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.
|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 an 18% higher win%||1|
I mentioned last week that our Group A kickers would have their work cut out for them if they wanted to catch up to Group B in a single week. They... were not up to the challenge. Not only did Group B score more points per game than Group A, they actually scored 9 more total points than Group A, which might not sound that impressive until you realize that two of the kickers in Group B were on bye. The remaining three Group B kickers totaled 36 points, while all five Group A kickers combined produced just 27.
This kicker performance should demonstrate that "good offense" is absolutely a thing, but it manifests in the ability to repeatedly move the ball into scoring position. Once the ball is in scoring position, whether the team walks away with a touchdown or a field goal is much more driven by luck, especially over small samples. Our Group A kickers averaged 8.21 points per game at the time of the prediction, largely because they were kicking lots of field goals and few extra points. Group B averaged 6.82 points per game because they were kicking lots of extra points but few field goals. But since the prediction, Group A's average fell to 6.67 points per game, while Group B's rose to 9.06.
As for our other active prediction... I took two samples of teams that were both winning 58% of their games. One of them had very high point differentials, and that group has won 63% of their games since. The other group had very low point differentials, and with one week to go that group has won 45% of its games. The more granular measure (point differential) has been predicting record going forward better than the less granular measure (pure wins and losses).
But this actually undersells the difference so far. Because the goal is accountability, I never change my predictions after they've been made (other than purely cosmetic changes such as changing which group I'm calling Group B, say). But I have to admit I screwed up when I made this prediction because I failed to anticipate the impact of games within each group. When Group A teams have played other Group A teams, their winning percentage is obviously 50% (because one team always wins and the other team always loses). The same thing happens when Group B plays itself.
When Group A has played anyone other than another Group A team, their record is 7-9 (44%). When Group B played anyone other than Group B, their record is 11-5 (69%). The spread in winning percentages there is 25%. Counting games within each group has the effect of making the results less extreme, which makes it harder for my prediction because I stipulated that I needed a sufficiently extreme result to declare a win (I said Group B needed to outperform Group A by at least 10%). In the future I'll remember to exclude those games, though in the present we're on pace to win regardless.
Everything Regresses. (Some Things Regress Less.)
One of my biggest goals with this column is to equip you with the tools and understanding to apply the concept of regression to the mean to your own fantasy football leagues, to give you the confidence to know what to look for and what to avoid. To achieve that goal, I give practical examples so you can see these principles in action.
I could simply tell you that yards per carry is a meaningless statistic and why. In fact, I do tell you that. But I figure it gets the point across much better if I also show you. So I predict that the best and worst players in yards per carry will both average a similar ypc going forward, and then you can watch the prediction come true again and again (and again and again and again and again and again-- we're 7-0 lifetime when picking on yards per carry).
I've also explained in the past that some statistics don't regress as much as others, so you shouldn't really base your strategy around that. But it occurs to me I've never given an example of what that looks like in practice. So for the first time in the history of the column, I'm going to bet against regression to the mean.
Many people think that yards per carry for a running back is equivalent to yards per pass for a quarterback, so you'd intuitively think that if one regresses so much, the other must as well. But yards per pass attempt is actually one of the most stable statistics we have. Players who average a high yards per carry in one sample tend to be close to average in another. Players who average a high yards per pass attempt in one sample tend to still be great in another.
To demonstrate this, I'm going to make a yards per attempt prediction that closely mirrors my yards per carry predictions. When I make my yards per carry predictions, I always start by creating a sample of players who have produced a minimum volume. In this case, I'll use the 21 quarterbacks who have passed for at least 2,000 yards so far this season. Then I sort that group from high to low in yards per carry, so I'll sort my quarterbacks by yards per attempt.
Once they're sorted, I try to find the breakpoint that provides the most dramatic volume difference, where the low-average guys are getting the most opportunities relative to the high-average guys. In this case, the bottom 5 passers in yards per attempt are throwing 11% more passes per game than the top 5 passers in yards per attempt, which is the largest such disparity I can find. So that's where I'll draw my line.
The bottom five quarterbacks in yards per attempt (minimum 2000 passing yards) are Carson Wentz, Daniel Jones, Joe Burrow, Ben Roethlisberger, and Tom Brady. This is our Group A. Collectively, they average 37.6 attempts per game for 249 yards, an average of just 6.63 yards per attempt.
The top five quarterbacks in yards per attempt (minimum 2000 passing yards) are Kirk Cousins, Russell Wilson, Deshaun Watson, Patrick Mahomes II, and Aaron Rodgers. This is our Group B. Collectively, they average 33.8 attempts per game for 283 yards, an average of 8.37 yards per attempt.
Despite Group A leading Group B in attempts per game by 11%, thanks to their higher per-attempt average Group B leads Group A in passing yards by 14%. If yards per attempt were like yards per carry, I would gleefully predict that through the magic of regression to the mean, Group A would pass Group B and average more yards per game going forward. But it's not, so instead I predict that despite a much lower passing volume, Group B will continue to dominate in yards per attempt by a big enough margin to maintain their lead in yards per game over the next four weeks.