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.
| STATISTIC FOR REGRESSION | PERFORMANCE BEFORE PREDICTION | PERFORMANCE SINCE PREDICTION | WEEKS REMAINING |
|---|---|---|---|
| Yards per Carry | Group A had 24% more rushing yards per game | Group B has 25% more rushing yards per game | None (Win!) |
| Yards per Touchdown | Group A scored 3% more fantasy points per game | Group A has 12% more fantasy points per game | None (Loss) |
| Margin of Victory | Average margins were 9.0 points per game | Average margins are 9.9 points per game | None (Win!) |
| Defensive INTs | Group A had 65% more interceptions | Group B has 43% more interceptions | 1 |
| Schedule Luck | Group A had 38% more wins | TBD | 1 |
Our "margin of victory" prediction caused much anxiety over the last four weeks, but the end result was a rather comfortable win. As I've mentioned, this was a fun prediction for me as I was essentially "flying blind"; I'd never studied this subject before and had to rely entirely on first principles. The win also illustrates a couple of really interesting facts about regression and about human nature.
First: I predicted that over the last four weeks the average margin of victory in all games would be between 9.0 and 10.5 points, and that was correct. But there wasn't a single week during that span where the average margin fell between 9.0 and 10.5 points. The weekly margins were instead 11.9, 10.9, 8.5, and 7.9 points. Which is a great illustration of why we run these predictions over larger sample sizes; in small batches, results are fairly random. But take enough observations, and they trend more and more strongly to their "true" level.
Second, it's interesting how the order of the data influences our perception of the data. Because the weeks happened in the order they did, this "felt" like a tense prediction that we were poised to lose until snatching victory at the very end. If the weeks had run in reverse order, we'd have spent weeks watching the total fall well below our lower limit and worrying that we'd overestimated regression in the scoring environment. If we'd run them in a scrambled order (say: 7.9, 11.9, 8.5, 10.9), our average would have been right in the predicted sweet spot for weeks, and a victory would have felt inevitable. The important thing to remember is that changing the order in which the data was presented wouldn't change the data, though.
It's human nature to ascribe value to trends and movement, but at the end of the day, the full data set is more important than the order it was presented.
As for what that full dataset suggests... NFL games really are meaningfully closer this year than they were last year. I noted after Week 6 that four of the first six weeks saw margins that were closer than ANY week from 2011. Two of the last four weeks managed the feat as well, which means six out of ten weeks in 2022 would have been the closest, most exciting weeks of the entire season last year. I'll leave it to smarter people to figure out why NFL games are suddenly so tight (though I've offered a few theories along the way), but rest assured that the trend is not a fluke.
As for our other two predictions, both are set to wrap up next week. Our "high-interception" teams are intercepting passes at a slightly higher rate than our "low-interception" teams still, but since their per-game edge has fallen from 230% down to 50%, the "low-interception" group continues to lead in total volume.
As for our schedule luck prediction, I've been having trouble accessing the leaderboard to check results from last week, so we'll leave this one in limbo and resolve it all at once next week. Isn't suspense fun?!
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.
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