Regression Alert: Week 3

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 Justin Jefferson is one of the top performers in my sample, then Justin Jefferson goes into Group A, and may the fantasy gods show 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 seven-year history, giving our top-line record (41-13, a 76% hit rate) and lessons learned along the way.

How to Predict Regression for Fun and Profit

Last week, we discussed what exactly regression to the mean was-- a mathematical tendency when sampling randomly from a dataset for extreme observations to be followed by less extreme observations. We also laid out the four goals of this column: 

1. to persuade you that regression is real and reliable,
2. to provide actionable examples to leverage in your fantasy league,
3. to educate you on how and why regression is working, and 
4. to equip you with the tools to find usable examples on your own.

This week, we're going to get started on goal #3. I'm a magician with one trick, but unlike any other magician you've met, I'm going to tell you how it works in advance.

We'll begin with a bad example of using regression to make decisions. Let's say that the average fantasy receiver scores 8 points per game. Let's also say that we have ten receivers who have averaged 18, 16, 14, 12, 10, 8, 6, 4, 2, and 0 points to this point.

Assume we know nothing about these receivers, not even their names. (This is the format our typical prediction will take-- when we choose a statistic that's ripe for regression, we'll simply be putting the top performers in one group and the bottom performers in another with no regard to any thoughts about their talent, their situation, their past history of production, or any other relevant factors.)

We would expect these scores to regress in the direction of the mean-- remember, regression is the statistical tendency for more extreme values to be followed by less extreme values. But we shouldn't expect all of these receivers to just average 8 points per game going forward; good receivers are more likely to outperform league average than bad receivers, so the top five receivers on that list are probably better on average than the bottom five.

Let's say we split the difference and expect receivers to score halfway between their production to date and league average. That would produce the following list:

Now, one could say something like, "Receiver #1 is destined to regress! He's averaging 18 points per game to this point, but we only expect him to average 13 points per game going forward! You should sell him now!"

The first two statements are undoubtedly true, but the third doesn't follow. We are merely invoking regression as a talisman rather than a lens for further analysis. Who would we sell him for? We could trade for Receiver #2, but Receiver #2 is likewise destined to regress. As is Receiver #3. As is Receiver #4. As is Receiver #5.

Every player on that list regressed, but the order and the relative size of the gaps remained the same. The best receiver remained the best receiver, and he continued to outscore #3 by exactly as much as #3 outscored #5. Regression will happen, but this exercise doesn't suggest any particular course of action we should take as a result.

For regression to be useful, we need to find examples we can act on. What this means is instead of focusing on the statistic we care about (such as fantasy points per game), we need to focus on statistics that contribute to the one we care about.