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.

Our Year to Date

Sometimes, I use this column to explain the concept of regression to the mean. In Week 2, I discussed what it is and what this column's primary goals would be. In Week 3, I explained how we could use regression to predict changes in future performance-- who would improve, who would decline-- without knowing anything about the players themselves. In Week 7, I explained why large samples are our biggest asset when attempting to benefit from regression. 

In Week 9, I gave a quick trick for evaluating whether unfamiliar statistics are likely stable or unstable. In Week 11, I explained the difference between regression and the gambler's fallacy, or the idea that players are "due" to perform a certain way.

Sometimes, I point out broad trends. In Week 5, I shared twelve years worth of data demonstrating that preseason ADP held as much predictive power as performance to date through the first four weeks of the season.

Other times, I use this column to make specific predictions. In Week 4, I explained that touchdowns tend to follow yards and predicted that the players with the highest yard-to-touchdown ratios would begin outscoring the players with the lowest. In Week 6, I explained that yards per carry was a step away from a random number generator and predicted the players with the lowest averages would outrush those with the highest going forward.

In Week 8, I broke down how teams with unusual home/road splits usually performed going forward and predicted the Cowboys would be better at home than on the road for the rest of the season. In Week 10, I explained why interceptions varied so much from sample to sample and predicted that the teams throwing the fewest interceptions would pass the teams throwing the most.

The Scorecard

The Cowboys have played significantly worse at home than on the road since our prediction-- but they had Dak Prescott for both road games and Cooper Rush for both home games, so it's still too early to tell how meaningful that is. Either way, given the early hole they've dug themselves into, it's looking less likely that their remaining road performances will be bad enough (or their remaining home performances good enough) to pull out a win on this prediction.

I was similarly worried about our interception prediction after a math error made it much harder than intended, but Group B continues to hold off Group A. All of the Group B teams are past their bye, while Group A still has four more to go, so we'll see if they don't catch back up.

Predicting the Past

Understanding regression to the mean is not just useful for predicting the future-- it's also handy for predicting the past. "Predicting the past?" you may scoff, "Surely that's not a thing." Reader, your skepticism wounds me-- predicting the past is called "retrodiction" and is very much a thing.

Why on earth would someone want to predict something that already happened? Because it's one of the easiest ways to check whether one's model is accurate.

For instance, in 1859, astronomer Urbain Le Verrier discovered that Mercury was "orbiting wrong"-- under the standard Newtonian model of gravity, its orbit should be a fixed ellipse, but instead the ellipse was itself slowly rotating around the sun over time.

(Le Verrier wasn't known to be shoddy with his calculations; thirteen years earlier, he had noticed several unexplained deviations in Uranus' orbit and, from those deviations, predicted not only the existence of Neptune-- an as-yet-undiscovered planet-- but also its precise location. This was an example of predicting the present, which unfortunately lacks a catchy name.)

Mercury's odd orbit remained a puzzle for more than 50 years until Albert Einstein began working on his own theory of gravity. One of the first tests of his new system was "predicting" what Mercury's orbit should look like. The fact that his model succeeded where Newton's failed helped convince him of its accuracy.

We may not be an Einstein or Le Verrier, but we also have a model. And we can also harness the power of retrodiction to reassure ourselves of its accuracy.

The Arrow of Time and Regression to the Mean

Most of the time, when we talk about regression to the mean in this space, we're talking about it from the beginning of the process. We take a starting state with large gaps between players or teams and predict an ending state where those gaps are much smaller.

But if regression operates that way (it does), if we're given an end-state with small gaps, we should be able to "predict" a prior starting state where those gaps were much larger (we can).

 One of my great hobby horses in fantasy football is the value of consistency. Or, more accurately, the lack of value. Fantasy GMs often prefer players they perceive as more consistent, saying they'd rather have a guy who scores 10 points every week for four weeks than a guy who scores 5 points in three weeks and 25 in the fourth. Both players totaled 40 points over the span, but the first was more consistent; he didn't leave you hanging in three of those weeks.

But setting aside whether consistency is predictable (it's mostly not), there's the question of whether it matters. How useful are those extra five points in those three weeks, really?

If you look at the current standings in your league, it might seem like those five points are extremely valuable. In one of my leagues, four teams have scored between 141.04 and 144.57, a difference of just 3.5 points. With margins that close, an extra five points here or there should be dispositive, right? 

Our model of regression would suggest otherwise-- an end state with narrow margins would "predict" prior states with larger margins. And indeed, that's exactly what we see; if these four teams all played each other every week, they would have played 66 games so far. Of those 66 games, just four (6.1%) would have been decided by five points or less. Just seven (10.6%) would have been within single digits-- just over half as many as were decided by 50 points or more (13 games, 19.7% of the sample). The average margin of victory would have been 32.1 points.

Am I cherry-picking the most extreme example? Not by a long shot. The closest two teams in any of my leagues currently average 113.102 and 113.100 points per game-- just two-thousandths of a point per game difference through eleven weeks. The average weekly margin between them was also 32.1 points, but that's a much larger relative margin in this league, given the significantly lower weekly scores.

We don't have to confine ourselves to fantasy scores. Alvin Kamara and Bijan Robinson have both played 11 games this season. Kamara has rushed for 782 yards and Robinson has rushed for 783, giving them per-game averages of 71.1 and 71.3 yards per game. If we compare their totals week by week, have they performed similarly? They have not; the average margin is 44.2 yards per game, a whopping 62% of their weekly average!

Retrodiction is great because the possible tests are endless; you are encouraged to pick any other pairs of fantasy teams or pairs of players and repeat the comparison for yourself. This model of regression-- extremely divergent data points over small samples that converge as we accumulate more observations-- predicts the past as accurately as it predicts the future.

Retrodiction can't guide our choices today; the arrow of time runs in one direction, and the window to profit from the past has long since closed. But when determining whether a model is trustworthy, retrodiction is as good as prediction, if not better. ("Better?" you scoff. Yes, in some ways-- there's less opportunity to inject observer bias, for one.)

This is an extraordinarily fortunate check because the future arrives slowly, one week at a time, while the past is available all at once.