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 touchdown rate, and Christian McCaffrey is one of the high outliers in touchdown rate, then Christian McCaffrey 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 my predictions from 2019 and their final results, here's the list from 2018, and here's the list from 2017.
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 talked about how the ability to convert yards into touchdowns was most certainly a skill, but it was a skill that operated within a fairly narrow and clearly-defined range, and any values outside of that range were probably just random noise and therefore due to regress. I predicted that high-yardage, low-touchdown receivers would outscore low-yardage, high-touchdown receivers going forward.
In Week 5, I talked about how historical patterns suggested we had just reached the informational tipping point, the time when performance to this point in the season carried as much predictive power as ADP. In general, I predicted that players whose early performance differed substantially from their ADP would tend to move toward a point between their early performance and their draft position, but no specific prediction was made.
In Week 6, I talked about simple ways to tell whether a statistic was especially likely to regress or not. No specific prediction was made.
In Week 7, I speculated that kickers were people, too, and lamented the fact that I'd never discussed them in this column before. To remedy that, I identified teams that were scoring "too many" field goals relative to touchdowns and "too many" touchdowns relative to field goals and predicted that scoring mix would regress and kickers from the latter teams would outperform kickers from the former going forward.
In Week 8, I noted that more-granular measures of performance tended to be more stable than less-granular measures and predicted that teams with a great point differential would win more games going forward than teams with an identical record, but substantially worse point differential.
In Week 9, I talked about the interesting role regression to the mean plays in dynasty, where the mere fact that a player is likely to regress sends signals that that player is probably quite good and worth rostering long-term, anyway. No specific prediction was made.
In Week 10, I explained why Group B's lead in these predictions tended to get smaller the longer each prediction ran and showed how a small edge over a huge sample could easily be more impressive than a huge edge over a small sample. No specific prediction was made.
In Week 11, I wrote that yards per pass attempt was an example of a statistic that was significantly less prone to regression, and for the first time I bet against it regressing.
In Week 12, I talked about "on pace" stats and how many of the players who wound up setting records were not the players who were "on pace" to do so.
In Week 13, I came up with a list of players who were getting hot just in time for the playoffs... and then explained why they probably weren't getting hot just in time for the playoffs, predicting that they'd cool off back to their normal production level going forward.
In Week 14, I offered the cold comfort that if you lose in the fantasy playoffs, the odds were never in your favor, anyway.
In Week 15, I made our last prediction of the year, once again looking at yard-to-touchdown ratios for touchdown regression. I also noted that if we cut the duration of our prediction in half, we could make up for it by doubling the size of our prediction to offset.
|Statistic for regression||Performance before prediction||Performance since prediction||Weeks remaining|
|Yards per Carry||Group A had 3% more rushing yards per game||Group B has 36% more rushing yards per game||Success!|
|Yard to Touchdown Ratio||Group A averaged 2% more fantasy points per game||Group B averages 40% more fantasy points per game||Success!|
|TD to FG ratio||Group A averaged 20% more points per game||Group B averages 36% more points per game||Success!|
|Wins vs. Points||Both groups had an identical win%||Group B has a 4% higher win%||Failure|
|Yards per Attempt||Group B had 14% more yards per game||Group B has 28% more yards per game||Success!|
|Recent Performances||Players were "hot" for the playoffs||Players regressed 97% back to their previous avg||1|
|Yard to Touchdown Ratio||Group A had 15% more points per game||Group B has 34% more points per game||1|
There's still a week to go, but at this point, we can all-but-officially close out our prediction that "hot" players would cool down. Players in our sample were averaging 15.6 points per game in recent weeks, but 11.1 points per game over the full season. In the three weeks since they averaged 11.6, 10.8, and 11.3 points per game, for a total average of 11.2 points per game. They haven't regressed in the direction of their season average, they've regressed all the way back to their season average. In order for the prediction to fail, these players would need to average 16.6 points per game next week, or a full point better than they were doing even on their hot streak.
Does this mean the last four weeks don't matter? Of course not. Consider Robert Woods. Over the first seven games of the season, he averaged 13.9 points per game. Over the next four, he averaged 20.9. That four-game stretch brought his full-season average up to 16.4 points per game. And in the three weeks since, he's averaged... 16.1 points per game. It's less than his performance over the last four games... but it's more than his performance over the first seven games, too. Instead, it's right at his average over the full season.
So a player's last four games certainly matter when predicting how he'll perform next, they just don't matter more than the player's first four games, or his third, fifth, seventh, and ninth games, or any other four-game sample. (The one exception would be if there was a dramatic change in a player's role; if a starting running back gets hurt, you should look at his backup's performances in games that the starter has missed.) Otherwise, if you have a league host that reports your players' full-season averages as well as their average in recent weeks, you can safely ignore the latter number because the former number already accounts for it.
As for our yard-to-touchdown prediction, everything so far has happened as expected. Group A averaged 54 yards per game at the time of prediction and 46 yards per game last week. Group B averaged 68 yards per game at the time of the prediction and 71 yards per game last week. Both groups' yardage totals remained substantially the same. But the touchdown totals changed dramatically; Group A fell from 0.70 touchdowns per game to 0.33 touchdowns per game, while Group B rose from 0.25 touchdowns to 0.29 touchdowns per game. As a result, Group B outscored Group A fairly handily.
More Things Regress Than You Might Expect
Two years ago, I wrote about the aging of the quarterback position in the NFL. By fantasy-point weighted age (which gives the most weight to the most productive quarterbacks), the position was the oldest it had been since 2008, as far back as I tracked. It broke the previous record which had been set in 2017. The position was old and getting ever older.
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