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 Justin Jefferson is one of the top performers in my sample, then Justin Jefferson goes into Group A, and may the fantasy gods show mercy on my predictions.

Most importantly, because predictions mean nothing without accountability, I report on all my results in real time and end each season with a summary. Here's a recap from last year detailing every prediction I made in 2022, along with all results from this column's six-year history (my predictions have gone 36-10, a 78% success rate). And here are similar roundups from 2021, 2020, 2019, 2018, and 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 explained that touchdowns follow yards, but yards don't follow touchdowns, and predicted that high-yardage, low-touchdown receivers were going to start scoring a lot more going forward.

In Week 5, we revisited one of my favorite findings. We know that early-season overperformers and early-season underperformers tend to regress, but every year, I test the data and confirm that preseason ADP is still as predictive as early-season results even through four weeks of the season. I sliced the sample in several new ways to see if we could find some split where early-season performance was more predictive than ADP, but I failed in all instances.

In Week 6, I talked about how when we're confronted with an unfamiliar statistic, checking the leaderboard can be a quick and easy way to guess how prone that statistic will be to regression.

In Week 7, I discussed how just because something is an outlier doesn't mean it's destined to regress and predicted that this season's passing yardage per game total would remain significantly below recent levels.

In Week 8, I wrote about why statistics for quarterbacks don't tend to regress as much as statistics for receivers or running backs and why interception rate was the one big exception. I predicted that low-interception teams would start throwing more picks than high-interception teams going forward.

Leaguewide, passing yards per game has risen for the second straight week. I wrote at the time that this was a long-term prediction that relied heavily on bad-weather games in November and December, so my level of concern remains low.

Group A and Group B threw the same number of interceptions last week, which would count as a loss if it stood (I specifically predicted fewer interceptions for Group B), but with three weeks to go, that seems relatively unlikely.

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.

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. Last year, Brock Purdy threw an interception on 2.4% of his throws. This year, he had yet to throw an interception through five games, so surely he was "due". Sure enough, he threw 5 interceptions in the next three weeks and now his INT% for the season is at 2.2%, right around where we expected it to be. Score one for the universe.

But those five interceptions came on 88 attempts, a 5.7% interception rate that was just as fluky and unlikely as the 0% interception rate to start the year. It wasn't "fate" that he'd go on such a streak, the universe doesn't have scales that it's secretly trying to balance. And even our entire framing is infected with our desire to see patterns; why was he only "due" to regress after his fifth interception-free game? Why not after his third? Why not after his sixth?

Imagine a six-year veteran player who averages one touchdown per game for his career-- let's call it 96 touchdowns in 96 games. (This number is implausible and would be likely to regress, but let's pretend it's stable to keep the math simple.) Imagine he scores 0 touchdowns over the first four games of the season; how many touchdowns would you expect him to score over the next four? Imagine instead that he scores 8 touchdowns over the first four games of the season; how many touchdowns would you expect him to score over the next four?

If you think he's "due" for extra touchdowns to make up for his cold start, or "due" for a touchdown-less streak after his hot start, you're falling prey to the gambler's fallacy. 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. The answer to both questions should be "four expected touchdowns over the next four games".

(Actually, if you want to be extra precise, after a cold start the player in question will now have scored 96 touchdowns in 100 games, so the expectation going forward should be 0.96 touchdowns per game, or about 3.8 touchdowns over his next four games. Similarly, after a hot start the player will be averaging 1.04 touchdowns per game for his career, which is about 4.2 touchdowns over the next four games in expectation; hot streaks and cold streaks should cause us to revise our estimate of a player's "true" performance level.)

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. Just because a player's performance deviated from expectations doesn't mean we should expect more deviations.