by Scott Kacsmar

Completion percentage has often been a simpleton's approach to quantifying a quarterback's accuracy. While we would still have to get some pretty advanced software to perfectly measure accuracy, we can do a better job of things just with game charting. For starters, not every pass is actually aimed with the intention of a completion. By breaking down every incompletion into classes, we can account for passes thrown away as well as drops.

Then there is the significance of how far the pass was thrown. If a quarterback wanted to complete 75 percent of his passes in a season, he could definitely hit that mark, but it would likely come at the expense of a productive offense. Since 2006, aimed passes thrown to receivers behind the line of scrimmage have been completed 87.3 percent of the time. Aimed passes that travel exactly 10 yards beyond the line of scrimmage are completed 59.2 percent of the time. At 20 yards, that rate dips to 44.7 percent.

It is also worth noting which field direction the pass was thrown: left, middle, or right. A 4-yard pass to a slot receiver coming over the middle is actually still a shorter throw than a 4-yard pass thrown to a curling wide receiver on the outside. On average, the further the ball has to travel, the less likely it is to get there accurately. We broke down passes thrown 1 to 20 yards downfield over the last decade by the three directions, and found that the middle is very advantageous.

Throws to the left and right are hardly distinguishable from one another, but once you get to 3-yard throws, the middle starts to separate. At 12 yards and deeper, throws to the middle are completed about 10 percent more often. We could probably do a whole piece on direction, but much of what's going on here is that a higher rate of passes over the middle (45.9 percent) go to running backs and tight ends than those thrown towards the left (36.3 percent) or right (40.5 percent). These positions historically have higher catch rates due to a closer playing proximity to the quarterback, hence shorter throws. They also get a lot of matchups with linebackers and safeties instead of cornerbacks, which usually are the athletes best suited for tighter coverage. Good quarterbacks can really exploit the seam passes in windows between the linebackers and safeties, and most dump-off passes also get checked down to the middle.

So we want a stat that will account for where the pass was thrown, how far it was thrown, and what the down-and-distance situation was. The end result is passing plus-minus. We have looked at receiving plus-minus in the past; this is the same concept, but for quarterbacks. Passing plus-minus estimates how many passes a quarterback completed compared to what an average quarterback would have completed, given the location of those passes. It does not consider passes listed as "Thrown Away," "Tipped at Line," or "Quarterback Hit in Motion." Player performance is compared to a historical baseline of how often a pass is completed based on the pass distance, the distance required for a first down, and whether it is on the left, middle, or right side of the field. Note that plus-minus is not scaled to a player’s total attempts.

Passing Plus-Minus: Top and Bottom Seasons

Since we are sitting on 10 seasons of data for this, and have never really published a formal study on the stat for quarterbacks, let's look at the top seasons since 2006. These are the 45 seasons to finish with at least a plus-20. (For the rest of the article we will express the numbers with a + or - sign.)

Top Seasons in Passing-Plus Minus (2006-2015) Rk Player Year +/-

Rk Player Year +/-

Rk Player Year +/- 1 Drew Brees 2011 +48.4 16 Philip Rivers 2011 +30.2 31 Aaron Rodgers 2010 +24.5 2 Drew Brees 2013 +42.6 17 Philip Rivers 2010 +30.1 32 Peyton Manning 2007 +23.8 3 Peyton Manning 2009 +42.3 18 Peyton Manning 2008 +29.5 33 Ben Roethlisberger 2009 +23.7 4 Drew Brees 2014 +39.6 19 Aaron Rodgers 2012 +29.2 34 Russell Wilson 2012 +23.3 5 Drew Brees 2009 +39.5 20 Tony Romo 2014 +28.5 35 Aaron Rodgers 2008 +22.8 6 Philip Rivers 2013 +39.4 21 Peyton Manning 2006 +27.7 36 Drew Brees 2007 +22.6 7 Peyton Manning 2012 +39.4 22 Russell Wilson 2015 +27.4 37 Tony Romo 2006 +22.1 8 Aaron Rodgers 2011 +33.9 23 Peyton Manning 2013 +27.4 38 Chad Pennington 2008 +21.8 9 Matt Schaub 2009 +33.7 24 David Carr 2006 +27.3 39 Matt Schaub 2008 +21.4 10 Kurt Warner 2008 +33.2 25 Philip Rivers 2008 +26.3 40 Aaron Rodgers 2013 +20.8 11 Matt Ryan 2012 +33.0 26 Ben Roethlisberger 2015 +26.2 41 Teddy Bridgewater 2015 +20.6 12 Drew Brees 2010 +32.9 27 Philip Rivers 2014 +26.0 42 Tom Brady 2011 +20.4 13 Tom Brady 2007 +32.0 28 Ben Roethlisberger 2014 +26.0 43 Drew Brees 2008 +20.3 14 Kurt Warner 2009 +31.2 29 Carson Palmer 2015 +25.1 44 Ben Roethlisberger 2007 +20.2 15 Philip Rivers 2009 +31.0 30 Kirk Cousins 2015 +24.6 45 Carson Palmer 2007 +20.1

Well, Drew Brees should love this stat. He only has four of the top five seasons. It's true that volume helps a lot here, but when you have volume and you are probably the most accurate passer in the league, you're going to dominate plus-minus.

This list is pretty top-heavy, with 16 quarterbacks (including most of the usual suspects) comprising the top 45. David Carr sticks out like a sore thumb for his 2006 season with Houston, but he did complete 68.3 percent of his passes that season and they were not all screens. You can also see Teddy Bridgewater and Kirk Cousins cracked this list for their 2015 performances. Time will tell if they develop into consistently solid quarterbacks, or if they belong in Carr's tier as one-offs.

Plus-minus does a good job of picking out bad quarterbacks with major accuracy issues. Here are the 22 seasons to finish at -20 or worse.

Worst Seasons in Passing Plus-Minus (2006-2015)

Rk Player Team Year +/-

Rk Player Team Year +/- 1 Blaine Gabbert JAC 2011 -39.6 12 Josh Freeman TB/MIN 2013 -23.0 2 Brett Favre GB 2006 -35.5 13 Mark Sanchez NYJ 2010 -22.7 3 Blake Bortles JAC 2014 -29.9 14 Brian Hoyer CLE 2014 -22.4 4 Derek Anderson CLE 2008 -28.6 15 Eli Manning NYG 2007 -22.3 5 Derek Anderson ARI 2010 -26.6 16 JaMarcus Russell OAK 2008 -22.2 6 JaMarcus Russell OAK 2009 -26.0 17 Mark Sanchez NYJ 2009 -21.8 7 Tyler Thigpen KC 2008 -25.5 18 Marc Bulger STL 2008 -21.8 8 Matthew Stafford DET 2009 -25.0 19 Mark Sanchez NYJ 2012 -21.1 9 Nick Foles STL 2015 -24.0 20 Jimmy Clausen CAR 2010 -20.5 10 Andrew Luck IND 2012 -23.4 21 Matt Cassel KC 2009 -20.4 11 Bruce Gradkowski TB 2006 -23.2 22 Derek Anderson CLE 2007 -20.3

Not a lot of good quarterback play here. Brett Favre struggled in his first season with Mike McCarthy, but did rebound in 2007. Eli Manning actually won his first Super Bowl after a rather weak regular-season performance. Andrew Luck's rookie season was inefficient, but still one of the more impressive examples of a quarterback carrying a team. The rest of the list is largely the other group of usual suspects from the last decade. Josh Freeman somehow managed to sink this low in 2013 despite attempting just 137 passes. Derek Anderson may have tricked a few people with his 29-touchdown 2007 performance in Cleveland, but even that season was a -20.3, and his three appearances are tied with Mark Sanchez for the most on the list. Blake Bortles will hope his rookie season isn't a sign of things to come like Blaine Gabbert's 2011 was for Jacksonville, but fortunately 2015 looks to be a step in the right direction.

2015 Passing Plus-Minus

These results are for the 2015 passers with at least 200 pass attempts. Again, the total number of passes will differ from the NFL total due to the removal of certain passes. To help express plus-minus as a rate stat, C%+ is also included.

2015 Passing Plus-Minus (Min. 200 Passes) Rk Player Team Passes C%+ +/-

Rk Player Team Passes C%+ +/- 1 Russell Wilson SEA 446 +6.2% +27.4 19 Joe Flacco BAL 383 -0.4% -1.4 2 Ben Roethlisberger PIT 449 +5.8% +26.2 20 Alex Smith KC 439 -0.5% -2.1 3 Carson Palmer ARI 495 +5.1% +25.1 21 Matt Hasselbeck IND 232 -1.0% -2.3 4 Kirk Cousins WAS 517 +4.8% +24.6 22 Tom Brady NE 589 -0.7% -4.3 5 Teddy Bridgewater MIN 395 +5.2% +20.6 23 Brian Hoyer HOU 349 -1.7% -5.9 6 Drew Brees NO 598 +3.3% +19.8 24 Peyton Manning DEN 314 -2.5% -8.0 7 Andy Dalton CIN 360 +4.0% +14.6 25 Blake Bortles JAC 555 -1.6% -8.9 8 Matt Ryan ATL 575 +2.2% +12.9 26 Eli Manning NYG 584 -1.7% -10.1 9 Philip Rivers SD 613 +1.9% +11.4 27 Blaine Gabbert SF 269 -3.8% -10.2 10 Tyrod Taylor BUF 364 +1.7% +6.1 28 Aaron Rodgers GB 523 -2.3% -11.9 11 Matthew Stafford DET 557 +1.0% +5.7 29 Andrew Luck IND 269 -4.5% -12.1 12 Sam Bradford PHI 492 +0.6% +3.1 30 Colin Kaepernick SF 229 -5.3% -12.2 13 Marcus Mariota TEN 346 +0.9% +3.0 31 Ryan Fitzpatrick NYJ 532 -2.7% -14.1 14 Ryan Tannehill MIA 540 +0.4% +2.0 32 Jameis Winston TB 504 -2.8% -14.2 15 Cam Newton CAR 460 +0.4% +1.8 33 Johnny Manziel CLE 212 -7.2% -15.3 16 Josh McCown CLE 271 +0.3% +0.7 34 Ryan Mallett BAL/HOU 229 -7.0% -16.0 17 Jay Cutler CHI 462 +0.1% +0.5 35 Derek Carr OAK 539 -3.1% -16.5 18 Brock Osweiler DEN 256 -0.5% -1.2 36 Nick Foles STL 311 -7.7% -24.0

Last season was a tough one for the quarterbacks we are used to seeing dominate such stats. In his prime, Peyton Manning was the top quarterback in plus-minus. He slipped to ninth in 2014, and that decline only continued with his first negative season in 2015, his swansong. Tom Brady had his second negative season in the last three years. Aaron Rodgers was at +15.0 or higher in each of the previous seven seasons, but sunk to -11.9 last year. Yes, Jordy Nelson matters when you consider Rodgers was +56.8 in his career on targets to Nelson. However, Rodgers was +28.0 to Randall Cobb from 2011-14 before a -2.2 connection in 2015. Davante Adams' -7.1 is by far the worst plus-minus season for any of Rodgers' targets in his career.

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Some quarterbacks were at their best in 2015, or at least gave the illusion of it. Russell Wilson's league-leading plus-minus of +27.4 was really built on the +16.7 he had when he went on an incredible run in the last seven games of the season. Ben Roethlisberger has had much better seasons throwing touchdowns and interceptions, but he may have been at his physical best throwing the ball in 2015 with a career-high +26.2. We lack 2005 data, but Carson Palmer's 2015 is his best season on record now. You might have thought the same could be said for MVP Cam Newton, but his 2013 season actually had a higher plus-minus at +6.2. Andy Dalton had his best season last year, though he has usually been middle of the pack in plus-minus, ranking 12th to 16th every year except for his rookie season. Matthew Stafford had his second positive season, and yes, things were better in nine games with offensive coordinator Jim Bob Cooter (+4.8) than they were with the fired Joe Lombardi (+0.9).

Teddy Bridgewater is likely to be a focal point in several of our quarterback studies this year. He did not fare well in Expected Failed Completions, looking like one of the league's more dink-and-dunk passers. But when it comes to plus-minus, Bridgewater has been quite good, ranking 15th as a rookie and fifth this year. Even on passes thrown 10-plus yards, Bridgewater still ranked 10th in plus-minus (+5.2) in 2015. While Bortles and Derek Carr each threw more touchdowns in 2015 than Bridgewater has in two seasons, the gap in passing efficiency is definitely in Bridgewater's favor. When we get around to looking at performance with pass pressure in 2015, you may be even more impressed by Bridgewater.

Say what you will about Chip Kelly's offense in the NFL, but he has helped make the job of completing passes easier on his quarterbacks. Nick Foles was +17.2 in his great 2013 season, but finished dead last at -24.0 with the Rams last year. Sam Bradford was -25.3 in his time with the Rams, but had his first positive season with the Eagles in 2015. Mark Sanchez's C%+ was -4.6% with the Jets, but improved to -1.4% (which, granted, is still not good) in two years with Philadelphia. Colin Kaepernick's plus-minus has gotten worse each season, but Kelly should be able to help him, or (gulp) Blaine Gabbert in San Francisco.

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Drop-Adjusted Passing Plus-Minus

Since plus-minus is all about getting the pass completed, and has nothing to do with what happens after the catch, we can make a clean adjustment for dropped passes. In 2010, his last playing season with the Colts, Peyton Manning finished fourth in plus-minus at +18.3. He was credited with 48 dropped passes, which were worth -31.1 plus-minus. In adjusting his plus-minus for drops, we do not simply add the 31.1 to his season total; we add the difference between the drops (48) and the plus-minus (31.1), which is +16.9, the highest of any season in the last decade. Adding +16.9 to Manning's statistics that season results in a drop-adjusted plus-minus of +35.2, good for third in 2010. Manning ranked first or third in every season he played from 2006 to 2013.

Manning and Brees have led the league four times each in drop-adjusted plus-minus since 2006. Tom Brady (2007) and Wilson (2015) are the only other quarterbacks to lead the league. Brees' 2011 season is still the highest (+57.1), and Manning's 2009 season has the highest adjusted C%+ (+9.8%).

This table looks at 2015 again with drop-adjusted plus-minus. Do we dare go for another acronym with DA +/-?

2015 Drop-Adjusted Passing Plus-Minus (Min. 200 Passes) Player Team Passes C%+ +/- Rk Drops DA +/- Rk Russell Wilson SEA 446 +6.2% +27.4 1 17 +32.5 1 Carson Palmer ARI 495 +5.1% +25.1 3 15 +31.2 2 Ben Roethlisberger PIT 449 +5.8% +26.2 2 12 +30.7 3 Kirk Cousins WAS 517 +4.8% +24.6 4 18 +29.9 4 Drew Brees NO 598 +3.3% +19.8 6 17 +25.9 5 Teddy Bridgewater MIN 395 +5.2% +20.6 5 15 +25.3 6 Matt Ryan ATL 575 +2.2% +12.9 8 33 +23.2 7 Andy Dalton CIN 360 +4.0% +14.6 7 14 +19.8 8 Philip Rivers SD 613 +1.9% +11.4 9 25 +19.7 9 Matthew Stafford DET 557 +1.0% +5.7 11 22 +12.8 10 Sam Bradford PHI 492 +0.6% +3.1 12 27 +11.3 11 Tyrod Taylor BUF 364 +1.7% +6.1 10 15 +10.9 12 Cam Newton CAR 460 +0.4% +1.8 15 19 +9.9 13 Ryan Tannehill MIA 540 +0.4% +2.0 14 24 +9.6 14 Marcus Mariota TEN 346 +0.9% +3.0 13 13 +7.4 15 Jay Cutler CHI 462 +0.1% +0.5 17 19 +6.0 16 Tom Brady NE 589 -0.7% -4.3 22 24 +3.5 17 Brock Osweiler DEN 256 -0.5% -1.2 18 13 +2.7 18 Player Team Passes C%+ +/- Rk Drops DA +/- Rk Josh McCown CLE 271 +0.3% +0.7 16 7 +2.6 19 Alex Smith KC 439 -0.5% -2.1 20 17 +2.6 20 Joe Flacco BAL 383 -0.4% -1.4 19 7 +0.5 21 Matt Hasselbeck IND 232 -1.0% -2.3 21 11 +0.2 22 Brian Hoyer HOU 349 -1.7% -5.9 23 19 -0.3 23 Eli Manning NYG 584 -1.7% -10.1 26 29 -0.7 24 Blake Bortles JAC 555 -1.6% -8.9 25 26 -1.4 25 Peyton Manning DEN 314 -2.5% -8.0 24 11 -3.5 26 Ryan Fitzpatrick NYJ 532 -2.7% -14.1 31 28 -4.5 27 Blaine Gabbert SF 269 -3.8% -10.2 27 17 -5.1 28 Aaron Rodgers GB 523 -2.3% -11.9 28 20 -5.3 29 Jameis Winston TB 504 -2.8% -14.2 32 23 -5.5 30 Derek Carr OAK 539 -3.1% -16.5 35 31 -6.7 31 Colin Kaepernick SF 229 -5.3% -12.2 30 8 -10.1 32 Johnny Manziel CLE 212 -7.2% -15.3 33 16 -10.4 33 Andrew Luck IND 269 -4.5% -12.1 29 6 -10.5 34 Ryan Mallett HOU/BAL

229 -7.0% -16.0 34 14 -11.2 35 Nick Foles STL 311 -7.7% -24.0 36 10 -20.4 36

While the Colts led the league in drops in 2014, they did not drop many last season when Andrew Luck was playing, which drops him from 29th to 34th in DA +/-, the biggest fall for any quarterback. Brady had the highest rise, going from 22nd to 17th. But 31 of the 36 passers stayed within two spots of their regular plus-minus ranking.

Finally, here is the full leaderboard since 2006 in DA +/- (min. 1,000 passes). This only includes the regular season.