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 break down a topic related to regression to the mean. Some weeks, I'll explain what it is, how it works, why you hear so much about it, and how you can harness its power for yourself. In other weeks, I'll give 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 I'm looking at receivers and Ja'Marr Chase is one of the top performers in my sample, then Ja'Marr Chase goes into Group A, and may the fantasy gods show mercy on my predictions.

And then, because predictions are meaningless without accountability, I track and report my results. Here's last year's season-ending recap, which covered the outcome of every prediction made in our eight-year history, giving our top-line record (46-15, a 75% hit rate) and lessons learned along the way.

Our Year to Date

Sometimes, I use this column to explain the concept of regression to the mean. In Week 2, I discussed what it is and what this column's primary goals would be. In Week 3, I explained how we could use regression to predict changes in future performance-- who would improve, who would decline-- without knowing anything about the players themselves. In Week 7, I illustrated how small differences over large samples were more meaningful than large differences over small samples. In Week 9, I showed how merely looking at a leaderboard can give information on how useful and predictive an unfamiliar statistic might be.

Sometimes, I use this column to point out general examples of regression without making specific, testable predictions. In Week 5, I looked at more than a decade worth of evidence showing how strongly early-season performances regressed toward preseason expectations.

Other times, I use this column to make specific predictions. In Week 4, I explained that touchdowns tend to follow yards and predicted that the players with the highest yard-to-touchdown ratios would begin outscoring the players with the lowest. In Week 6, I showed the evidence that yards per carry was predictively useless and predicted the lowest ypc backs would outrush the highest ypc backs going forward. In Week 8, I discussed how most quarterback stats were fairly stable, but interceptions were the major exception.

In Week 10, we looked at how passing performances were trending down over the years and predicted this year would set new lows for 300-yard passing games. 

The Scorecard

Group B finally had a week with more interceptions than Group A, but they still maintained their overall lead. Unless they collectively throw seven more interceptions than Group A this week, our prediction will close with another win.

As for our other active prediction, Week 10 saw just two teams eclipse 300 passing yards—the Lions and the 49ers. "On pace" stats are worse than useless on such small sample sizes, but if the rest of the season goes anything like last week, we'll beat our target by more than 50%.

Gambler's Fallacy and Regression to the Mean

Before we start today's discussion, a quick quiz: 

Imagine a receiver plays especially well over the first eight games of a sixteen-game season, averaging 100 yards per game (on pace for 1600 total). Imagine that we also happen to know this player is overperforming; his "true mean" performance level is just 80 yards per game. How many yards per game should we expect this receiver to average for the full year?

We'll get to the answer in a bit.

The goal of this column is to convince you to view regression to the mean as a force of nature, implacable and inevitable, a mathematical certainty. I can generate a list of players and, without knowing a single thing about any of them, predict which ones will perform better going forward and which will perform worse. I like to say that I don't want any analysis in this column to be beyond the abilities of a moderately precocious 10-year-old.

But it's important that we give regression to the mean as much respect as it deserves... and not one single solitary ounce more. 

This is difficult because regression is essentially the visible arm of random variation, and our brains are especially bad at dealing with genuine randomness. We're just not wired that way. We see patterns in everything. There's even a name for this hardwired tendency to "discover" patterns in random data: Apophenia.

A fun example of apophenia is pareidolia, or the propensity to "see" faces in random places. Our ancestors used to tell stories of the "Man in the Moon". We... type silly faces to communicate emotion over the internet. Yes, pareidolia is why I can type a colon and a close paren and you'll immediately know that I'm happy and being playful. :)

Our ability to "see" these faces is surprisingly robust. -_- is just three short lines, and not only do most people see a face, they also mentally assign it a specific mood. '.' works as well. With small changes, I can convey massive differences in that mood. (^.^) and (v.v) are remarkably similar, yet the interpreted moods are drastically different.

Another Face of Apophenia