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. 

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.

The Scorecard

We close out our "yard-to-touchdown ratio" prediction with one of the weirder weeks I can remember. Seven Group B receivers played last week, and only three gained more than 10 receiving yards. Two of them finished the day with negative yards-- DeVonta Smith with -2 and Jameson Williams with -4. As a result, our "high-yardage" receivers saw their yardage advantage almost completely disappear; they averaged 60.6 yards per game since our prediction compared to 60.2 for the "low-yardage" receivers.

Ironically, they were saved by their touchdown production-- 0.5 touchdowns per game vs. 0.43 for our "touchdown-heavy" group. As a result, they managed to flip the script and outscore Group A since our prediction.

Last Week, our "low-ypc" backs finished with a 6.1 ypc while our "high-ypc" backs had just 4.4, and I noted that since ypc was functionally random, that was as likely as not to flip back in Week 7. It did; our "high-ypc" backs averaged 5.5 (driven by an absurd 32 carries for 345 yards from Derrick Henry and Saquon Barkley) vs. 4.0 for our "low-ypc" backs. Order was restored to the universe. 

Of course, our Group B backs got 17.5 carries vs. 13.1 for Group A, so they still rushed for about the same amount (69.3 yards per game vs. 71.4). That was always the prediction; given Group B's workload advantage, Group A would need to maintain an unsustainable ypc to keep pace. Over a single week, they were up to the challenge. Over an entire month? We'll see.

Unlikely Things are the Most Likely Thing

Every year I devote a few of my predictions to some of the most notoriously unreliable statistics in football-- yards per carry, touchdown rate, and the like. I discuss why they're so unreliable, share some research to that effect, and then demonstrate how we can exploit that unreliability to make a profit. 

For my other predictions, I like to leave myself open to the universe. For instance, In 2021, an announcer during a Titans game mentioned Tennessee had scored twice as many rushing touchdowns as passing touchdowns, which sounded interesting. I checked how unusual that was historically and predicted regression. In 2022, I saw a tweet that the season featured the lowest average margin of victory since 1932. I drilled into the data and found that it wasn't being driven by outliers, so it was likely to regress a little, but not much. In 2023, the talk of the season was the decline in passing yards. I predicted that based on typical in-season trends, not only would they stay low, they'd actually get even lower.

Each of these things was unlikely. It was unlikely that the 2021 Titans would become the first team since the 2009 Dolphins to rush for double-digit touchdowns and pass for half as many as they rushed for. It was unlikely that 2023 would see a decade-long positive passing trend halted and reversed. It was staggeringly unlikely that 2022 would feature the closest NFL games since before World War II. If you were placing bets before the season, you likely could have gotten great odds on any of those.

But I know heading into the season that by the time midseason rolls around, something unlikely will be happening, even if I had no idea what it might be. Because "no unlikely outcomes" is far and away the most unlikely outcome of all.

Enter the 2024 Dallas Cowboys.

Dallas has played three road games and three home games so far this season. On the road, they're 3-0, winning by a combined total of 24 points. At home, they're 0-3, losing by a whopping 66 combined points. This is very unusual; teams typically play better at home than on the road.

(If we extend back to the last two games of 2023, Dallas has lost its last four home games by 82 points and won its last four road games by 52 points, a staggering 134-point swing.)

Timo Riske of Pro Football Focus studied extreme home/road splits to see what happened to the team going forward. I didn't need to read the results to have a fairly good guess about what it would show.

Bold prediction: they regressed to historical norms. https://t.co/LLjQkDO9gx

— Adam Harstad (@AdamHarstad) October 17, 2024

Why is it that in 2022 and 2023 I thought the close games and low passing totals were a meaningful trend, but in 2021 and 2024 I thought the Titans' run/pass splits and the Cowboys home/road splits were likely just statistical noise? Let's walk through a few things I look for when evaluating sustainability.

1) Large Sample Size

We covered this ground pretty thoroughly last week. In the case of the rise in close games and decline in passing, we were looking at a sample of over 100 games. For the Titans and the Cowboys, we're looking at a sample of 6 games each.

Weird stuff is much more likely to happen by chance alone over smaller samples.

2) A Non-Arbitrary Sample

This is a big one. In statistics, there's a practice called "data snooping" (or "data dredging"), where you look through a very large dataset for unusual patterns. Individually, those patterns are all unlikely to happen by chance alone, but if you look in enough places, it's a virtual certainty you'll find one somewhere (demonstrated rather famously by XKCD).

The odds of any individual 6-game sample producing a 90-point swing between home and road point differential are minuscule. But there are a lot of 6-game samples in an NFL season. So far this year, there have already been 54; every team that hasn't had a bye yet has two different, overlapping samples (Weeks 1-6 and 2-7), while every team with a bye has had one. What are the odds that one of those 54 would be sufficiently extreme? Better. It just so happened that the extreme split was in Dallas.

And there's no reason to confine ourselves to 6-game samples, either. We're looking at 6 games only because that's the sample that shows a pattern. If the pattern showed up over a 4-game sample or an 8-game sample, we'd be evaluating that instead.

Unless you registered your hypothesis for the specific team and the specific phenomenon and the specific sample size in advance, the odds are great any oddity of this nature you find is just selection bias. (Everything interesting usually is.)

On the other hand, we might not have anticipated the swings in "passing yards per game" and "average margin of victory", but no one can accuse us of manipulating the sample; both observations included every single game of the season to that point. Much mischief can result when we can manipulate the endpoints. It's always safer to make inferences when we can't.

3) Consistent Performance

When I looked at the data on the average margin of victory, the thing that struck me the most was how consistent it was. Four of the first six weeks had a lower margin of victory than any week from the season before. The other two weeks still would have ranked in the bottom third.

When you're underperforming the previous low mark four times in the first six tries, that indicates there's probably something significant at work. The Cowboys, on the other hand, won their last two road games by 3 and 5 points (the latter against the 2-5 New York Giants); hardly consistent with the theory that this is an especially good road team. They lost at home to the Ravens by 3 (albeit with the help of a fortunate onside kick); hardly indicative of a terrible home team.

Dallas' extreme splits are largely the result of a blowout win on the road against the hapless Cleveland Browns and two blowout losses at home to the Saints and Lions. We've not seen the same sort of consistency, which means it's more likely just a weird quirk of chance.

4) A Workable Theory

Ideally, when wondering whether a statistical oddity is "real" or not, we have some sort of explanation on hand for why it's happening. This point is less important than the others; it's very easy to fall into the trap of manufacturing a just-so story to "explain" things after the fact.

For instance, reports are surfacing this week about how the players hate that fans are given tours of the training facility while they're trying to prepare for the game. Maybe Dallas does better on the road because they have fewer interruptions? Or maybe I'm just gathering together whatever unrelated facts I can find and trying to smash them together into a cohesive narrative.

But still, part of the reason I was less skeptical of the passing yardage decline is because we had a good story behind it. The NFL is a cyclical sport where offense and defense take turns gaining the upper hand. Defense had been ascendent, especially behind the rise of the Cover 2 and its ability to limit explosive passing.

Again, I don't want to harp too much on this one because I think it's neither necessary nor sufficient. I didn't have a great story to explain why NFL games were suddenly so much closer in 2022, but I still believed the trend was real. If the data is solid, you don't need to know why it's happening. But all else being equal, having a good explanation can be useful.

Back To The Cowboys

Hopefully, you can see why when I see the Cowboys' bizarre home/road splits, my default assumption is that they're a fluke and likely to regress heavily going forward.

Indeed, Mr. Riske found 53 teams with a 60-point swing between their home and road point differential over any 6-game span. Collectively, those 53 teams averaged a point differential of +21.9 in their remaining home games and -12.6 in their remaining road games-- right in line with established home-field advantage.

So that's going to be our prediction. Remember all those words last week about how we ideally want large samples to maximize our chances of success? We're throwing it all out the window.

I haven't looked at the rest of Dallas' schedule (if they have a lot of tough games scheduled at home, this could perhaps be foolish), but this column is all about putting our money where our mouth is, so I predict that over the remainder of the season, Dallas has a better point differential at home than on the road. It's weird that they've done so much better on the road to this point, but just because it's weird doesn't mean it's meaningful.