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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.
Statistic For Regression
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Performance Before Prediction
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Performance Since Prediction
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Weeks Remaining
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Yards per Carry
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Group A had 20% more rushing yards per game
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Group B has 30% more rushing yards per game
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Success!
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Yard:Touchdown Ratio
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Group A had 23% more points per game
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Group B has 47% more points per game
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Success!
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Mahomes averaged 2.2 touchdowns per game
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Mahomes averages 2.0 touchdowns per game
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Failure
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Yard:Touchdown Ratios
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Group B had 76% more point per game
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Group B has 146% more points per game
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Success!
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Mahomes TDs Redux
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Mahomes averaged 2.2 touchdowns per game |
Mahomes averages 2.3 touchdowns per game
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1
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Yards per Carry Redux
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Group A had 22% more rushing yards per game
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Group B has 44% more rushing yards per game
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2
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At the time of our prediction, Group A tight ends were averaging 24 yards per game and 0.37 touchdowns per game, while Group B tight ends were averaging 70 yards and 0.19 touchdowns per game. In the four weeks since our prediction, both groups have seen their yard-per-game levels remain more or less flat; Group A averages 23 yards per game and Group B averages 66.
But, as predicted, both groups saw their touchdown totals regress strongly toward a level more commensurate with that yardage production. Our "high-touchdown" group saw their touchdown-per-game average fall from 0.37 to 0.25. Our "low-touchdown" group saw their touchdown-per-game average rise from 0.19 to 0.46. Yes, our "low-touchdown" tight ends scored more touchdowns after our prediction than our "high-touchdown" tight ends scored before our prediction. The result was Group B clearing our initial bar (doubling up Group A in fantasy production) with plenty of room to spare.
After two weeks of cruising, Patrick Mahomes II' hot streak hit a bit of a snag this week with only one passing touchdown. I predict that he'll be held out of the end zone entirely this upcoming week (Kansas City has a bye). Mahomes will need to score three touchdowns coming out of the bye if he's going to make good on our early prediction of ten touchdowns in his next four games.
Finally, with a more realistic sample our two running back groups are now a little bit closer, but Group A has still seen its yard per carry average fall from 5.1 to 4.4 while Group B's has risen from 3.6 to 4.2, leaving Group B ahead still on volume.
Units Regress Too
As some of you know, I also write a weekly column for Footballguys analyzing kickers' prospects and recommending players with favorable matchups who might be available on waivers. A large part of the process is just identifying bad defenses because teams (and, by extension, their kickers) tend to score more points against bad defenses than they do against good ones. Yes, shocking, I know.
Overall the process works well, but occasionally you'll get a situation where a defense you thought was awful might not be nearly so bad after all. Through their bye week, the Atlanta Falcons had an atrocious defense that surrendered more than 30 points per game on average. In the two weeks since their bye, however, the same defense has given up only nine total points, catching opportunistic streamers unaware.
Now, there's some interesting discussion to be had about whether we should expect Atlanta's defense to be good or bad going forward based on patterns and trends. With eight games of awful play and two games of great play, I'd tend to still believe a unit is pretty bad overall.
But the more interesting observation (and more relevant to today's column) is that for any given unit performing at an extreme level— whether that's extremely good or extremely bad— a lot of things like had to go right (or wrong) to reach that point. And given that extreme performances are reliant on both the unit being good (or bad) and a lot of things going right (or wrong), they should be pretty strongly susceptible to the forces of regression.
Don't get me wrong; anyone streaming kickers will still want to target awful defenses because it's more likely that awful defenses are actually bad than it is that middling defenses are actually bad. It's just that streamers should temper expectations about how likely those awful defenses are to remain... well, awful.
(This doesn't just apply at the level of an entire unit. Each aspect of that unit regresses, too. Defenses that have been awful against opposing tight ends will likely be less awful going forward. Offenses that have committed an abundance of turnovers will likely show better ball security going forward. And so on.)
This seems to me like exactly the sort of testable hypothesis that would be a perfect fit for Regression Alert, so that's what we're going to do. We're going to predict that the most extreme units in the NFL will all regress towards the mean going forward. But rather than make this a vague prediction, I want to make this a precise and quantifiable prediction so that we can put it on the Scorecard.
To this end, we need to quantify just how "extreme" specific units are. Additionally, I'd like to adjust everything for strength of schedule just to ensure that any regression is genuine and not a result of, say, facing a few strong defenses in a row. To this end, allow me to introduce you to the Simple Rating System.
Simple Rating System (or SRS) measures how many points a team scores above the NFL average. And then it adjusts that total based on the number of points the opposing defenses have allowed relative to NFL average. And then it adjusts that latter total based on the number of points the opposing defenses' opposing offenses have scored relative to NFL average. And so forth.
An example: Let's say that Team A scores 24 points per game and the NFL average is 21 points per game. We could say that the team is three points better than the NFL average. But let's say this team has faced a very easy schedule, playing against defenses that have allowed 25 points per game on average. Suddenly, Team A looks a lot worse; in fact, now they're 1 point per game *below* average. And we can adjust those defenses based on their own strengths of schedule, and repeat the process until eventually all values converge.
If you're still confused... just know that "SRS" means "how many points more (or less) a particular unit is scoring (or allowing) relative to what we'd expect a perfectly average team to score (or allow) against the same schedule".
Like most football statistics, SRS can be found on Pro Football Reference. At the moment, here are the five best offenses in the NFL (along with how many points they're outperforming an average NFL offense by): Baltimore (+11.0), Kansas City (+6.4), Tampa Bay (+5.7), Seattle (+5.2), and San Francisco (+5.1). The five worst offenses are Washington (-9.4), Miami (-7.1), Cincinnati (-6.9), the New York Jets (-6.0), and Chicago (-4.9). On average, those ten units are 6.77 points per game better or worse than a typical NFL team.
On defense, the best units to this point are New England (+9.2), San Francisco (+6.3), Chicago (+4.8), New Orleans (+4.2), and Minnesota (+3.6). The worst units are Miami (-8.6), Tampa (-8.4), the New York Giants (-6.1), the New York Jets (-4.3), and Arizona (-4.2). On average, these ten units are 5.97 points per game better or worse than a typical NFL team. In total, all twenty units combined are an average of 5.37 points per game better or worse than an average NFL offense or defense.
Over the next four weeks, I would expect those twenty units to moderate and see their SRS move toward zero. If I'm right, if I divide their SRS in four weeks by their SRS today, I should get a number less than 100%. (If these units become more extreme, we'll get a number greater than 100%.) So that's the prediction: the collective SRS of these twenty units (as expressed as a percent of their current SRS) will be less than 100%.
And here's one more bonus prediction. It's a well-established finding that defensive performance is less consistent than offensive performance. If that's true, the ten defensive units will see their SRS decline by a greater amount than the ten offensive units.
Here's how we'll measure and track that: I'll take offensive SRS in four weeks (as a percentage of current offensive SRS) and divide it by defensive SRS in four weeks (as a percentage of current defensive SRS). If defensive performance regressed more than offensive performance, this should give us a number greater than 100%. If offensive performance regressed more than defensive performance, we'll get a number less than 100%.
I'm just laying out my methodology in such explicit detail here so that I can track it and hold my prediction accountable. Going forward you don't need to worry about the nuts and bolts, you can just pay attention to the larger question: will the most extreme offenses and defenses regress to the mean going forward? And will the most extreme defenses tend to regress more strongly than the most extreme offenses? Stay tuned in the coming weeks to find out.