Photo: Kevin Jairaj, 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 touchdown rate, and Christian McCaffrey is one of the high outliers in touchdown rate, then Christian McCaffrey 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. 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. Over four seasons, I have made 30 specific predictions and 24 of them have proven correct, a hit rate of 80%.

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 talked about yard-to-touchdown ratios and why they were the most powerful regression target in football that absolutely no one talks about, then predicted that touchdowns were going to follow yards going forward (but the yards wouldn't follow back).

In Week 5, we looked at ten years worth of data to see whether early-season results better predicted rest-of-year performance than preseason ADP and we found that, while the exact details fluctuated from year to year, overall they did not. No specific prediction was made.

In Week 6, I taught a quick trick to tell how well a new statistic actually measures what you think it measures. No specific prediction was made.

In Week 7, I went over the process of finding a good statistic for regression and used team rushing vs. passing touchdowns as an example.

For the second consecutive week, one of my favorite predictions wraps up in another win for the column. At the time of the prediction, Group A averaged a touchdown for every 66 yards while Group B was scoring once for every 400 yards. I posited that both groups would likely regress to somewhere in the 100-200 yard per touchdown range, and since yards tended to be more stable and Group B was getting a lot more of them, Group B would outscore Group A going forward.

And that's exactly what happened. Since our prediction, our "high-touchdown" receivers have scored once for every 137 yards while our "low-touchdown" receivers have scored once for every 155 yards. The high-touchdown cohort is still converting yards to touchdowns at a (very slightly) better rate, but because Group B had so many more yards, they actually finished the prediction with more overall touchdowns per game (0.417 to 0.406). Which, combined with their yardage edge, gave them a convincing win, scoring 9.04 points per game vs. Group A's 8.03 points per game.

As for our passing vs. rushing touchdown prediction, things are tighter than the percentages would suggest simply because the teams in question scored so few times overall. Two teams were held out of the end zone, three more scored one of each type of touchdown, and the Titans logged two passing scores against just one rushing score.

(Humorously, the prediction was inspired by the idea that Derrick Henry would score fewer rushing touchdowns, and Henry was indeed held out of the end zone. But he logged his first career passing touchdown, instead.)

Interceptions Are Also Pseudoscience

Two years ago, I wrote about how interception rate was very nearly as unstable from one sample to the next as my favorite punching bag, yards per carry. I cited research, including findings by fellow Footballguy Danny Tuccito that while we only needed a sample of 396 pass attempts before a quarterback's yard per attempt average is as much a result of skill as luck, it takes a sample 1681 pass attempts before interception rate stabilizes in the same way. (For context, yards per carry requires 1978 carries to stabilize and represent equal parts skill and luck.) People dramatically underestimate just how much luck is involved in whether a pass gets picked off or not.

Patrick Mahomes II

Turnover-worthy throws:
6, Tied for 12th with seven others, including Rodgers, Herbert and Jackson

Interceptions:
9, Tied for 1st

— Kevin Cole (@KevinColePFF) October 27, 2021

In fact, given how unstable interception rates are, my biggest lament is simply that interceptions... don't really matter for fantasy football. In most scoring systems quarterbacks are only penalized one or two points per turnover. Sometimes there's not any penalty at all. (My favorite scoring system penalizes players 4.5 points per turnover, which makes identifying regression much more valuable, but such setups are rare.)

Otherwise, we can predict that guys with a lot of interceptions will likely throw a lot fewer going forward, but this doesn't produce much actionable insight when it comes to fantasy football. With one notable exception.

You see, while interceptions play a virtually negligible role in quarterback scoring, they're a massive part of defensive scoring. And they're just as random for defenses as they are for quarterbacks, if not more so. (Justin Fields and Zach Wilson will still be the same people a week from now, but their opponents will be different.) Which means fantasy defenses that have been excelling on the back of unsustainable interception rates are probably due for a reckoning, while solid units that have been good at getting sacks and keeping opposing teams out of the end zone but haven't been getting as many takeaways are due for a boost.

To this point, the Dallas Cowboys, Buffalo Bills, Los Angeles Rams, Tampa Bay Buccaneers, New Orleans Saints, New England Patriots, Green Bay Packers, Indianapolis Colts, Houston Texans, and Los Angeles Chargers are all averaging at least one interception per game. Collectively, those teams have 85 interceptions in 66 games, or 1.29 interceptions per game. This is our Group A.

On the other end of the spectrum, the New York Jets, San Francisco 49ers, Seattle Seahawks, Jacksonville Jaguars, Pittsburgh Steelers, Miami Dolphins, Cleveland Browns, Atlanta Falcons, Washington Football Team, Detroit Lions, Denver Broncos, Las Vegas Raiders, Chicago Bears, Minnesota Vikings, Carolina Panthers, Baltimore Ravens, Kansas City Chiefs, Tennessee Titans, and Cincinnati Bengals average fewer than 0.75 interceptions per game; with 64 interceptions in 127 games, they're picking off 0.50 passes per game. That's our Group B.

To this point, Group A has intercepted 33% more passes than Group B. Thanks to the magic of regression (and the larger sample), I predict that Group B will intercept more passes over the next four weeks than Group A.