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 2021, 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.

The yards per carry prediction is the closest thing to a sure thing in the regression toolkit, but I always like to remind you that one day, it, too, will fail us. Maybe this is the prediction that breaks the winning streak, but I'm not sweating it after a single week. One of the key elements of regression-- one we'll be discussing in greater detail later-- is that results tend to be more extreme over small samples only to normalize over larger ones.

One interesting note (that underlines why I don't handpick my groups): the three Group A backs I thought would bury the prediction (Christian McCaffrey, Bijan Robinson, and Breece Hall) had the lowest ypc of the bunch, while the three that I thought would carry the prediction (D'Andre Swift, James Cook, and Raheem Mostert) had the best days of the group. Again, no conclusions should be drawn from a single week, but it's nice to remind myself from time to time why I just trust regression rather than trying to cherry-pick our samples myself.

PLAYING THE HITS

If you go see Lynyrd Skynyrd live, you know they're playing Sweet Home Alabama and Freebird. The Stones are going to play (I Can't Get No) Satisfaction. KISS is going to play Rock and Roll All Nite and Detroit Rock City, and of course, Ozzy is eventually going to get around to Crazy Train.

Similarly, Regression Alert loves delving into the back catalog for obscure stats and deep cuts from time to time, but we know where our bread is buttered and aren't shy about serving up the hits, either. Last week we played our old classic "Yards Per Carry is Pseudoscience". This week we have our seminal work "Touchdowns Follow Yards (But Yards Don't Follow Back)". Next week we're going to really drive the crowd nuts with our smash "Revisiting Preseason Expectations". But that's getting ahead of ourselves.

First, let's talk about touchdowns. Actually, before we talk about touchdowns, let's talk about vocabulary.

sto·chas·tic
adjective
randomly determined; having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.

Touchdowns are stochastic. Over his career, Cam Newton rushed for 70 touchdowns in 140 games, an average of 0.5 touchdowns per game. We could say that's his "true production level", and over a sufficiently long timeline, we'd probably expect him to conform to that, averaging 0.5 touchdowns per game.

Despite that being his true production level, though, guess how many times Cam Newton rushed for half a touchdown in a game? As far as I can tell (and I have researched this topic extensively), it has never happened. Instead, he either scores zero touchdowns... or he scores one touchdown. (Sometimes, he scores two touchdowns, and once, he even rushed for three touchdowns.) Because they are binary outcomes, we can analyze Cam Newton's rushing touchdowns statistically, but we cannot predict them precisely.

Yards don't behave like that. Over his career, Cam Newton averaged 38.6 rushing yards per game. But it's not like every week he's either getting you 0 yards or else he's getting you 75 yards. Instead, more games than not, he's getting you somewhere between 20 and 60 yards. His yardage total is much more consistent from game to game than his touchdown total.

One way to measure consistency is something called standard deviation, which measures how much something varies around the average. The standard deviation of Newton's rushing yardage is 24.5 yards. The standard deviation of Newton's rushing touchdowns is 0.65 touchdowns.

Now, these numbers are not directly comparable. Standard deviations for large values are naturally bigger than standard deviations for small values. (Consider: if you switched to "feet rushing per game" rather than "yards rushing per game", the standard deviation would triple despite the underlying game-to-game variation remaining unchanged.)

But if you divide a player's standard deviation by that player's average, you get something called the coefficient of variation, or CV. CV is a way to compare how volatile different statistics are. The CV of Newton's yards is 64%, meaning it tends to vary by about 64% of his overall average. The CV of Newton's touchdowns is 130%. Touchdowns are much more random from week to week than yards are— in Newton's case, about twice as random, according to CV. (For those curious, the CV of Newton's rush attempts was 42%; "usage" stats like attempts tend to be more stable from week to week even than yards.)

Not only are they more unstable, but touchdowns are also much more valuable than yards. In most scoring systems, one extra touchdown is worth the equivalent of 60 extra yards. Which means if Newton caught the high side of variance and scored a few extra touchdowns early in the year, it could dramatically inflate his fantasy production to date. And if he caught the low side of variance and failed to reach the end zone, it could leave him far lower than we'd otherwise expect.

This gives rise to my favorite statistic for regression: yard-to-touchdown ratios. Some players are really, really good at getting yards and/or not quite as good at scoring touchdowns. For years, Julio Jones was the most famous example of this; if he never plays another snap of professional football, he will retire averaging 216 receiving yards for every touchdown he scored. This is a very high average, but there are other wide receivers in this general range: Andre Johnson averaged 203 yards for every touchdown, Henry Ellard averaged 212, etc.

Other players are really, really good at getting touchdowns but typically aren't commensurately good at getting yards. For his career, Davante Adams scores a touchdown for every 111 yards he gains receiving. Again, this is a very low average but not historically implausible; Dez Bryant averaged 102 yards for every touchdown, while Randy Moss was all the way down at 98 yards per touchdown.

Importantly, the yard-to-touchdown ratio is not a measure of player quality. Over 2016 and 2017, Davante Adams averaged 940 yards and 11 touchdowns. Over 2021 and 2022, Davante Adams averaged 1535 yards and 12.5 touchdowns. It should go without saying that Adams played much, much better in the last two years than he did in 2016 and 2017 despite averaging a "worse" yard-to-touchdown ratio. All else being equal, a guy who gains 1,500 yards and 10 touchdowns is better than a guy who gains 1,000 yards and 10 touchdowns.

If you asked who was the best receiver in the NFL at various points over the last decade, you might plausibly have heard Jones (216 yards per touchdown), Justin Jefferson (203 yards per touchdown), Michael Thomas (180 yards per touchdown), DeAndre Hopkins (161 yards per touchdown), Stefon Diggs (152 yards per touchdown), Antonio Brown (148 yards per touchdown), Calvin Johnson (139 yards per touchdown), Cooper Kupp (138 yards per touchdown), Odell Beckham (133 yards per touchdown), Tyreek Hill (131 yards per touchdown), Ja'Marr Chase (123 yards per touchdown), or Adams (111 yards per touchdown). (Similarly, I could easily find mediocre or even bad receivers who span the whole yard-to-touchdown spectrum; Devin Funchess averaged 108 yards per touchdown, but he's no Davante Adams.)

Over the long term, receivers tend to average between 100 and 200 yards per touchdown with a median around 140, and the majority of the league clustered between 120 and 180. Any rate that falls in that range is plausibly sustainable and perhaps a true representation of a player's relative skill at scoring touchdowns. (It's also plausibly not; Stefon Diggs averaged 110 yards per touchdown from 2017 to 2018 and 190 yards per touchdown from 2019 to 2020. Both samples were fairly large-- at least 29 games in each-- and neither was representative of his "true" career rate of 152 yards per touchdown.)

But while any rate within the "sustainable band" may or may not be representative, any rate outside that band is definitely going to regress. And that's good for us because over small samples the stochastic nature of touchdowns means we see a lot of rates falling outside of the sustainable band.

So let's pit the receivers with a lot of yards but very few touchdowns against the receivers with a lot of touchdowns but very few yards and see what happens. There are 44 receivers right now with at least 20 fantasy points (using standard scoring-- 1 point per 10 yards, 6 points per touchdown-- to exaggerate the yardage vs. touchdowns split). Sixteen of those receivers are averaging more than 200 yards per touchdown (removing Mike Williams, who is done for the season), while sixteen are averaging fewer than 100. Our "high-yardage" receivers average 33.7 points compared to 26.7 points for our "high-touchdown" group.

Now, this isn't very sporting-- our Group B is starting the prediction out ahead-- so let's make it interesting. The six highest-scoring receivers in Group B are Keenan Allen, Justin Jefferson, Deebo Samuel, Puka Nacua, Stefon Diggs, and Amon-Ra St. Brown. These are phenomenal receivers! Let's kick out everyone but Nacua.

Meanwhile, the bottom six receivers in Group A are K.J. Osborn, Tyler Lockett, Brandon Johnson, Tee Higgins, Kendrick Bourne, and Josh Reynolds. Lockett and Higgins are proven stars, so they can stay, but we'll boot the other four out.

(I know I was just writing about how I don't pick my samples, but the code is more what you'd call "guidelines" than actual rules. I'm absolutely allowed to add or remove names to the lists provided it increases the degree of difficulty for when regression eventually kicks in.)

Removing most of the worst players from Group A and most of the best players from Group B leaves us with 23 players. Collectively, the Group A receivers average 9.9 points per game, while the Group B receivers average 9.7. This still isn't a very big lead, but we're left with a conundrum. We could remove some of the better players from Group A or the worse players from Group B, which would widen the gap but make it less impressive if Group B eventually closed it. On the other hand, the best players remaining in Group B (JaMarr Chase, CeeDee Lamb, A.J. Brown) are also the three lowest scorers left, so removing them would put Group B back in front again.

So we'll stop tweaking the groups and get to the prediction. We're left with twelve members of Group A: Mike Evans, Courtland Sutton, Romeo Doubs, Jordan Addison, Brandon Aiyuk, Marquise Brown, Jakobi Meyers, Garrett Wilson, Gabe Davis, Jayden Reed, Tee Higgins, and Tyler Lockett. These twelve receivers are averaging 54.6 yards and 0.72 touchdowns per game, good for 9.9 fantasy points.

Similarly, we have eleven members of Group B: Puka Nacua, Tutu Atwell, Nico Collins, Amari Cooper, Chris Olave, George Pickens, DK Metcalf, Michael Pittman, CeeDee Lamb, A.J. Brown, and JaMarr Chase. These eleven receivers are averaging 85.3 yards but just 0.18 touchdowns per game, good for 9.7 fantasy points.

Group A only leads Group B by about 1.3% through three weeks, but I predict that even though we have removed many of the best players from Group B and the worst players from Group A, Group B will still outscore Group A over the next four weeks (aided by the forces of regression).