Photo: Imagn Images

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.

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.

THE SCORECARD

In Week 2, I laid out our guiding principles for Regression Alert. No specific prediction was made.

In Week 3, I discussed why yards per carry is the least useful statistic and predicted that the rushers with the lowest yard-per-carry average to that point would outrush the rushers with the highest yard-per-carry average going forward.

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 our Yards Per Carry bet, Group A managed to edge back ahead on the back of a 15-carry, 219-yard day by Isaiah Crowell. Absent that performance, Group B would have once again averaged more yards per game and more yards per carry than Group A.

I don't mean to suggest that we just ignore that game, but it does highlight two important principals. First, this is why I like using larger samples. The smaller the group of players being compared, the fewer weeks the comparison spans, the more a single outlier event will dominate the comparison.

Secondly, the fact that it's Isaiah Crowell that's carrying Group A shows why I never cherry-pick who goes into which group. At the time I made the prediction, I figured having Isaiah Crowell in Group A would have lowered Group A's per-game averages, not raised it. Instead, he's outrushed everyone except for Ezekiel Elliott.

There's one more week to go on that prediction, and Group B merely has to out-rush Group A by about 5 yards per game to still pull it out.

Meanwhile, as far as our second prediction goes, touchdowns have indeed been following yards. Both Group A and Group B scored four touchdowns in ten receiver games, (not counting Odell Beckham Jr's passing score for Group B).

One of those ten receiver games for Group B came from Brandin Cooks, though; Cooks left the contest with a concussion before recording a single target. Meaning the "low-touchdown" Group B receivers were once again reached the end zone at a higher rate than the "high-touchdown" Group A receivers. Two weeks left to go.

When Yards per Target is Off Target

Given my disdain for yards per carry, you might assume that I am similarly dismissive of yards per target. You wouldn't be wrong, but that disdain needs to be qualified. Much more than yards per carry, yards per target measures a player's role as much as (or more than) it measures how well that player performs that role.

What do I mean by this? There are currently 44 different wide receivers who average at least 50 yards per game receiving. In total, those 44 receivers average 8.96 yards per target.

John Brown and Sterling Shepard are both on that list of 44 receivers. Brown averages 9.00 yards per target, while Shepard averages 8.69. Given all this information, you might think that Brown and Shepard were both performing at a pretty sustainable level. But they are not. They are two of the top candidates for regression going forward.

If they're going to regress, perhaps you think that Brown's yards per target might decline slightly, while Shepard's would improve. But no, the exact opposite is the case; no receiver who is averaging 50 yards per game or more is underperforming his expected yards per target to a greater degree than John Brown, while Sterling Shepard ranks 12th in terms of yards per target over expectation.

Yards per target, you see, is inextricably linked to yards per reception. Deep threats naturally average more yards per target than possession receivers. In fact, the correlation between yards per reception and yards per target is 0.70, which means yards per reception alone explains about half of the variation in yards per target.

John Brown is averaging more than 20 yards per catch, the second-highest figure in the league. There are three other receivers averaging over 50 yards per game and over 17 yards per reception, and each of those three receivers currently has a yard-per-target average of over 12. For such a prolific deep threat, you'd expect 10.51 yards per target, so Brown is underperforming expectations by 1.51 yards per target.

Shepard, meanwhile, averages 10.86 yards per reception, third-lowest among the 44 qualifying receivers. Since yards per reception serves as an upper limit on yards per target, Shepard's 8.69 per-target average is rather remarkable— naively, we'd expect fewer than 7 yards per target from a receiver with so few yards per catch.

The best-fit formula for expected yards per target is 2.86 + 0.367 * (yards per reception). If we take the 44 receivers who average at least 50 yards per game, run them through that formula, and compare to their actual yards per target, we find that these receivers are collectively overperforming by 1.29 yards per target.

This is partly selection bias— players who overperform are more likely to cross the 50 yards per game threshold than players who underperform. And this is also partly just a reflection of the fact that there really is a player quality component to yards per target, it's just mostly lost amid the noise of variations in role and a few outlier plays. Since we're looking at the most prolific receivers in the league, though, it's no surprise that on net they're above average.

But that 1.29 average overperformance masks a huge diversity. At the bottom of the list, we have John Brown, (underperforming by 1.51 yards). At the top, we have DeSean Jackson, (averaging a ludicrous 20+ yards per target, more than 8 full yards better than our expectation).

There are twelve wide receivers who are currently overperforming expectations by at least 2 yards per target. Those twelve receivers are DeSean Jackson, Brandin Cooks, Michael Thomas, Tyler Lockett, Calvin Ridley, Martavis Bryant, Mike Evans, Jordy Nelson, Cooper Kupp, Dede Westbrook, Tyreek Hill, and Sterling Shepard. This is your Group A.

On the other end, there are twelve receivers who are overperforming by 0.5 yards or fewer. (Remember, this is an elite sample, so "overperforming by 0.5 yards" is actually underperforming relative to their peers.) Those twelve receivers are John Brown, Michael Crabtree, Antonio Brown, Quincy Enunwa, Donte Moncrief, Jarvis Landry, Allen Robinson, T.Y. Hilton, Corey Davis, Demaryius Thomas, Stefon Diggs, and Odell Beckham Jr This is your Group B.

Through five weeks, Group A averages 6.8 targets, 5.2 receptions, and 79.1 receiving yards per game. Group B averages 9.7 targets, 5.4 receptions, and 67.9 yards per game. Despite Group A leading Group B in receiving by 16%, Group B will leverage their massive target advantage to handily outperform Group A in receiving yards per game over the next four weeks.