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.
In Week 16 I charted how incoming talent tended to ebb and flow over time, which led to positions trending older or younger in a process which was itself prone to regression.
|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 108% back to their previous avg||Success!|
|Yard to Touchdown Ratio||Group A had 15% more points per game||Group B has 11% more points per game||Success!|
Today we close the books on our last two predictions of the season. Our "hot" players essentially regressed as predicted; they averaged 11.28 points per game from Weeks 1-12 but 15.89 points per game from Weeks 9-12; over Weeks 13-16 that fell back to 10.89 points per game, right in line with their full-season averages.
Now, some of the players in the sample did not, in fact, appear to regress. T.Y. Hilton averaged 7.98 points over the full season but 10.90 over the preceding four weeks. In his case, it seemed that this hot stretch was a harbinger for things to come as Rivers seemingly rediscovered the receiver and Hilton averaged 17.68 the rest of the way. But this is why we make rigorous predictions; four weeks ago, why would one have preferred T.Y. Hilton to, say, Marques Valdez-Scantling, who averaged 9.10 points over the full season and 12.68 over his last four weeks? Valdez-Scantling averaged 5.03 points per game over the last four weeks, including 0 (or fewer!) yards in three out of the four games.
This is why we use group averages; while individual outcomes are noisy, when you average them out you can clearly see the trend emerge.
Similarly, one could look at Davante Adams scoring three touchdowns last week and ask whatever happened to that touchdown regression he was due for? Adams and Mike Evans were both in the "negative regression" bucket and put up 30+ points in the championship game; they were league-winners. Jeff Wilson and Nelson Agholor were listed as candidates for negative regression and they both scored 20+. Adam Thielen, JuJu Smith-Schuster, and Jimmy Graham scored 15+. Where was the regression we were promised?
But on the other side of the ledger, Stefon Diggs lived up to his expected positive touchdown regression, joining Adams and Evans in scoring 30+ points. And CeeDee Lamb, Brandin Cooks, Myles Gaskin, and Michael Gallup all topped 20 points, with 7 combined touchdowns in Week 16 after combining for just 12 touchdowns in the fifteen weeks prior. Indeed, the headliners in Group A obscure the fact that our "high-touchdown" players scored 12 times in 25 combined games, while our "low-touchdown" cohort scored... 13 times in 18 games. One more touchdown in seven fewer games.
At the time of our prediction, players in Group A were scoring one touchdown for every 77 yards from scrimmage while players in Group B were scoring one for every 277 yards. Since our prediction, Group A scored one touchdown for every 156 yards while Group B scored one for every 146. A "nose for the end zone" isn't really a thing, it's mostly just random noise; over a long timeline, touchdowns tend to follow yards.
Our Final Report Card
To wrap up the season, I wanted to look back not just at this year's predictions, but at every prediction over the last four years. Remember, I'm not picking individual players, I'm just identifying unstable statistics and predicting that the best and the worst players in those statistics will both regress towards the mean, no matter who those best and worst players might be.
Sometimes this feels a bit scary. Predicting that stars like Davante Adams and Tyreek Hill, in the middle of historically great seasons, are going to start falling off is an uncomfortable position. But looking back at our hit rate over time makes it a bit easier to swallow.
- 2017: 6-2
- 2018: 5-1
- 2019: 7-2
- 2020: 6-1
- Overall: 24-6 (80%)
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