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 I'm looking at receivers and Cooper Kupp is one of the top performers in my sample, then Cooper Kupp 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. At the end of last season, I provided a recap of the first half-decade of Regression Alert's predictions. The executive summary is we have a 32-7 lifetime record, which is an 82% success rate.

If you want even more details, here's a list of my predictions from 2020 and their final results. Here's the same list from 2019 and their final results, here's the list from 2018, and here's the list from 2017.

The Scorecard

In Week 2, I broke down what regression to the mean really is, what causes it, how we can benefit from it, and what the guiding philosophy of this column would be. 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 discussed the tendency for touchdowns to follow yards and predicted that players scoring a disproportionately high or low amount relative to their yardage total would see significant regression going forward.

In Week 5, I revisited an old finding that preseason ADP tells us as much about rest-of-year outcomes as fantasy production to date does, even a quarter of the way through a new season. No specific prediction was made.

In Week 6, I explained the concept of "face validity" and taught the "leaderboard test", my favorite quick-and-dirty way to tell how much a statistic is likely to regress. No specific prediction was made.

In Week 7, I talked about trends in average margin of victory and tried my hand at applying the concepts of regression to a statistic I'd never considered before, predicting that teams would win games by an average of between 9.0 and 10.5 points per game.

In Week 8, I lamented that interceptions weren't a bigger deal in fantasy football given that they're a tremendously good regression target, and then I predicted interceptions would regress.

In Week 9, I explained why the single greatest weapon for regression to the mean is large sample sizes. For individual players, individual games, or individual weeks, regression might only be a 55/45 bet, but if you aggregate enough of those bets, it becomes a statistical certainty. No specific prediction was made.

In Week 10, I explored the link between regression and luck, noting that the more something was dependent on luck, the more it would regress, and predicted that "schedule luck" in the Scott Fish Bowl would therefore regress completely going forward.

Gambler's Fallacy and Regression to the Mean

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 very subtle changes, I can convey massive differences in that mood. (^.^) and (v.v) are remarkably similar, and yet the interpreted moods are drastically different.

(Did I start this entire digression just to have a thinly-veiled excuse to post some of my favorite emoticons? ¯\_(ツ)_/¯)

Another less-endearing manifestation of apophenia is formally called the gambler's fallacy (and informally called "the reason Las Vegas keeps building bigger casinos"). We look at random sequences of events and instead of seeing faces, we see trends. A roulette wheel might land on 7 three times in six spins, and suddenly we think the number 7 is "hot". Or a wheel might not land on 00 for three hundred straight spins, and now we believe that 00 is "due". But randomness doesn't work that way; the odds of a roulette wheel landing on a number when it's "hot" are exactly the same as the odds of it landing on that number when it's "cold" (1 in 38 on an American-style "double zero" roulette wheel).

It's very tempting to see regression to the mean as the universe's enforcement mechanism for the gambler's fallacy. Through three weeks, Austin Ekeler had 219 yards but no touchdowns. Ekeler is ordinarily a fairly good touchdown scorer, so surely he was "due". And then Ekeler scored 10 touchdowns over his next 5 games, so score one for the universe, except now he was scoring too much and he was "due" for some zero-touchdown days.

But a player's "true touchdown rate" after a long cold streak is exactly the same as his "true touchdown rate" after a long hot streak. Regression to the mean doesn't magically force cold streaks to follow hot streaks to restore balance to the universe. In fact, a player is just as likely to follow up a hot streak with another hot streak as he is to follow it with a cold streak.

Since taking over as a starter in 2020, Austin Ekeler has scored 33 touchdowns in 35 games. His "true scoring rate" is probably around a touchdown per game. From that perspective, his 10 touchdowns in 9 games are right around what we should have expected. But that doesn't change the fact that his huge scoring outburst was still an unlikely outcome. The universe doesn't have scales that it's secretly trying to balance. After three games without a score, the most likely outcome over the next five games was... about a touchdown per game. After ten touchdowns in five weeks, the most likely outcome over the next five games is... about a touchdown per game.

This burning need to find patterns, whether any patterns exist or not, can be a real hindrance in fantasy football. When we see a player on a lucky streak, we'll think he's "hot" and his luck will continue going forward. Or we'll think he's "due" and his luck will reverse going forward.

But the universe, the very nature of randomness itself, is unimpressed by our expectations. This is why many smart analysts prefer the term "reversion to the mean" instead of "regression to the mean", because it doesn't imply any specific directional force. When a player is coming off a particularly lucky stretch, the most likely result isn't another lucky stretch. And it's not an unlucky stretch, either. The expectation instead should be neutral luck. The expectation should be that the player in question simply... reverts back to his true mean going forward.