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.

Regression and Large Samples

One of the key features of regression to the mean is that outlier performances are significantly more likely over small samples. If I flip a coin that's weighted to land on heads 60% of the time, that means there's still a 40% chance it lands on tails. Given those odds, landing on tails wouldn't be very surprising at all. But if I flipped the same coin a million times, the odds of seeing Tails come up more often than Heads dwindles down to nothing.

This idea that variance evens out over larger samples is one of the key insights in fantasy football. Why do top DFS players compete with so many different lineups every week? The answer is not, as is commonly believed, because it increases their expected return on investment. Indeed, every DFS player has a "best" lineup, a lineup that they think is most likely to win that week, and every other lineup that player submits actually decreases expected payout (because it's a worse lineup than the best lineup).

So why submit so many different lineups? Because outlier performances are significantly more likely over small samples. By using 20 lineups in a week, top players reduce the amount of money they'd be expected to win, but they also reduce the chances of a single injury or bad performance wiping out their entire bankroll, and that's a worthwhile trade.

Why is it that three weeks at the beginning of the year don't give us enough information to outperform ADP, but five weeks do? Because three weeks is too small of a sample for the outlier performances to have all washed out sufficiently, and five weeks is not.

This is why the preferred practice around here is to select groups of players or teams to compare in our predictions. If we selected a single player, we'd be wrong much more often (much like betting heads on a weighted coin will still lose 40% of the time). By bundling players into similar groups of five or ten, it becomes much more likely that we'll see the overall pattern emerge.

This is also why the preferred practice around here is to let predictions run for four weeks. I'd love to let them run for even longer, sometimes, but a clearly-defined endpoint is critical for accountability, to prevent me from just running the prediction until Group B pulls ahead and then immediately closing it and declaring it a success.

The fact that outliers are more common on smaller samples tends to manifest in our results over time, too. We usually see Group B take its biggest lead in the week or two after the prediction and then watch that lead shrink over the remaining weeks, for instance. At the same time, when Group B does trail, it likewise typically does so in the week or two immediately after the prediction before pulling back ahead in Weeks 3 and 4.

Indeed, I always report the size of the lead in either direction (that darn accountability thing again), but this is usually misleading. A 20% lead over four weeks is significantly more impressive (as in "less likely to happen by chance alone / more likely to be a result of genuine signal") than a 30% lead over one week. (Consider: if Group B leads Group A by 30% after one week, then a 30% edge by Group A in the next week will erase that lead. If Group B leads Group A by 20% after four weeks, then a 30% edge by Group A in the next week will still leave Group B 10% ahead, provided all sample sizes are roughly equal.)

Here's another illustration of the impact of small differences over large samples. For those of you who have been watching football for long enough, you probably remember the 2004 NFL season. The 2003 season closed with the New England Patriots beating the Indianapolis Colts 24-14 in a game that wasn't as close as the final score might suggest. The Colts complained that the Patriots' defensive backs were hitting receivers more than five yards beyond the line of scrimmage, which violated the rules as written, and the referees let it slide.

Over the offseason, the NFL's competition committee decided it would place a "point of emphasis" on ensuring officiating crews began calling contact downfield in line with the rules as written. NFL defenses adjusted by being less physical in coverage and passing offenses exploded, setting numerous records, headlined by Peyton Manning's own 49-touchdown season. After 2004, the NFL quietly dropped the point of emphasis, officiating crews went back to letting contact six or seven yards downfield slide, and offenses dropped off again.

In 2003, the league-wide average for yards per pass attempt was 6.6. In 2004, it spiked all the way to 7.1. In 2005, it fell back down to 6.8. (For context, yards per attempt in each of the last three seasons has been 7.2, 7.1, and 7.1; the 2004 season was essentially 15 years ahead of its time.)

That was it. Three-tenths, five-tenths of a yard per pass attempt, that was the difference between a stifling defensive environment and a wide-open offensive environment. When an offense dropped back to pass in 2004, the result was approximately 7.5% better than when it dropped back to pass in 2003.

On a player level, a 0.3-0.5 extra yards per attempt isn't a big difference. So far this season, Jimmy Garoppolo leads Joe Burrow by 0.41 yards per attempt, though I suspect most would say Burrow has been the better player.

But that's a difference of half a yard on a couple of hundred attempts. This was a difference of half a yard... over 16,354 attempts. Despite attempting 139 fewer passes, the league as a whole passed for an extra 5169 yards in 2004. It basically conjured an entire 1984 Dan Marino out of thin air. That half yard per attempt was a massive change given the sheer number of attempts in question. That small difference was much more impressive over a large sample.

What does this mean for us? It means if we want to make a sure profit in fantasy football by betting on regression to the mean, we're going to need to place a lot of bets. Trading away one player or acquiring another simply because they have a profile that suggests regression is a positive move in expectation, but the range of possible outcomes is massive. It could work out really well, it could work out terribly. Weighted coins still flip tails sometimes.

It also means that the more bets we place on regression to the mean, the more our upside becomes capped. With larger samples, the odds of hitting big on every bet decline. The larger our sample, the smaller our potential rate of return.

But just like top DFS players, when you have a genuine edge, it can often make sense to turn to safer profits over gambling on the potential to strike it big while leaving yourself fully exposed to the consequences if the flip doesn't go your way.