Photo: USA Today Sports

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

The Scorecard

Returning readers, you know how this works by now, but for new readers here's the deal. Every week I take a look at a specific statistic that is prone to regression and identify high and low outliers in that statistic, and then I wave my hands in the air and shout “regression!”

But since predictions aren't any fun without someone holding your feet to the fire afterward, I don't stop there. I lump all of the high outliers into Group A. I lump all of the low outliers into Group B. I verify that Group A is outperforming Group B. And then I predict that Group B will outperform Group A over the next four weeks.

I don't get to pick and choose my groups, beyond being free to pick and choose what statistics are especially prone to regression. If I'm tracking yards per target, and Antonio Brown is one of the high outliers in yards per target, then Antonio Brown goes into Group A and may the fantasy gods show mercy on my predictions.

And then, groups chosen and predictions made, I track my progress. That's this.

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.

In Week 6, I looked at quarterbacks who were throwing too many or too few touchdowns given the amount of passing yards they were accumulating, then predicted that the underperformers would score more fantasy points than the overperformers going forward.

In Week 7, I looked at receivers who were catching too many or too few touchdowns based on their yardage total, then predicted that the underperformers would score more fantasy points than the overperformers going forward.

In Week 8, I revisited yards per carry, again predicting that the high-carry, low-ypc group would outrush the low-carry, high-ypc group going forward.

In Week 9, I went back to yard to touchdown ratios, predicting that the low-touchdown group would close the gap substantially with the high-touchdown group going forward.

In Week 10, I discussed the pitfalls of predicting regression over 4-week windows. No specific prediction was made.

In Week 11, I once more delved into the theory behind regression and highlighted the importance of not cherrypicking which players are “too good” or “not good enough” to regress.

In Week 12, I took one more shot at touchdown regression for quarterbacks, predicting that the low-touchdown cohort would close the gap with the high-touchdown cohort going forward.

In Week 13, I decided to close the predictions out with a bang, sorting the top 100 skill position players in yards per touchdown ratio and predicting that the third with the fewest touchdowns would outperform the third with the most touchdowns going forward.

In Week 14, I delved into Alvin Kamara's aberrant touchdown rate, whether sometimes outliers were actually indicators, and whether anyone could possibly be “regression-proof”.

In Week 15, we took a break before the end-of-season wrapup articles this week and next.

It's been obvious for weeks that the second quarterback prediction would fail as badly as the first, but now it's official. What happened at the position this year? Is this an aberration, or is there something I've overlooked? Those are the key questions for today as we delve into our further analysis.

Do Quarterbacks Regress?

By the very definition of regression, no one should be immune. But based on quarterback performances this season, it seems like that's exactly the case. Which means one of two things must be true.

Possibility #1: This year was a fluky year for quarterback performances.
Possibility #2: I screwed up.

(What does possibility #2 look like? If a metric that I assumed was unstable— in this case, touchdown rate— was actually more stable than other positional statistics— for example, yards per game— then it should regress less than everything else, meaning the guys I tagged as most likely to regress were actually least likely.)

I've delved a lot into yard to touchdown ratios in the past, but every time I've been looking at running backs and wide receivers. I've assumed that quarterbacks behaved similarly given research I've seen on the instability of a player's touchdown rate from year to year, (and my knowledge of the nature of touchdowns in general).

But introducing assumptions introduces potential sources of error, and since there's clearly been error here this year, I think it's important to test those assumptions.

For starters, I want to note just how much of an outlier this year's passing touchdown values have been. Deshaun Watson and Carson Wentz both end this season with fewer than 100 yards per passing touchdowns. They become two of just six quarterbacks since 1999, (as far back as I have queryable data), to earn that distinction.

Do quarterbacks producing at levels that high resist regression? To test, I pulled all quarterbacks since 1999 who over their team's first 10 games (A) threw for at least 1,000 yards, and (B) averaged fewer than 110 passing yards per touchdown. Discarding the three quarterbacks from this year, (Watson, Wentz, and Aaron Rodgers), left me with 26 qualifying passers. How did those passers fare over their final six games?

Here's the raw data, including each player's Yard:TD ratio over the first 10 and last 6 games of the season.

(“Average” here is a weighted average— the total of all passing yards over the last six games divided by all passing touchdowns over the last six games— so seasons like Peyton Manning's 2013 will influence it more than seasons like David Garrard's 2010.)

Remember, when I first introduced the concept of passing yard to touchdown ratios I mentioned that 140 yards per passing touchdown seems to be about the limit of first-ballot Hall of Fame types like Peyton Manning, Tom Brady, and Drew Brees. Notice what the average ratio was for these high performers over the last six games? Yup, 140 yards per touchdown.

(You may also remember when I introduced the concept that I mentioned Aaron Rodgers was in his own category, down at 125 passing yards per touchdown. Counting this year, Rodgers makes six appearances on this list, double that of second-place Peyton Manning and triple anyone else. He really is the best touchdown-thrower in league history, or at least the most prolific.)

Meanwhile, Carson Wentz and Aaron Rodgers started four games over the final six weeks of the season, and in those four games, they combined to average 105.1 passing yards per touchdown. This is not entirely unprecedented— three seasons on the table above had a lower ratio— but it's also clearly an outlier. Even if we restrict ourselves to just Aaron Rodgers, in seasons where he averages fewer than 110 yards per touchdown over the first ten games, he averages 132 yards per touchdown over the final six.

It's nice to check the work here and see that the theory is sound. Regression is a natural outgrowth of randomness, but the nature of randomness is, tautologically speaking, random. Sometimes regression just doesn't “work”.

But reviewing the data, whether the final outcome was favorable or not, I'm confident that the call itself was the right one, and I won't hesitate to make it again in the future. If a quarterback throws a disproportionate number of touchdowns relative to his passing yards, he's probably going to regress, regardless of what Carson Wentz did or did not do this year.