Photo: USA Today Sports

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. On a case-by-case basis, it's easy to find reasons why any given player is going to buck the trend and sustain production. So I constrain myself and remove my ability to rationalize on a case-by-case basis.

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. Here's a similar list from 2017.

The Scorecard

In Week 2, I opened with a primer on what regression to the mean was, how it worked, and how we would use it to our advantage. No specific prediction was made.

In Week 3, I dove into the reasons why yards per carry is almost entirely noise, shared some research to that effect, and predicted that the sample of backs with lots of carries but a poor per-carry average would outrush the sample with fewer carries but more yards per carry.

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 talked about why quarterbacks tended to regress less than other positions but nevertheless predicted that Patrick Mahomes II would somehow manage to get even better and score ten touchdowns over the next four weeks.

In Week 7, I talked about why watching the game and forming opinions about players makes it harder to trust the cold hard numbers when the time comes to put our chips on the table. (I did not recommend against watching football; football is wonderful and should be enjoyed to its fullest.)

In Week 8, I discussed how yard-to-touchdown ratios can be applied to tight ends but the players most likely to regress positively were already the top performers at the position. I made a novel prediction to try to overcome this quandary.

In Week 9, I discussed several of the challenges in predicting regression for wide receiver "efficiency" stats such as yards per target. No specific prediction was made.

Our Patrick Mahomes II prediction officially comes to a close, though there wasn't really any suspense. Mahomes was on his way to clear it with ease until an injury early in the second week brought him down and rendered the rest a formality. This is the danger of predictions around individual players— they're especially vulnerable to individual injuries. This officially goes in the books as a loss, but since it's a shame to waste a perfectly good prediction, we'll informally track Mahomes over the next three weeks and see how he does, anyway.

Our high-touchdown tight ends have actually put up a good fight so far. Three members of Group A caught just a single pass this weekend, but that one pass was for a touchdown. But all four of our Group B tight ends are officially in the end zone since the prediction was made, and their yardage advantage has proven insurmountable. Overall, our high-touchdown tight ends and our low-touchdown tight ends are both averaging 0.5 touchdowns per game.

WHAT METRICS REGRESS?

Answer: all metrics regress.

A more interesting question is "what metrics regress the most?" And as we discussed last week, 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. Tatum Bell
7. C.J. Spiller
8. Darren Sproles
9. Tony Nathan
10. Robert Smith
11. Christian McCaffrey
12. Derrick Ward
13. Marv Hubbard
14. Wendell Tyler
15. Justin Forsett
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, Mark Ingram, and Ahmad Bradshaw.

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, of the 168 qualifying backs, there are six Hall of Famers who don't even rank in the top 50% in yards per carry (Franco Harris, Marcus Allen, 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. Tom Brady
4. Russell Wilson
5. Drew Brees
6. Tony Romo
7. Philip Rivers
8. Kirk Cousins
9. Steve Young
10. Jared Goff
11. Matt Ryan
12. Dak Prescott
13. Ben Roethlisberger
14. Kurt Warner
15. Joe Montana
16. Dan Marino
17. Matt Schaub
18. Andrew Luck
19. Carson Wentz
20. Jameis Winston

Here you see four Hall of Famers (Young, Warner, Montana, Marino), four more first-ballot locks (Rodgers, Manning, Brady, Brees), and maybe four or five guys ranging from "on the right track" to "probably going to make it". You might notice that 14 of those 20 players are currently active, too; 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. Ken Anderson
13. Bob Griese
14. Philip Rivers
15. Russell Wilson
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 five more either already have a solid Hall of Fame argument or are certainly building one, (Roethlisberger, Rivers, Anderson, Ryan, Wilson). 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 (even more than yards per target last week), 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 20 running backs averaging between 50 and 90 yards per game rushing, (not including Kerryon Johnson, who is done for the season). The top five in yards per carry are Devin Singletary, Matt Breida, Mark Ingram, Phillip Lindsay, and Carlos Hyde, who have collectively logged 520 carries for 2664 yards, good for 68.3 yards per game and 5.12 yards per carry. Here's your Group A.

The bottom five in yards per carry are Derrick Henry, Todd Gurley, David Montgomery, Sony Michel, and Le'Veon Bell, who have collectively logged 637 carries for 2302 yards, good for 56.1 yards per game and 3.61 yards per carry. This is your Group B.

Based on their per-carry advantage, Group A is averaging 22% more rushing yards per game than Group B despite Group B receiving 17% more carries per game. Going forward, those yard-per-carry averages are going to both regress towards the mean, and Group B's volume advantage will likely result in more rushing yards overall.