Photo: Imagn Images

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

For those who are new to the feature, here's the deal: every week, I dive into the topic of regression to the mean. Sometimes I'll explain what it really is, why you hear so much about it, and how you can harness its power for yourself. Sometimes I'll give some practical examples of regression at work.

In weeks where I'm giving practical examples, I will select a metric to focus on. I'll rank all players in the league according to that metric, and separate the top players into Group A and the bottom players into Group B. I will verify that the players in Group A have outscored the players in Group B to that point in the season. And then I will predict that, by the magic of regression, Group B will outscore Group A going forward.

Crucially, I don't get to pick my samples, (other than choosing which metric to focus on). If the metric I'm focusing on is 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.

Most importantly, because predictions mean nothing without accountability, I track the results of my predictions over the course of the season and highlight when they prove correct and also when they prove incorrect. Here's a list of all my predictions from last year and how they fared.

THE SCORECARD

In Week 2, I laid out our guiding principles for Regression Alert. No specific prediction was made.

In Week 3, I discussed why yards per carry is the least useful statistic and predicted that the rushers with the lowest yard-per-carry average to that point would outrush the rushers with the highest yard-per-carry average going forward.

In Week 4, I explained why touchdowns follow yards, (but yards don't follow back), and predicted that the players with the fewest touchdowns per yard gained would outscore the players with the most touchdowns per yard gained going forward.

In Week 5, I talked about how preseason expectations still held as much predictive power as performance through four weeks. No specific prediction was made.

In Week 6, I looked at how much yards per target is influenced by a receiver's role, how some receivers' per-target averages deviated from what we'd expect according to their role, and predicted that the receivers with the fewest yards per target would gain more receiving yards than the receivers with the most yards per target going forward.

In Week 7, I demonstrated how randomness could reign over smaller samples, but regression dominates over larger ones. No specific prediction was made.

In Week 8, I discussed how even something like average career length could be largely determined by regression-prone fluctuations in incoming talent. No specific prediction was made.

In Week 9, I looked at running backs scoring touchdowns at an unsustainable rate and posited that even Todd Gurley must return to earth.

In Week 10, I delved into the purpose of regression alert and the proper takeaways. No specific prediction was made.

After a complete wipe-out in the first week, our low-touchdown running backs came back and outscored our high-touchdown running backs in week 2 of the prediction to make things interesting again. With just two weeks left they'll need a pair of strong showings if they're going to pass Group A outright, but at least things are back on the right track.

I also want to make a note about the Week 6 Yards per Target prediction. That one struggled the whole way, with Group A remaining ahead of Group B with each update. Last week, I devoted this space to discussing what kind of lessons we might learn from its failure. With the benefit of one additional week, it has become a bit more clear that the proper takeaway is "random is random". In week 10, (the week after the prediction closed), several receivers returned healthy and ready to go and Group B demolished Group A, pulling them ahead for the first time since I initially made the prediction.

In this case, maybe the problem wasn't the samples I chose, but rather the window that I chose. I'll revisit again at the end of the season and see if Group B can keep it up.

What metrics regress?

Answer: all metrics regress.

A more interesting question is "what metrics regress the most?" And the answer here is "whatever metrics are least measuring something intrinsic to the player himself".

Player production is a result of a lot of different factors. There's the player's skill, but also the scheme he plays in, the contributions of his teammates, the defenses he faces, and even just random chance. The more "player skill" dominates the equation, the more stable production will be between samples. The more non-skill factors dominate the equation, the less stable production will be.

Take yards per carry, one of my favorite punching bags. Yes, it matters how good a player is. But yards per carry is very sensitive to outliers; if a player has 200 carries, a single 80-yard run will have boosted his yards-per-carry average by 0.4. And long runs are often a product of luck; blocking needs to be there, defenders need to be out of position. Most importantly, in order to run for 80 yards, you need to be at least 80 yards away from the end zone. If the exact same play happened at the opposing 20-yard line instead, it would have resulted in a 20-yard run and the running back would average 0.3 fewer yards per carry!

There are a lot of ways to get a feel for what kind of statistics are most influenced by factors other than player skill. Some of them are hard and require complicated statistical analysis. My favorite one is unbelievably simple, though: just look at some leaderboards.

If a statistic is mostly a measure of intrinsic skill, you'd expect only extremely skilled players to rate near the top of the leaderboard. If a statistic is mostly a measure of random chance, you'd expect the top of the leaderboard to be an eclectic mix of stars and nobodies. Statisticians call this concept "face validity", (how well the outputs of a statistic match our intuitions of what those outputs should be). I call it the "Leaderboard test".

Here's the leaderboard test in action using poor old yards per carry. Since the merger, here are the top 20 running backs in career yard per carry average, (minimum 500 carries):

1. Bo Jackson
2. Jamaal Charles
3. Mercury Morris
4. Barry Sanders
5. Napoleon Kauffman
6. Darren Sproles
7. Tatum Bell
8. C.J. Spiller
9. Tony Nathan
10. Robert Smith
11. Derrick Ward
12. Marv Hubbard
13. Wendell Tyler
14. Justin Forsett
15. Adrian Peterson
16. Greg Pruitt
17. O.J. Simpson
18. James Brooks
19. Felix Jones
20. Stump Mitchell

There are some really good backs on that list! There are also a lot of guys who were huge disappointments, (Felix Jones, Tatum Bell, C.J. Spiller), guys who were mediocre journeymen (Derrick Ward, Justin Forsett), and guys I'm willing to bet most of you had never heard of (Wendell Tyler, Marv Hubbard, Greg Pruitt). If you raise the threshold to qualify to 1,000 attempts, you'll prune out many of those less-impressive names, but you'll replace them with other names like Charlie Garner, Ahmad Bradshaw, and Mark Ingram.

Even with a 1,000-carry minimum, only four of the top twenty backs in yards per carry since the merger are Hall of Famers, (assuming Adrian Peterson makes it, probably a fairly safe bet). By comparison, there are four Hall of Fame running backs who rank outside the top 100 in yards per carry since the merger! (Curtis Martin, Jerome Bettis, John Riggins, and Floyd Little).

On the other hand, here's the post-merger leaderboard for my favorite compound quarterback stat, Adjusted Net Yards per Attempt. ANY/A is yards per attempt including sacks with a bonus for touchdowns and a penalty for interceptions, so it combines every aspect of a quarterback's production into one number.

1. Aaron Rodgers
2. Peyton Manning
3. Jared Goff
4. Tom Brady
5. Drew Brees
6. Tony Romo
7. Philip Rivers
8. Russell Wilson
9. Steve Young
10. Matt Ryan
11. Kirk Cousins
12. Ben Roethlisberger
13. Kurt Warner
14. Joe Montana
15. Dan Marino
16. Dak Prescott
17. Matt Schaub
18. Carson Wentz
19. Andrew Luck
20. Jeff Garcia

You might notice that 13 of those 20 players are currently active; the league is much more efficient passing the football today than it was in the '70s. If you adjust that list for era, you get this:

1. Steve Young
2. Joe Montana
3. Roger Staubach
4. Peyton Manning
5. Dan Marino
6. Aaron Rodgers
7. Tom Brady
8. Dan Fouts
9. Drew Brees
10. Tony Romo
11. Kurt Warner
12. John Brodie
13. Ken Anderson
14. Bob Griese
15. Philip Rivers
16. Jeff Garcia
17. Trent Green
18. Billy Kilmer
19. Ben Roethlisberger
20. Matt Ryan

Eleven of those twenty players are either in the Hall of Fame or are a lock to get in on the first ballot, (Manning, Brady, Brees, and Rodgers), and four more either already have a solid Hall of Fame argument or are certainly building one, (Roethlisberger, Rivers, Anderson, Ryan). Excluding Len Dawson and Joe Namath, (who made the Hall of Fame based on what they did before the merger, not after), Ken Stabler is the only Hall of Fame quarterback ranked lower than 41st by this metric, and Stabler took 27 years to make it in.

Based on the leaderboard test, you can see that ANY/A is heavily, heavily influenced by a player's skill. Which is why you'll never see me feature ANY/A (or even yards per attempt) in Regression Alert. Yes, players with an unnaturally high ANY/A will regress to the mean... but not anywhere near as much as players who rank unnaturally high in a low-signal statistic like yards per carry.

Again, there are lots of other ways to identify which statistics are especially ripe for regression, but I love the simplicity of the leaderboard test. If you're ever wondering whether someone's performance is sustainable, the quickest and easiest thing to do is just look at what other players join him at the top of the leaderboard. If he's surrounded by stars, odds are good he'll be able to keep it up. If there are a bunch of journeymen, mediocre starters, and no-names around him, then bet hard on regression.

And since we've spent all this time trashing yards per carry again, we might as well make an example of it one last time. There are currently 22 running backs averaging between 50 and 90 yards per game rushing, (not including Marshawn Lynch, who is on injured reserve). The top seven in yards per carry are Aaron Jones, Nick Chubb, Matt Breida, Melvin Gordon, Kerryon Johnson, Phillip Lindsay, and Marlon Mack, who have collectively logged 696 carries for 3933 yards, good for 67.8 yards per game and 5.65 yards per carry. This is your Group A.

The bottom seven in yards per carry are Jordan Howard, David Johnson, Lamar Miller, Sony Michel, Adrian Peterson, Alvin Kamara, and Saquon Barkley, who have collectively logged 920 carries for 3735 yards, good for 62.3 yards per game and 4.06 yards per carry. This is your Group B.

Thanks to a blistering yards per carry average, Group A has averaged 9% more rushing yards per game than Group B to this point in the season despite Group B posting a dominant 28% lead in carries per game. Going forward, those yard-per-carry averages are going to both regress hard towards the mean and Group B will handily outrush Group A over the next four weeks.