Introducing ANY/A Differential

The favorite passing stat of many in the advanced stat world is adjusted net yards per attempt, or ANY/A.

Despite this, there does not exist on the internet (to my knowledge) any database of single game ANY/A, or, more interestingly, ANY/A differential and its correlation with winning football games.  You can get yards per attempt differential correlated with wins, or passer rating differential -- but not ANY/A differential.

I took both challenges on in my spare time this past week to bring you such data today.  And as the season rolls forward, I will continue looking back into seasons past to both establish a database of single game ANY/As and also see what use ANY/A might serve as a predictive tool.

To start, the first 4 weeks' worth of ANY/A has been calculated for every game.  In case you are unaware of the formula, as defined by Pro-Football-Reference, it goes as follows:

passing yards + (TDs * 20) - (INTs * 45) - sack yards
----------------------------------------------------------------------------------
pass attempts + sacks

For the weeks so far, I took every quarterback's ANY/A and compared it to the ANY/A of his opponent.  I then compared the offensive points scored of each team -- that is, total points minus special teams and defensive touchdowns (oh, and if the winning quarterback was taken out of a blowout game late for the 2nd-stringer to mop up, any points he might have scored were dismissed).

The two resulting differentials were then put side-by-side to see how often ANY/A differential matched offensive point differential.  62 games have been played so far (not counting the most recent Thursday game), and in all but 8 of the contests ANY/A differential correlated with offensive point differential.  In other words, the team with more adjusted net yards per attempt also scored more points in about 87% of games played in 2013.

The actual correlation coefficient of ANY/A differential to offensive point differential is a pretty awesome 0.83 through 4 weeks.

As I said, I will keep looking back into past seasons to see the correlation, as well as move forward this season with ANY/A as a possible predictive tool.  Perhaps even more awesome, however, by establishing quarterback and team ANY/A for single games, we can see defensive performance in a new way.

Defensive ANY/A takes into account a defensive's ability to (a) create turnovers, (b) cause pressure, and (c) play well in the secondary.  Perhaps more than any one stat, it can be used to holistically categorize and rank passing defenses from front to back.

What follows this week is the ranking of each team in ANY/A differential: offensive ANY/A minus defensive ANY/A.  Below that are my thoughts on a couple games using ANY/A as the primary statistical tool.

 Team Differ. Offense Defense Denver Broncos 4.73 10.97 6.24 New Orleans Saints 4.25 7.98 3.73 Detroit Lions 3.3 7.74 4.44 Seattle Seahawks 2.92 6.2 3.28 Kansas City Chiefs 2.83 6.09 3.26 Indianapolis Colts 2.21 6.32 4.12 New England Patriots 1.7 6.59 4.89 Tennessee Titans 1.34 6.46 5.12 Carolina Panthers 0.38 5.93 5.55 Houston Texans 0.24 5.2 4.96 Cleveland Browns 0.19 7.14 6.95 San Diego Chargers 0.07 8.47 8.4 Chicago Bears 0.07 5.87 5.81 Buffalo Bills 0.06 5.34 5.28 Dallas Cowboys 0.04 4.64 4.6 Minnesota Vikings -0.06 6.07 6.12 San Francisco 49ers -0.07 5.3 5.37 New York Jets -0.49 4.95 5.44 Philadelphia Eagles -0.55 7.56 8.12 Tampa Bay Buccaneers -0.85 3.73 4.58 Cincinnati Bengals -0.86 5.71 6.58 Atlanta Falcons -0.87 7.12 8 Green Bay Packers -0.94 7.7 8.63 Miami Dolphins -1.28 5.24 6.52 Baltimore Ravens -1.3 4.81 6.11 Pittsburgh Steelers -1.57 5.6 7.16 Arizona Cardinals -1.68 4.61 6.29 Washington Redskins -1.72 6.32 8.05 Oakland Raiders -2.31 5.47 7.79 New York Giants -2.41 4.31 6.72 St. Louis Rams -3.05 5.4 8.44 Jacksonville Jaguars -4.45 2.21 6.66

This chart can be viewed in a sort-able fashion by following this link to a Google Document.  Also in the document are several other spreadsheets with the information mentioned above.

I'll conclude with some thoughts on a few of today's outings as considered through the lens of adjusted net yards per pass attempt.  If you have any thoughts/ideas on how this statistic might be used, or if you would enjoy seeing single game ANY/A data for past seasons, please reply with words of encouragement and/or suggestions.

Can the Dallas Cowboys stop Peyton Manning?
Peyton Manning leads the league in ANY/A in 2013, just as he did in 2012.  Through 4 games, he is posting a ridiculous 10.96 adjusted net yards per attempt.

With only 5 sacks acquiesced in 161 dropbacks (sacks + attempts), the 37 year old veteran is being protected at a better rate than any other quarterback.  He is showing his appreciation with league-leading numbers in all the following: 9.42 yards per pass, 75% completion rate, 16 touchdowns, and 0 interceptions.

The Dallas Cowboys rank 9th in defensive ANY/A so far, but that comes against a struggling Sam Bradford, a "why did I draft David Wilson in the 2nd round of my fantasy draft?" Eli Manning, and a Chiefs squad led by Alex Smith in his 200th new offensive system.

The best preview of this match might be Dallas' contest last week against San Diego.  Philip Rivers ranks 2nd to Manning in our featured stat and he handled the Cowboys to the tune of a 9.51 ANY/A, throwing 3 touchdowns and only being sacked once and picked off once.

Rivers is starting this season very strong, but even he could only dream of the run Manning is enjoying through 4 games.  Thus, if the Dallas defense and coaching staff are going to prevent any quarterback from winning today, it will be their usual target: Tony Romo.

Colin Kaepernick's roller-coaster ride continues
San Francicso's burgeoning young star, Colin Kaepernick, posted the 7th highest single game ANY/A of the year so far in his first bout against Green Bay at 11.32.  He followed that up with a Blaine Gabbert-esque -0.90 in Seattle.  Indeed, only Kaepernick and Gabbert have recorded negative ANY/A games in 2013.

For the following two weeks, the cycle of variance continued: Kaepernick had trouble against the Colts (3.13) in Week 3, but bounced back 4 days later verse St. Louis (7.64).  Which of these kids will show up in today's contest with the Texans is anyone's guess, and probably only something 49ers Head Coach Jim Harbaugh and Offensive Coordinator Greg Roman can control.

On the other side of the line of scrimmage, the Houston defense will do their best to make Kaepernick's performance his third dud of the season.  The squad ranks 9th in defensive ANY/A and has 13 sacks, but they are giving up over 110 yards on the ground per game.  A heavy dose of Frank Gore worked for San Francisco last week against St. Louis, and the team might be wise to stay the course.

After all, more dropbacks for Kaepernick provide more opportunities for last season's Defensive Player of the Year, J.J. Watt, to wreak havoc.  His 2 batted passes so far are below his 2012 pace, But J.J. "Swatt" still has 4 sacks, 6 QB hits, and 13 hurries in only 126 snaps rushing the passer -- meaning he leads the league in Pass Rush Productivity for 3-4 DEs (as measured by Pro Football Focus' Signature Stats).

The best way to neutralize this weapon may be to run the ball away from him.  If the 49ers do that, Kaepernick should enjoy a second week of highs on the variance swing.

Bad time for a back-up as Titans take on Kansas City
Coming into Week 5, Jake Locker was one of only two quarterbacks (Peyton Manning being the other) to attempt at least 30 passes this season without throwing an interception.  He was averaging a more-than-respectable 6.46 ANY/A -- which believe it or not is good for top 10 in the league.

Replacing him for at least the month of October is Ryan Fitzpatrick.  The former Buffalo Bill averaged a bottom-third 5.33 ANY/A through 4 years of football there, and he brings that level of below-par play to a Kansas City squad with the 1st ranked ANY/A defense in the NFL.

The Chiefs, under new Defensive Coordinator Bob Sutton, are killing opposing quarterbacks with the deadly combination of sacks and interceptions.  They lead the league in downing the signal-caller behind the LOS with 18 sacks for 118 yards.

The team also has 5 picks.  With Fitzpatrick averaging a high 3.7 INT% in Buffalo, we can expect Sutton's crew, with returning cornerback Brandon Flowers, to take advantage of the gunslinger.

Game of the Week: Seattle @ Indianapolis
The Seahawks and Colts are 13th and 12th in offensive ANY/A and 2nd and 4th on the other side of the ball, respectively.  The two are more evenly matched on the raw ANY/A data rankings than any other Week 5 pair.

If this game were in Seattle, one would expect them to win; but the undefeated NFC West leaders are a different team on the road, where they have taken two games only by a combined 8 points.  This includes an overtime victory last week verse a Houston squad that would have won were it not for a late-inning gaffe by quarterback Matt Schaub.  Through 4 weeks, 8 games have had offensive point differentials not go the way of ANY/A differential, and last week in Texas was one of them.

Andrew Luck is the better quarterback, and it will show at home in the 4th quarter as Seattle takes their first loss of the season in a close defensive struggle.

9 Responses to “Introducing ANY/A Differential”

1. Xavier Weisenreder says:

Why are 45 and 20 chosen as the co-efficients for interceptions and TD's respectively?

2. John Black says:

They is clearly a gap in dis logic which I addressed I my blog post called the "ANY A-Hole"

3. NateTG says:

> Despite this, there does not exist on the internet
> (to my knowledge) any database of single game
> ANY/A

No guarantees that its' correct, but it's relatively straightforward to generate from existing play-by-play data. Enjoy:
http://pastebin.ca/2463299

YMMV, no liability for correctness, etc.

The coefficients seem pretty random to me too, especially considering that you're posting this on a site which also offers a relatively sophisticated expected points model. Wouldn't EPA per passing play be a more sensible number. (It's more work to produce, so I probably won't do it, but looking at median ANY/A or EPA/A may be more informative since interceptions are infrequent enough to be random-ish.)

> see what use ANY/A might serve as a predictive tool.

Brian has posted here about passing success rate - which is really close to ANY/A - as, I think, one of the better predictors of performance.

4. Unknown says:

If I'm not mistaken, those coefficient values (or something very close) were originally used in the seminal work, "The Hidden Game of Football". It's been a while since I've perused through the book, and I honestly don't recall if there is a detailed explanation of how the estimate was derived. But you'll find those are pretty common coefficient values used by a lot of stat geeks and analytic types in this context. Whether those values have persisted out of "tradition" or some other indefensible reason, I don't know. But my guess is that there is a logic behind them. I just don't know it off the top of my head.

5. Chase Stuart says:

Correlating ANY/A with wins: http://www.footballperspective.com/correlating-passing-stats-with-wins/

6. Anonymous says:

For the interception coefficient, should the number scale for throws further downfield, as those are both more likely to be intercepted and have less of an impact when they are?

7. Andrew Carroll says:

@Xavier,
Chase Stuart did the most recent work to make TDs worth 20 yards rather than 10 here: http://www.pro-football-reference.com/blog/?p=633

@Chase,
Speaking of Chase! Yes, I was aware of that post, Chase. I should have linked to it, but forgot to as I moved forward. I meant more specifically that ANY/A differential had not been correlated with wins.

@Anonymous regarding down-field INTs,
That sounds a bit more like the work being done in EPA/WPA. ANY/A does not take account of where on the field an interception takes place. It is simple in that regard, but it always amazes me how useful simple stats can be.

@NateTG,
That is awesome! Thank you. And, yes, I was not attempting to submit ANY/A as a replacement of any other stat. It just interested me that we have data on "passer rating differential" and we have individual game data for other passing stats, but not for ANY/A. It is a project I wanted to work on for a bit and figured it was worth a post or two as the season moves along here, at a place where people would understand it and comment.

8. SportsGuy says:

ANY/A is going to correlate pretty well with point differentials because, well, TDs are points aren't they?

Does ANY/A correlate to future ANY/A better with or without the TD adjustment?

9. James says:

Xavier/Andrew, Brian has a post from a few years ago on the 45 yard coefficient for interceptions. As mentioned above it's from the Hidden Game of Football, but Brian went on to show that an interception is worth 60 yards in today's NFL. Personally, I like to resolve the discrepancy by thinking of the 45 yard figure as a 25% regression on the randomness of interceptions.