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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 I'm looking at receivers and Cooper Kupp is one of the top performers in my sample, then Cooper Kupp 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. At the end of last season, I provided a recap of the first half-decade of Regression Alert's predictions. The executive summary is we have a 32-7 lifetime record, which is an 82% success rate.
If you want even more details, here's a list of my predictions from 2020 and their final results. Here's the same list from 2019 and their final results, here's the list from 2018, and here's the list from 2017.
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 discussed the tendency for touchdowns to follow yards and predicted that players scoring a disproportionately high or low amount relative to their yardage total would see significant regression going forward.
In Week 5, I revisited an old finding that preseason ADP tells us as much about rest-of-year outcomes as fantasy production to date does, even a quarter of the way through a new season. No specific prediction was made.
In Week 6, I explained the concept of "face validity" and taught the "leaderboard test", my favorite quick-and-dirty way to tell how much a statistic is likely to regress. No specific prediction was made.
In Week 7, I talked about trends in average margin of victory and tried my hand at applying the concepts of regression to a statistic I'd never considered before, predicting that teams would win games by an average of between 9.0 and 10.5 points per game.
In Week 8, I lamented that interceptions weren't a bigger deal in fantasy football given that they're a tremendously good regression target, and then I predicted interceptions would regress.
In Week 9, I explained why the single greatest weapon for regression to the mean is large sample sizes. For individual players, individual games, or individual weeks, regression might only be a 55/45 bet, but if you aggregate enough of those bets, it becomes a statistical certainty. No specific prediction was made.
|STATISTIC FOR REGRESSION
|PERFORMANCE BEFORE PREDICTION
|PERFORMANCE SINCE PREDICTION
|Yards per Carry
|Group A had 24% more rushing yards per game
|Group B has 25% more rushing yards per game
|Yards per Touchdown
|Group A scored 3% more fantasy points per game
|Group A has 12% more fantasy points per game
|Margin of Victory
|Average margins were 9.0 points per game
|Average margins are 10.5 points per game
|Group A had 65% more interceptions
|Group B has 56% more interceptions
After a worrying couple of weeks, our "average margin" prediction is very well-positioned to win. How well-positioned? The original prediction was "average margin of victory over the next four weeks would be between 9 and 10.5 points". Thanks to an exceptionally close week (winners won by just 8.5 points per game, on average), the margin is right on 10.5 points, which means if it comes in under that mark we'll win, and if it comes in over we'll lose. Things are still very much up in the air, but for a prediction that was a little outside our usual comfort zone, results are encouraging.
To this point in the season, defenses are averaging 0.75 interceptions per game. When we made our prediction, the "high-interception" sample was averaging 1.28, the "medium-interception" sample was averaging 0.88, and the "low-interception" sample was averaging 0.38. Since interceptions are dominated by luck, we expected all of those numbers to strongly regress toward the league average, and indeed, in the three weeks since the "high-interception" sample averages 0.82, the "medium-interception" sample averages 0.68, and the "low-interception" sample averages 0.70.
The "high-interception" group maintains a very slight edge, but given that all three groups are averaging totals that are difficult to distinguish from league average, our "low-interception" group's total volume advantage remains substantial.
Luck Be a Lady...
I often like to stress that outcomes are the result of a combination of intrinsic factors and random chance. If a running back has a huge rushing day, there are plenty of contributors, including how fast that running back is, how good he is at breaking tackles, how well he read his blocking, how good the defense he faced was, how well his teammates were playing, whether the other running backs on the roster were healthy or hurt, what situations he was given his opportunities in (you can't run for 80 yards when you're getting a carry at the 50-yard line, after all), and numerous other factors.
Some of those factors are pretty stable, usually because they're intrinsic to the player himself. Guys who are good at breaking tackles in one game tend to be good at breaking tackles in the next game, too. Other factors are essentially just random chance. Players very rarely face the same defense in consecutive weeks, for instance.
The more an outcome is driven by intrinsic factors, the less it will regress between samples. The best example of this would be something that is 100% intrinsic, like height. If you take the five tallest players and the five shortest players in one sample, they're going to remain the five tallest and five shortest players in the next sample. They're not going to "regress" until they're all league-average height or anything. The gap between the best and the worst remains static from one sample to the next. Height is entirely intrinsic.
On the other hand, the more a factor is driven by luck, the more it will regress between samples. The best example would be something that is 100% luck-based, like correctly calling the pre-game coin flip. If one team has won eight consecutive coin flips and another team has lost eight consecutive coin flips, they'd still have the exact same expectation for how many of the next eight coin flips were likely to go in their favor. The gap between the "best" and the "worst" disappears between samples. Coin flips are entirely chance.
There's not really anything interesting in football that isn't a blend of intrinsic factors and random chance, though. As a result, from one sample to the next the gap doesn't stay the same, but it doesn't disappear entirely, either. Instead it usually just shrinks a bit. (How much depends entirely on the ratio of intrinsic factors to random chance.)
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