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Regression Alert: Passing Touchdowns, Too, Must Pass

Even Hall of Famers can only throw so many touchdowns per yard gained.

Welcome to Regression Alert, your weekly guide to using regression to predict the future with uncanny accuracy.

The Scorecard

Before we get into this week's statistics, let's look back at how previous predictions have fared. Each prediction in this column takes the following form: identify a statistic that is prone to regression, gather all of the players doing best into that statistic into Group A, gather all of the players doing worst in that statistic into Group B, note how much Group A has outperformed Group B to that point, then predict that Group B will outperform Group A going forward.

By and large, I'm not allowed to cherrypick which players I think will regress and which won't. If my process puts Antonio Brown into Group A... well then, Antonio Brown is in Group A. If it puts Isaiah Crowell into Group B, then Isaiah Crowell is in Group B.

(The one exception is for players with atypical roles; short-yardage backs are unlikely to see their ypc increase, change-of-pace backs are unlikely to see their rush attempts increase, etc.)

A key component of this format is accountability. All predictions are trackable and testable. Through immediate feedback, we are able to learn and improve. So here's where things stand at the moment.

In Week 2, I outlined what regression was, what it wasn't, and how it worked. No prediction was made.

In Week 3, I listed running backs with exceptionally high and low yards per carry averages and predicted that the low-ypc cohort would outperform the high-ypc cohort over the next four weeks.

In Week 4, I looked at receivers who were overperforming and underperforming in yards per target and predicted that the underperformers would outperform the overperformers over the next four weeks.

In Week 5, I compared the predictive accuracy of in-season results to the predictive accuracy of preseason ADP. Outside of a general prediction that players would tend to regress in the direction of their preseason ADP, no specific prediction was made.

Statistic for regressionPerformance before predictionPerformance since predictionWeeks remaining
yards per carry Group A had 60% more rushing yards per game Group B has 8% more rushing yards per game 1
yards per target Group A had 16% more receiving yards per game Group B has 6% more receiving yards per game 2

And now, on to the next prediction.

Touchdowns Follow Yards

The seeds for this column were planted two years ago in a piece titled “Touchdowns Follow Yards, (But Yards Don't Follow Back)”. The idea was that players tended to have a specific yard-to-touchdown ratio that they trended towards, and while that specific ratio could vary from player to player, all of those ratios existed within a specific range. I noted players who were outside that range and predicted that they'd regress.

They regressed so quickly and thoroughly that I wrote a follow-up piece just two weeks later, (laying the basis for this column's “predict and track” framework). And then this last offseason I further revisited the topic to see if something like yards per reception might predict yard:TD ratios.

As you can see, this is one of my favorite metrics for regression, and one of the reasons why is because most owners don't even think of it. Obviously, a player averaging a ton of yards per game will probably regress, and sure, a 6.0+ yards per carry average is probably coming down... but doesn't 300 yards and 4 touchdowns through five games seem like a nice sustainable pace for a good WR? But at a 75:1 yard to touchdown ratio, it's not; that receiver is overproducing and will likely regress over the rest of the season.

Today, we're going to look at quarterbacks, inspired by everyone's favorite rookie phenom. To start with, I wanted to get a sense of the reasonable range of yard:TD ratios for a quarterback. I took the top 100 passers (by total passing yards), since 1980; this wound up being everyone with 14,700 yards or more, with players like Josh McCown and Mark Sanchez falling just inside the cutoff and players like Joey Harrington and David Carr falling just outside.

For those 100 passers, I calculated career yard:TD ratios. The first thing that became obvious is that, unlike at wide receiver, there is a very clear and unambiguous relationship between quarterback quality and yard:TD ratio. Aaron Rodgers ranks 1st, Peyton Manning 2nd, Brady 3rd, Romo 4th, Favre 6th, Brees 7th, Young 8th, Russell Wilson and Andrew Luck 9th and 10th.

Cunningham, Marino, Rivers, Montana, Kelly, Warner, and Roethlisberger also land in the top 25. Meanwhile, the only Hall of Famer in the bottom-25 is Troy Aikman way down at 98th, though Emmitt Smith probably bears much of the blame for that. Bernie Kosar and Steve McNair also find themselves down there, but otherwise, the best quarterbacks you'll find in this range are uninspiring multi-year starters like Matt Schaub, Joe Flacco, or Sam Bradford.

Unsurprisingly given how top-heavy the list was, there is a strong negative correlation between yards per attempt and Yard:TD ratio of -0.576. In other words, better quarterbacks have lower Yard:TD ratios.

On a hunch, I compared yard:TD ratios to debut season to see if perhaps the trend towards passing had pushed the ratio down any in recent years. The correlation was -0.008, so no relation. yard:TD ratios seem to be pretty stable from year to year, at least in the 16-game era.

Beyond noting that how good a quarterback is plays a big role in how sustainable his production will be, it's worth noting just what kind of yard:TD ratios might be reasonable at the position. On the top end, Rodney Peete averaged 215 yards for every touchdown, Jim Harbaugh averaged 204, and everyone else is below 200.

Aaron Rodgers has the best ratio with 123 yards for every passing touchdown. Anything lower than 123, therefore, is unsustainable. But I'd venture a little bit further, even. Second behind Rodgers is Peyton Manning with 133 yards per touchdown, and third is Tom Brady with 135.

Further, only 18 of the 100 quarterbacks had a yard:TD ratio below 150. 9 of those 18 are either in the Hall of Fame or are first-ballot locks. Three more, (Rivers, Romo, and three-time Player of the Year Randall Cunningham), are fringe Hall of Fame candidates. Two more, (Luck and Wilson), are certainly on pace to make a credible Hall of Fame case.

That leaves just 4 of 18 players below 150 yards:TD who unambiguously weren't Hall of Fame caliber. The first is Danny White, the last notable dual-position player in the league, serving as both quarterback and punter over the best 4-year stretch of offense in Dallas Cowboys history, (better than anything produced by Meredith, Staubach, Aikman, or Romo).

The next two were Joe Ferguson and Steve Bartkowski, both of whom would resolve to over 150 yards:TD if I hadn't used 1980 as a cutoff. And the final one was Dave Krieg, a solid long-time quarterback who finished his career with 146 passing yards for every passing touchdown.

Given that, I'd say that unless he's a potential Hall of Famer, a quarterback's “true” yard:TD ratio almost certainly falls in the 150-200 yard range. If the player *IS* a likely Hall of Famer, perhaps they can support a ratio in the 135-150 range. And if the player in question is Aaron Rodgers, it's at least possible that his “true” yard:TD ratio is around 125.

The Prediction

I've arbitrarily created four designations. “Bad starter” should be expected to average around 180 yards per TD. “Good starter” should be expected to average around 160 yards per TD. “Hall of Famer” (Tom Brady, Drew Brees, Russell Wilson, Andrew Luck) should be expected to average around 140 yards per TD. And “Aaron Rodgers”, (Aaron Rodgers), should probably be expected to average about 125 yards per TD.

(Note: someone like Ben Roethlisberger, Cam Newton, or Matt Ryan might eventually make the Hall of Fame, but they don't have a demonstrated history of low yard:TD ratios, which is why I've not included them in the “Hall of Famer” category.)

And with those designations in hand, I can calculate how many passing touchdowns each player “should” have based on their passing yardage to date and find who is overperforming or underperforming the most.

Using a scoring system that awards 1 point per 20 yards passing, 4 points per touchdown, and -1 point per interception, there are 24 quarterbacks who have started four or five games and averaged at least 16 fantasy points per game. Case Keenum and Jacoby Brissett are backups who only hold the job until the starter(s) return; removing them leaves us with 22 names.

Of those 22 names, Philip Rivers, Cam Newton, Drew Brees, and Eli Manning have all scored less than a half point per game away from where they were expected.

Deshaun Watson, Dak Prescott, Derek Carr, Alex Smith, Aaron Rodgers, Matthew Stafford, Trevor Siemian, Carson Wentz, and Kirk Cousins are all outperforming expectations by at least 0.5 points per game. This is our Group A.

Carson Palmer, Marcus Mariota, Matt Ryan, Ben Roethlisberger, Jared Goff, Tom Brady, Russell Wilson, Andy Dalton, and Jameis Winston, on the other hand, are all underperforming expectations by at least 0.5 points per game. This is our Group B.

Anecdotally, Group A looks like the more impressive bunch to me, and indeed, they lead group 2 in fantasy points per game by 12.5% at 22.6 to 20.1. But that lead is largely just touchdown luck; in terms of expected fantasy points per game based on historical yard:TD ratios, Group B actually leads Group A, 21.4 to 20.6.

So that's the prediction. Over the next four weeks, Group B averages more fantasy points per game than Group A.

For those interested, here's the raw yard:TD ratio for all passers with at least 25 attempts this year.

PlayerPassing YardsPassing TDsYard:TD Ratio
Deshaun Watson 1072 12 89.33
Aaron Rodgers 1367 13 105.15
Derek Carr 753 7 107.57
Dak Prescott 1192 11 108.36
Blake Bortles 827 7 118.14
Matthew Stafford 1116 9 124
Kevin Hogan 377 3 125.67
Alex Smith 1391 11 126.45
Trevor Siemian 888 7 126.86
Sam Bradford 382 3 127.33
Mitchell Trubisky 128 1 128
Carson Wentz 1362 10 136.2
Drew Brees 1135 8 141.88
Kirk Cousins 1004 7 143.43
Philip Rivers 1365 9 151.67
Tyrod Taylor 910 6 151.67
Russell Wilson 1222 8 152.75
Cam Newton 1237 8 154.63
Tom Brady 1702 11 154.73
Matt Cassel 162 1 162
Eli Manning 1338 8 167.25
Jameis Winston 1198 7 171.14
Andy Dalton 1220 7 174.29
Jared Goff 1365 7 195
Josh McCown 1020 5 204
Joe Flacco 823 4 205.75
Mike Glennon 833 4 208.25
Ben Roethlisberger 1269 6 211.5
Matt Ryan 1109 5 221.8
Case Keenum 895 4 223.75
Jay Cutler 706 3 235.33
Carson Palmer 1574 6 262.33
Marcus Mariota 792 3 264
EJ Manuel 265 1 265
DeShone Kizer 851 3 283.67
Brian Hoyer 1211 4 302.75
Jacoby Brissett 997 2 498.5