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 Ja'Marr Chase is one of the top performers in my sample, then Ja'Marr Chase 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 eight-year history, giving our top-line record (46-15, a 75% hit rate) and lessons learned along the way.
Our First Prediction of the Year
Last week, I laid out the three key insights when predicting regression.
Principle #1: Everything regresses to the mean.
Principle #2: Not everything regresses at the same rate.
Principle #3: Not everything has the same mean.
I also provided a hypothetical example of how to leverage these insights, breaking receiver production into its component parts and noticing how certain components would regress more or less strongly than others, changing the overall level of production at different rates.
That's all well and good with hypothetical receivers; does it work with real ones, too? Why yes, it does.
This column's origins date back to 2015, when I wrote about how, for receivers, touchdowns tend to follow yards but yards don't tend to follow touchdowns, then provided a list of the receivers who were averaging the most and fewest yards for every touchdown scored.
Within just two weeks, that list had completely flipped on its head. The "high-touchdown" receivers suddenly couldn't reach the end zone, and the "low-touchdown" receivers couldn't stop scoring. I've revisited this prediction thirteen more times for Regression Alert, and for twelve of those predictions, the "low-touchdown" group immediately rallied and outscored the "high-touchdown" group over the next month.
On average, the high-touchdown receivers (our "Group A") were outscoring the low-touchdown receivers (our "Group B") by 15.5% at the time of the prediction. On average, Group B outscored Group A by 19.9% over the next month-- a 35.4% total swing.
Stochastic
Why do the low-touchdown receivers do so well here? Let's start with some new vocabulary.
sto·chas·tic
adjective
randomly determined; having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.
Touchdowns are stochastic. Over his career, Cam Newton rushed for 77 touchdowns in 155 games, an average of 0.5 touchdowns per game. We could say that's his "true production level", and over a sufficiently long timeline, we'd probably expect him to conform to that, averaging 0.5 touchdowns per game.
Despite that being his true production level, though, guess how many times Cam Newton rushed for half a touchdown in a game? As far as I can tell (and I have researched this topic extensively), it has never happened. Instead, he either scored zero touchdowns... or he scored one touchdown. (Sometimes, he scored two touchdowns, and once, he even rushed for three touchdowns.) Because they are binary outcomes, we can analyze Cam Newton's rushing touchdowns statistically, but we cannot predict them precisely.
Yards don't behave quite the same way. Over his career, Cam Newton averaged 38.6 rushing yards per game. But it's not like every week he's either getting you 0 yards or else he's getting you 75 yards. Instead, more games than not, he's getting you somewhere between 20 and 60 yards. His yardage total is much more consistent from game to game than his touchdown total.
Using Standard Deviations
One way to measure consistency is something called standard deviation, which measures how much something varies around the average. The standard deviation of Newton's rushing yardage is 24.5 yards. The standard deviation of Newton's rushing touchdowns is 0.65 touchdowns.
Now, these numbers are not directly comparable. Standard deviations for large values are naturally bigger than standard deviations for small values. (Consider: if you switched to "feet rushing per game" rather than "yards rushing per game", the standard deviation would triple despite the underlying game-to-game variation remaining unchanged. The standard deviation of "inches rushing per game" would be twelve times higher, still!)
But if you divide a player's standard deviation by that player's average, you get something called the coefficient of variation, or CV. CV is a way to compare how volatile different statistics are. The CV of Newton's yards is 64%, meaning it tends to vary by about 64% of his overall average. The CV of Newton's touchdowns is 130%. Touchdowns are much more random from week to week than yards are— in Newton's case, about twice as random, according to CV. (For those curious, the CV of Newton's rush attempts was 42%; "usage" stats like attempts tend to be more stable from week to week even than yards.)
Not only are they more unstable, but touchdowns are also much more valuable than yards. In most scoring systems, one extra touchdown is worth the equivalent of 60 extra yards. If Newton rushed for "too many" touchdowns early in the year, it could dramatically inflate his fantasy production to date. If he rushed for "too few", it could leave him far lower than we'd otherwise expect.