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.
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.
|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 11.9 points per game||3|
The writing had been on the wall for a couple of weeks, but we officially close the books on our first failed prediction of the season; in fact, this is the first time this particular prediction has failed in the six-year history of Regression Alert. I'm not especially surprised that it failed. If you make an 80-90% bet often enough, eventually, it's going to go bad. But I'm a little surprised by how it failed.
The core observation of the yard-to-touchdown ratio prediction is that there is a narrow "sustainable" range of rates at which players can convert yards into touchdowns. Players who are averaging fewer than 100 yards per touchdown are going to start scoring less. Players who are averaging more than 250 yards per touchdown are going to start scoring more. And that's exactly what happened. Group A averaged one touchdown for every 57 yards at the time of the prediction; it averages one per every 207 yards since. Group B averaged a touchdown for every 378 yards at the time of the prediction; it averages one per 148 since. Group B actually outscored Group A with 0.36 touchdowns per game against 0.31.
No, it's the secondary observation that let us down. Usually, when yard-to-touchdown ratio stabilizes, it's the yards that stay constant and the touchdowns that regress. In this case (as mentioned above) the touchdowns regressed just fine, but the yards changed dramatically. Group A went from 48 yards per game at the time of the prediction to 64 yards per game since. Group B plummeted from 84 yards per game at the time of the prediction down to 53 since. It wasn't a single injury or a single outlier player or a fluky big game that did it, either; Group A was up pretty much across the board, and Group B was down pretty much across the board.
No real takeaways other than that random things behave randomly.
As for our second prediction, the average margin rebounded from its aberrant early-season low mark. It passed our predicted range, but it's hard to say so soon whether that's a bad sign or just random noise. We'll have to wait another week or two to see.
Interceptions Are Also Pseudoscience
Three 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 of 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.
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.
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