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.

In Week 12, I used a simple model to demonstrate why outlier performances typically require a player to be both lucky and good.

In Week 13, I talked about how a player's mean wasn't a fixed target and predicted that rookie performance would improve later in the season.

In Week 14, I mentioned that hot and cold streaks are mostly a mirage and that all players tend to regress strongly toward their full-season averages.

I wrote last week about how both Group A and Group B had an identical yards per carry advantage since our prediction. Well... so much for that-- Group A averaged 5.57 yards per carry in Week 14 while Group B averaged 3.17, the highest and lowest averages we've seen in any week in either of our two failed yards per carry predictions, ending any hope of a last-minute comeback.

Group A's yards per carry did regress overall, falling from 5.05 to 4.40, which is around league average. But Group B's ypc remained low, and its workload cratered. While our first ypc prediction saw the groups regress (but not enough to cover the initial aggressive prediction), this time Group A saw its lead widen from where it was at when the prediction was made. Just a cursed year overall for yards per carry.

Our rookie prediction is faring better so far. The points per game hasn't moved, but that's an artifact of the Tank Dell injury-- excluding his performance prior to the prediction and his zero in Week 13, rookie scoring is up 10%. More importantly, 62% of rookies have seen their scoring rise. It should continue to rise higher still over the next two weeks.

Some of our best predictions have come up short this year, but our "hot players regress" prediction doesn't look like it'll join them. In the first week of action, we saw the hottest players in fantasy football regress nearly 100% of the way back to their full-season average.

Your Best Team Is Probably Going To Lose

My s*** doesn't work in the playoffs. My job is to get us to the playoffs. What happens after that is f****** luck.
-Billy Beane

We spend all year working to get our teams into the playoffs. We seek out every edge we can exploit. We learn about regression to the mean, and we harness the forces of randomness to carry us onward.

But randomness does not hold a harness well. It is wild, and it is chaotic. And so, despite our efforts, our most likely reward for reaching the postseason is a season-ending loss.

It's important to realize that this is not a failure on our part. It's tempting to think that we can control the chaos; we can find the exact right sleeper against the exact right matchup and push ourselves over the finish line. Or maybe we're focused on the order and not the chaos. Maybe most teams are more likely than not to lose, but certainly not our best ones. Certainly, our 12-2 team, armed with a bye and outscoring all competition by 10 points per game, has at least a better-than-a-coinflip shot at the title.

That's simply not the case. Sure, someone is going to end the season holding a trophy. But for any given team, it's more likely than not that someone isn't you.

I wrote a column a couple of years ago about how understanding regression allowed us to reverse-engineer the present to make predictions about the past. I showed that if you took two teams that had very similar per-game averages and looked back over the weeks, you'd find that they virtually never had similar weekly scores.

I looked at one team that had scored 1258.81 points and another team that had scored 1251.86 points. The average point-per-game difference between them at the time was 0.6, but the average margin between them in any given week was 36.37 points. (The median was 34.23, and the teams featured more weeks with a gap larger than 50 points-- four times-- than a gap closer than 15 points-- just twice.)

This is a sobering reminder that if your team is averaging, say, 10 points per game more than your playoff opponent, that 10-point lead might just mean you would have beaten them in eight out of the fourteen previous weeks instead of just seven. Even a 20-point margin is easily surmountable.

Over the years, I've come up with a lot of different methodologies for estimating the chances a team would win a championship, and all of those approaches led me to the same place: the best team in the league typically has around a 1-in-3 chance of winning it all. If it's extraordinarily strong, the type of team that comes along once every five years, that chance might rise as high as 2-in-5. But that's about as high as it goes.

A 33% shot at a title suggests you have just a 57% chance to win each of your two playoff games (assuming you're armed with a bye and also assuming your odds are the same for both games -- which they aren't). A 40% chance implies a 63% chance to win each individual game.

Most people balk at the idea that the better team wins just 55-60% of the time in the playoffs, but there's actually a clever way to exploit the structure of the playoffs to verify that this is true. In leagues that grant a bye to the top two teams, the semifinals will always feature two teams with a bye playing two teams without a bye. If we assume the teams with the bye are better than the teams without the bye, then we can say how often a team with the bye should win the title based on how likely it is that the better team wins.

If the better team is 50/50 to win, then teams with byes should win 50% of the championships. If the better team wins 55% of the time, we should expect to see 58% of championships go to teams with a bye. If the better team wins 60% of the time, that should be 65%. If the better team wins 70% of the time, teams with byes should win 78% of all titles, and if the better team wins 80% of the time, teams with a bye should win 90% of the titles.

I checked the history of my two oldest leagues, and teams with a bye have won 16 out of 26 championships, which suggests a 57% per-game win rate for higher-seeded teams against lower-seeded teams. 26 leagues is not a lot to go on, but I found a dataset from the 2021 season of around 1,000 leagues with similar scoring and lineup requirements. In those leagues, teams with a bye won 58% of the championships-- 31.9% for the #1 seed, 26.4% for the #2 seed. (Neither of those values is as high as the 33% estimate I led off with at the top, but remember that sometimes the best team is not the #1 seed.)

That observed result implies just a 57.8% chance for a higher-seeded team to beat a lower-seeded team in the playoffs. This is why I regret to inform you that you will probably lose in the coming weeks.

But that's actually kind of the beauty of fantasy football. If it were a perfectly deterministic game where all the outcomes were known in advance, none of us would be nearly as invested in it. It's precisely because everything hangs on a razor's edge that we get so worked up.

I genuinely think not enough people in the Fantasy Football community understand this, but: The randomness is a feature of the game, not a bug, and many fewer people would be interested in playing if the best player won every league more often. https://t.co/YIAH9xhYrr

— Chris Towers is going to make it through this year (@CTowersCBS) December 11, 2023

Part of the beauty of Fantasy Football is that someone who does this as their job only has a slightly better chance to win a league every season than the person who spends a few hours listening to podcasts or reading a Start/Sit column. That's a feature of the game, not a bug.

— Chris Towers is going to make it through this year (@CTowersCBS) December 11, 2023

If you've reached the playoffs, I genuinely hope you do the unlikely and win it all. (Also, let's be real here: a 1-in-3 shot isn't all that unlikely.) If you do, I hope knowing your victory was unlikely makes it that much sweeter.

But if you come up short, try not to beat yourself up. Recognize that it's the nature of the game, that this randomness and unpredictability is what makes it so dang fun. And most importantly, remember that there will always be next year.

(Though you probably won't win then, either.)