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 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.

Most importantly, because predictions mean nothing without accountability, I report on all my results in real time and end each season with a summary. Here's a recap from last year detailing every prediction I made in 2022, along with all results from this column's six-year history (my predictions have gone 36-10, a 78% success rate). And here are similar roundups from 2021, 2020, 2019, 2018, and 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 explained that touchdowns follow yards, but yards don't follow touchdowns, and predicted that high-yardage, low-touchdown receivers were going to start scoring a lot more going forward.

In Week 5, we revisited one of my favorite findings. We know that early-season overperformers and early-season underperformers tend to regress, but every year, I test the data and confirm that preseason ADP is still as predictive as early-season results even through four weeks of the season. I sliced the sample in several new ways to see if we could find some split where early-season performance was more predictive than ADP, but I failed in all instances.

In Week 6, I talked about how when we're confronted with an unfamiliar statistic, checking the leaderboard can be a quick and easy way to guess how prone that statistic will be to regression.

In Week 7, I discussed how just because something is an outlier doesn't mean it's destined to regress and predicted that this season's passing yardage per game total would remain significantly below recent levels.

In Week 8, I wrote about why statistics for quarterbacks don't tend to regress as much as statistics for receivers or running backs and why interception rate was the one big exception. I predicted that low-interception teams would start throwing more picks than high-interception teams going forward.

In Week 9, I explained the critical difference between regression to the mean (the tendency for players whose performance had deviated from their underlying average to return to that average) and the gambler's fallacy (the belief that players who deviate in one direction are "due" to deviate in the opposite direction to offset).

In Week 10, I discussed not only finding stats that were likely to regress to their "true mean", but also how we could estimate what that true mean might be.

In Week 11, I explained why larger samples work to regression's benefit and made another yards per carry prediction.

It's Not Better To Be Lucky Or Good. It's Better To Be Both.

The league leader in any statistic is going to regress. This is true even when the league leader is Tyreek Hill, Patrick Mahomes II, or Christian McCaffrey. The best players are more likely to lead the league in one category or another, but even when the best players are leading the league, they're still going to regress because you can't lead the league unless you're both lucky and good.

Why is this? Let's illustrate using a simple model. Let's say we have 26 running backs who we will name A through Z. We'll stipulate that RB A is the best touchdown scorer in the league, with a "true mean" of 15 touchdowns per season. RB B is the second-best scorer, with a mean of 14.5 touchdowns. RB C is the third best with a mean of 14, and so on down to RB Z, who is the worst touchdown scorer, with a true mean of just 2.5 touchdowns per year.

As we've seen so far this year, actual performance fluctuates around a player's true mean, so let's assume that year-to-year touchdown production is normally distributed centered on a player's mean with a standard deviation of four touchdowns. (This means that performances further from a player's true mean are significantly rarer than performances closer to the true mean.)

I quickly simulated 20 seasons with those parameters, and in those 20 "seasons", the best running back only led the league in touchdowns twice. The second-best back led once, the third-best back led four times, the fourth-best back led once, the fifth-best back led five times, the sixth-best back led twice, the seventh-best back led once, and the eighth-best back led twice.

(If you're counting at home, you might notice that only adds up to 18 seasons. The 12th-best running back scored 18.3 touchdowns once to lead the league, and the 16th-best running back-- a below-average player with a "true mean" of just 7.5 touchdowns-- got an all-time lucky roll to score 20.3 touchdowns. If this sounds implausible, recall that Jamaal Williams led the NFL in rushing touchdowns in 2022 with 17; over the rest of his career, he's only rushed for 13.)

The average league leader scored 19.1 touchdowns, and the "worst" league leader scored 16.6 times. Recall that the best player in the league had a "true mean" of just 15 touchdowns, and now you see why the league leader is almost certainly both lucky and good; if there are ten great players, it's a virtual certainty that at least one or two of them will have a lucky season, so for the best player to remain ahead, he'll need some luck of his own, too.

And not just "some" luck, either. On average, the league-leading player outperformed his true mean by 6.4 touchdowns, which means they landed around the 95th percentile of their personal range of outcomes, a level players should only be expected to reach in around one out of every 20 seasons.

This doesn't mean being good isn't important, though; across all 20 seasons, the top RB averaged 13.8 touchdowns per year, which is a hair below the expected 15, indicating it was a slightly unlucky streak overall. That's still good for the 3rd-best average in the sample. The third-best RB led all players with 15.6 (hence those four league-leading seasons vs. just two for the top RB), while the second-best RB had 14.5, right on the expected average.

Good players with high true means are valuable in fantasy, not because they tend to be the best performers over any given stretch, but because they're more productive at any given level of "luck". Their unlucky seasons are better than anyone else's unlucky seasons, and their lucky seasons are better than anyone else's lucky seasons. They need less luck to lead the league than anyone else. (In our 20 simulated seasons, only one player led the league without surpassing the 60th percentile of their range of possible outcomes; naturally, this was RB A, the best player in the group.)

Now, this is just a toy model; reality is infinitely more complex than this. Distributions are not quite normal; standard deviations can vary from player to player. But the principles are sound, and they apply to much more than the NFL's statistical leaders: wealth, GPA, career success, test scores, parenting, you name it. In any competitive field in which there is a talent component and a luck component, the top showings in that field will invariably belong to participants who were both lucky and good.

Another place where this is true? Your fantasy football leagues. There's a measure of team quality called All-Play Win Percentage (or AP%) that measures what your record would be if you played every other team in the league every week (so that the team with the highest score would go 11-0 against the other teams, while the team with the second-highest score goes 10-1, and so on down the line).

Any deviation between AP% and actual winning percentage is luck; it's a quirk of the specific schedule a team actually faced relative to the countless schedules it could have faced. Over a long timeline, actual win% trends towards all-play win%.

Over a short timeline, though? If you check the team with the best winning percentage in all of your leagues, I suspect you'll find that it is almost always among the top teams in the league (as measured by AP%)... and also that it has almost always gotten a lucky schedule (meaning its actual win% is higher than its all-play win%).

The bigger the pool of competitors, the more likely this is the case. (There's a better chance the leader has been lucky in a 16-team league than in an 8-team league.) Also, the larger the sample, the less likely this is the case (because luck tends to even out over time-- the ranking of our 26 simulated running backs was much closer to their true average across all 20 seasons combined than it was in any individual season).

(As an aside, this is why double-headers are a useful mechanism for ensuring the best teams make the playoffs. They essentially double the sample size of games played during the season and, as a result, reduce the role of luck.)

If this sounds an awful lot like what I've been saying all year-- outliers regress, bigger outliers regress more, larger samples are useful to ensure that regression-- well, that's because it is. But it's useful to know the mechanism behind these observations, especially when we find ourselves betting against a star player who looks unstoppable on the field. The fact that he looks unstoppable means he's probably really good. But it also means things have probably been going his way, too. And that's unlikely to continue.