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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.
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.
In Week 9, I explained the critical difference between regression to the mean (the tendency for players whose performance had deviated from their underlying average to return to that average) and the gambler's fallacy (the belief that players who deviate in one direction are "due" to deviate in the opposite direction to offset).
In Week 10, I discussed not only finding stats that were likely to regress to their "true mean", but also how we could estimate what that true mean might be.
In Week 11, I explained why larger samples work to regression's benefit and made another yards per carry prediction.
In Week 12, I used a simple model to demonstrate why outlier performances typically require a player to be both lucky and good.
|Statistic Being Tracked
|Performance Before Prediction
|Performance Since Prediction
|Yards Per Carry
|Group A had 42% more rushing yards/game
|Group A has 10% more rushing yards/game
|Group A had 7% more points/game
|Group B has 38% more points/game
|Teams averaged 218.4 yards/game
|Teams average 219.7 yards/game
|Group A threw 25% fewer interceptions
|Group B has thrown 11% fewer interceptions
|Yards Per Carry
|Group A had 10% more rushing yards/game
|Group A has 22% more rushing yards/game
I'm beginning to think this just might not be a good year for yards per carry predictions.
Our first prediction failed for the expected reason. We predicted workloads would remain stable, and they were. We predicted yards per carry would regress, but they didn't. That wasn't shocking, because the whole point of the yards per carry prediction is that yards per carry does unpredictable things over small samples.
Our second prediction is currently failing for the unexpected reason. We predicted yards per carry would regress, and to this point, it has. Group A fell from 5.05 ypc to 4.24. Group B rose from 3.80 ypc to 4.16. The difference between groups was 1.25 at the time of the prediction, and it's 0.08 since.
On the other hand, workloads have nearly completely flipped. Group A rose from 13.1 carries per game to 16.4. Group B fell from 15.7 carries per game to 13.7. An illustrative example: two weeks ago, Raheem Mostert had zero 20-carry games in his career. Today, he has two.
There are still two weeks to go, but so far, things aren't looking great.
Most Players Regress. Rookies Progress.
We've talked this season about how everyone regresses to the mean, but everyone's mean is different. Thinking of player performance as random fluctuations around a fixed "true mean" is useful. But it's not maximally accurate.
Just as means can vary from player to player, they can also change over time. Randall Cunningham was one of the most prolific rushing quarterbacks in history. In his 20s, he averaged 41.1 rushing yards per game at 7.0 yards per carry. This was his "true mean".
In his 30s, he averaged 14.7 rushing yards per game at 4.7 yards per carry. This was also his true mean. Quarterback rushing tends to age much like running back rushing, with even the most prolific runners finding themselves running less frequently and less successfully.
How do you estimate a mean that's a moving target? There are techniques one could use, such as more heavily weighting recent games in the average to pick up on trends in performance. Or one could develop a good working knowledge of general trends (such as quarterback rushing declining around age 30) and update expectations accordingly.
Today we're going to do the latter. Players tend to score the same number of fantasy points in the first half and the second half of the season. But I have working knowledge of one class of player whose performance tends to trend up over time: rookies.
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