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 break down a topic related to regression to the mean. Some weeks, I'll explain what it is, how it works, why you hear so much about it, and how you can harness its power for yourself. In other weeks, I'll give 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 Jaxon Smith-Njigba is one of the top performers in my sample, then Jaxon Smith-Njigba goes into Group A, and may the fantasy gods have mercy on my predictions.

And then, because predictions are meaningless without accountability, I track and report my results. Here's last year's season-ending recap, which covered the outcome of every prediction made in our nine-year history, giving our top-line record (51-17, a 75% hit rate) and lessons learned along the way.

Our Year to Date

In Week 2, I laid out the four primary goals of Regression Alert. The first was to persuade you that regression to the mean is a real, actionable force in fantasy football. The core of that effort is making specific, concrete predictions based on nothing but regression to the mean and tracking the results over time. Here's a list of every prediction we have made so far:

1. I predicted that high-volume, low-ypc running backs would outrush lower-volume, higher-ypc backs over the next four weeks (Week 4).
2. I predicted that high-yardage, low-touchdown receivers would outscore low-yardage, high-touchdown receivers (Week 6).

The Scorecard

Our Yards per Carry prediction has gone sideways enough that it merits a genuine postmortem next week when we close it out (there's virtually no chance of Group B scoring enough to come back at this point). I'll save a detailed analysis until then.

Our Yards per Touchdown prediction only had 13 players to start, and 5 of them missed last week (four were on bye, one was injured), so there's not enough data to discuss at this point. The only interesting note is that the eight receivers who played scored only a single touchdown between them, and it was by a receiver in the "low-touchdown" cohort. 

Regression and Large Samples

I touched on this briefly last week when discussing how few receivers we were grouping into our prediction, but outlier performances are significantly more likely over small samples.

This influences how we select our regression candidates in two ways. First, it explains why we focus on the far edges of the distribution—because of the small samples provided by an NFL season, the most extreme values in any given statistic are most likely chance-driven outliers. Second, it explains why we gather so many players into each group for our prediction—the smaller the sample of players, the less likely that sample conforms to the expected distribution going forward.

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 dwindle down to nothing.

Similarly, if I single out one outlier player for regression, I'm more likely to be right than wrong... but I still might have a 40% chance of being wrong. If I bundle a bunch of outlier players together, though, the odds of being wrong fall substantially. Same idea behind running predictions for multiple weeks—the longer the better, though I do like to have a clearly defined endpoint to make it easier to register our wins and losses for the year.

Larger Samples for Fun and Profit?

This idea that variance evens out over larger samples is one of the key insights of high-volume fantasy football players. 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.

In larger tournaments, they might estimate their best lineup has a 1% chance of winning while their second-best lineup only has a 0.9% shot. But if they only played the 1% lineup, it would take 69 weeks (about four years) before they passed the point where their odds of winning at least one tournament were greater than 50%. By using both the 1% and 0.9% lineups, that falls to 37 weeks. If they added a lineup with a 0.8% chance of winning, that falls to 26 weeks. The lineups might be worse, but the more you enter, the quicker luck tends to strike.

(Of course, larger samples reduce variance in both directions. A DFS player who submits 20 lineups is far less likely to lose their entire bankroll, but they're far less likely to double it, too. And multi-entering big tournaments reduces the time until they finally win one but greatly increases the cost, decreasing the proportionate return on investment.)

Larger Differences on Smaller Samples