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.
In Week 11, I broke down the very important distinction between "mean reversion" (the tendency of players to perform around their "true talent level" going forward, regardless of how they have performed to date) and "gambler's fallacy" (the idea that overperformers or underperformers are "due" for a correction).
In Week 12, I talked about how much of a team's identity was really just random noise and small samples and projected that some of the most rush-heavy teams would skew substantially more pass-heavy going forward.
In Week 13, explained why the optimal "hit rate" isn't anywhere close to 100% and suggested that fantasy players should be willing to press even marginal edges if they want to win in the long run.
In Week 14, I sympathized with how tempting it is to assume that players on a hot streak can maintain that level of play but discussed how larger (full-season) samples were almost always more accurate. I predicted that the hottest players in fantasy would all cool down substantially toward their full-season averages.
In Week 15, I discussed several methods of estimating your championship odds and explained why virtually every team is more likely to lose than to win.
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 50% more interceptions | None (Win!) |
Schedule Luck | Group A had 38% more wins | Group A had 4% more wins | None (Loss*) |
Offensive Identity | Group A had 12% more rushing TDs | Group A had 4% more rushing TDs | None (Loss) |
"Hot" Players Regress | Players were performing at an elevated level | Players have regressed 118% to season avg. | 2 |
Our rush vs. pass touchdown bet was tied heading into Week 15, but unfortunately, we weren't able to pull it out as teams in our sample passed for 10 scores but rushed for 12. Of the eleven teams in our sample, nine finished with at least as many passing touchdowns as rushing ones, but the two exceptions were enough to sink us; the two teams from Pennsylvania collectively passed for 9 touchdowns and rushed for 18 over the last four weeks (including passing for zero and rushing for six last week alone).
Our "hot" players are regressing nicely, though. Much like with Tee Higgins in Week 14, I've discarded Jonathan Taylor's game in Week 15 because he was injured so early. I don't want to mistake injury for regression. Even without it, our "hot" players are averaging 11.83 points per game through two weeks, which is close to (but slightly below) their season-long average of 12.75 and substantially below their "hot" average of 17.74. Out of 24 remaining players, 19 have regressed at least two-thirds of the way toward their overall average and 23 have regressed at least 25% of the way back. The lone exception, the lone "hot" player who has maintained (and even built on) his recent strong play is Juwan Johnson, whose 22.7 points in his lone game since the prediction blows his "hot" average of 10.3 points per game out of the water.
Regression Sometimes Arrives Late, but it Always Arrives
I've written several times this year about how regression to the mean works best over larger samples. Track more players, follow for more weeks, and the regression becomes more obvious. Individual players and individual games can and frequently do buck the trend. In fact, they might only be a 55% bet to regress. But if you bundle enough 55% bets together, they become a 95% bet.
This creates the fundamental tension of the column. I want to be right, of course, but "check back with me next season" doesn't really cut it. We want faster feedback than that. I've settled on four weeks as an acceptable compromise; long enough to wash out some of the randomness, short enough to stave off impatience.
But four weeks isn't a magical number, and more is always better. As a case study, I wanted to revisit our failed "yard-to-touchdown ratio" prediction from way back in Week 4.
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