Photo: Dale Zanine, USA Today Sports

Join the Footballguys Daily Update

Start your morning with our roundup of the most important stories in football - with the fantasy insight you need to make league-winning decisions. Delivered straight to your inbox, 100% free.

Subscribe Now

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 the metric I'm focusing on is yards per target, and Antonio Brown is one of the high outliers in yards per target, then Antonio Brown goes into Group A and may the fantasy gods show mercy on my predictions. On a case-by-case basis, it's easy to find reasons why any given player is going to buck the trend and sustain production. So I constrain myself and remove my ability to rationalize on a case-by-case basis.

Most importantly, because predictions mean nothing without accountability, I track the results of my predictions over the course of the season and highlight when they prove correct and also when they prove incorrect. Here's a list of all my predictions from last year and how they fared. Here's a similar list from 2017.

The Scorecard

In Week 2, I opened with a primer on what regression to the mean was, how it worked, and how we would use it to our advantage. 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 why touchdowns follow yards, (but yards don't follow back), and predicted that the players with the fewest touchdowns per yard gained would outscore the players with the most touchdowns per yard gained going forward.

In Week 5, I talked about how preseason expectations still held as much predictive power as performance through four weeks. No specific prediction was made.

In Week 6, I talked about why quarterbacks tended to regress less than other positions but nevertheless predicted that Patrick Mahomes II would somehow manage to get even better and score ten touchdowns over the next four weeks.

In Week 7, I talked about why watching the game and forming opinions about players makes it harder to trust the cold hard numbers when the time comes to put our chips on the table. (I did not recommend against watching football; football is wonderful and should be enjoyed to its fullest.)

In Week 8, I discussed how yard-to-touchdown ratios can be applied to tight ends but the players most likely to regress positively were already the top performers at the position. I made a novel prediction to try to overcome this quandary.

In Week 9, I discussed several of the challenges in predicting regression for wide receiver "efficiency" stats such as yards per target. No specific prediction was made.

In Week 10, I proposed a "leaderboard test" to quickly tell whether a statistic was noisy (and more prone to regression) or stable (and less prone to regression). I illustrated this test in action and made another prediction that yards per carry would regress.

In Week 11, I mentioned that many unexpected things were at the mercy of regression to the mean, highlighting how the average age of players at a given position tends to regress over time as incoming talent ebbs and flows.

In Week 12, I predicted that because players regress, and units are made up of players, units should regress, too. I identified the top five offenses, bottom five offenses, top five defenses, and bottom five defenses, and predicted that after four weeks those twenty units would collectively be less "extreme" (defined as closer to league average). Because offense tends to be more stable than defense, I added a bonus prediction that the defenses would regress more than the offenses.

In Week 13, I delved into how interceptions were the only quarterback stat that is mostly noise and predicted that the most interception-prone quarterbacks in the league (yes, including Jameis Winston) would start throwing fewer interceptions than the least interception-prone quarterbacks in the league.

In Week 14, I talked about how big of a role schedule luck plays in fantasy football outcomes and how, as luck in its purest form, it regresses mercilessly.

In Week 15, I presented a brief history of players who had once been considered regression-proof, demonstrated how much they'd regressed, and called into question whether any current players were actually regression-proof as a result.

Today we close out our unit-level prediction and find that, yes, units regress just like individuals do. In the last four weeks, our very worst defenses have gotten 1.2 (schedule-adjusted) points per game better, while our very worst offenses have gotten 1.1 (schedule-adjusted) ppg better. Our very best defenses have gotten 0.8 schedule-adjusted points per game worse, while our best offenses have gotten... actually, they've gotten 0.2 schedule-adjusted points per game better.

The biggest driver behind that offensive improvement was San Francisco's 48 points against the Saints, who had a Top 5 defense at the time. Something, something, small sample sizes. Still, overall our most extreme units became noticeably less extreme, and our defenses regressed more strongly than our offenses.

As for our interception prediction, our low-INT group has thrown 41 picks vs. just 27 for our high-INT group. On a per-game basis, Group B has seen its interception average fall by about a quarter-interception per game (from 1.25 to 1.00), while Group A has seen its interception rate rise by a roughly equivalent amount (0.54 to 0.78).

There's technically still one week to go, but at this point, the prediction is all but settled. For Group A to stage a come-from-behind win, they'd need to average 0.2 interceptions per game over the last week while Group B threw a whopping 2 picks each.

Best of Luck

If there's a common throughline to Regression Alert it's that chance plays a larger role in football than most are comfortable admitting. Call it randomness, call it luck, call it what you will, but it dominates the rate at which running backs break long runs, the rate at which receivers reach the end zone, the rate at which quarterbacks score touchdowns, even the rate at which offenses and defenses score and allow points.

And as big of a factor as chance is in football, it's even more so in fantasy football, where in addition to everything above, factors we have no control over whatsoever (such as which team we face in a given week) are responsible for as much or more of our success as how good our team is.

You're almost certainly familiar with Bill James, the father of sabermetrics in baseball and probably the man who has done more for sports analytics than anyone else in history. Bill James has a formula he calls his "favorite toy", a simple tool to estimate how likely a given player is to reach a given statistical milestone. For instance, Matt Stafford has 41,000 career passing yards and is about to turn 32; given what we know about aging in football, how likely is it that Stafford reaches 60,000 passing yards for his career? As the name "favorite toy" suggests, the formula isn't meant to be very rigorous and scientific. It's mostly just meant as a fun way to get into the right ballpark.

If I had a "favorite toy" like James, it would probably be a tool to quickly estimate a team's championship odds based on its regular-season production. I've already written five articles on the topic, from using a team's share of pooled all-play wins to discussing the capriciousness of playoff matchups to using probability trees based on existing brackets and future projected points to multiplying out theoretical probabilities to just correlating regular-season performance to playoff performance on an individual level.

Every time I address this topic, I try to stress that if you have a good team, your championship odds are probably nowhere near as good as you think they are. And if you have a bad team they're probably nowhere near as bad as you think they are, either. Each of these methods yielded title odds somewhere between 30 and 50%. The best odds I've ever found using any method were 56%, and that was using a truly historic team that had a bye and a soft bracket.

I'm obviously not Bill James; if I was, I probably would have found a satisfactory quick-and-dirty estimate my first time out, but instead, I'm out here continuing to hack away at the problem. For my new approach this year, I've taken the entire thirteen-year history of my oldest dynasty league, ranked all 130 team-seasons by points scored relative to league average through thirteen weeks, and tracked which teams walked away with a title.

Based on this data, for teams that are in the 90th-99th percentile all-time, about 31-38% of them have won a title. (The exact percent depends on the outcome of this week's game.) 23% of teams in the 80th-89th percentile won a title, as did 23% of teams in the 70th-79th percentile. 8% of teams in the 60-69th percentile won, while the 50th-59th percentile has won either 0% or 8% (depending on this weekend's game).

Finally, all teams in the bottom 50% combined have produced a single title, a win rate of just 1.5%. (That title is a story all its own; it went to a team in the 16th percentile that finished 9th out of 10 in points scored but lucked into a playoff berth and then posted the most dominant three-week postseason performance in our league's history.)

Since this is a 10-team league, by chance alone you'd expect a 10% shot at a championship in any given year. The fact that the best teams can push this up to 35% is certainly laudable; they've more than tripled their odds. But on the other hand, it's a bit depressing. The best teams our league has ever seen were roughly twice as likely to lose in the playoffs as they were to win a title.

Indeed, this year was no exception; my friend Tom had the second-best regular-season team in our league's history, only to set a record for most points scored in a playoff loss. It's unfortunate that his diligence won't be rewarded by a title, but it's not especially surprising.

Every time I discuss these realities I have people tell me that it's depressing. Personally, I find it liberating. It's freeing to know that when my best teams lose (as they usually do), it's not because of any personal failing on my part. Any wins should be cherished even more knowing how rare and special they are; any losses should be forgiven knowing how strongly the deck was stacked against me to begin with.

But beyond questions of comfort, the point of this column is to set aside familiar narratives and search for the signal among the noise. To approach football and fantasy without illusions or delusions. And that means seriously grappling with the fact that our successes are far more a result of luck than skill.

And with that thought in mind, to any readers who are still alive for a title, I wish for you a heaping dose of that necessary luck.