there is a fascinating chart on page 123 of this book (1988 edition). It gives figures, over a period from 1984-86, on completion percentages and interception percentages from every five yard increment on the field. From the opponant's 16 yard line to the 6 yard line, it is more difficult to move the ball than from other positions on the field (completion percentage falls from about 50% to about 43% and interception percentages climb from about 3.6% to about 4.5%. But, from the five yard line to the end zone, it is actuall a little easier to move the ball than it is from other areas of the field---completion percentage remains steady at 49% but interception percentage is only 3.3%. Another line of figures reveals that, over the last 16 yards, the percentage of sacks and "forces" are much lower---about 7% compared to 9.6% overall, but from five yards in the percentage of sacks and "forces" is only 5.1%.
What does this chart tell us. Well, it agrees with the Roper model up to a point---the five yard line, but from five yards in---it doesn't agree with the Roper model at all. It is just as easy to move those last five yards as it is from anywhere else on the field, perhaps easier. The Roper model breaks down and James is absolutely correct---we should not be giving a bonus of any type for TD passes. In Pete Palmer's, et als, book, they promise to explain the 10 yard bonus. They never do. It is utterly illogical.
Adjusted yards per attempts to convert various non-yardage pieces of information into equivalent yardage. Throwing an interception in terms of yardage shows up as 1 attempt and zero yards, but clearly it's worse than your run-of-the-mill incompletion. Scoring touchdowns gives zero additional yards beyond a completion to the 1-inch line on the stat line but clearly it's better. Thus the bonuses and penalties. One may nitpick about the size of the bonus or penalty but they should definitely be there.
As for TD%, INT% and whatnot affecting passer rating... Well, yes, they do affect passer rating. But this wasn't using passer rating as a performance metric so I don't see how that's related. Nothing is being double-counted, they're two separate metrics that attempt to quantify the same thing -- performance. The only real question would be when the two metrics disagree, which is more accurate.
Re: Reply to Post #10 from MattieShoes
The actual reference to the ten yard bonus occurs on page 50 of the 1988 edition of the Hidden Game of Football. It reads, "Touchdowns, we figure, should get a bonus of 10 additional yards. This is because the scoring potential from the 1-yard line is still only a bit over 6 points (instead of a full 7). Thus the final inch into the end zone is worth almost a full point. Since it normally takes about 12 yards of offense to score a point, the actual accomplishing of a touchdown is worth a ten yard bonus."
"We'll get into this in a great deal more detail later."
But, the authors never did go into detail. As other readers have pointed out, the authors give us no analytical or statistical explanation for the ten yard bonus. They leave us hanging with some vague idea that the last inch into the end zone equals .96 points (one point for a PAT minus 4% for missed PATs) which, in turn, equals about 12 yards of offense which somehow becomes a ten yard bonus for the QB.
Obviously, I'm not into math, but I do know that a QB can't throw a one inch TD pass---at least not officially. Also, on page 100 of the HGOF the authors state that, "Actually, it takes 15 or 16 yards to produce a point because most possessions result in only a few yards and no points at all."
Again, I'm not into math, but does any of this make any sense to anybody?