I still follow my favourite pro football team, the Minnesota Vikings, and last year they hired a new General Manager who was unlike the previous GM in that not only was he a big believer in analytics, he actually had worked in the analytics area for years before moving into an executive position. The first NFL draft under the new GM and head coach was much more in line with what the public analytics fans wanted — although the result on the field is still undetermined as only one player in that draft class got significant playing time. Freddie deBoer is a fan of analytics, but he wants to help people understand what the frequently misunderstood term “regression to the mean” actually … means:

Kwesi Adofo-Mensah, General Manager of the Minnesota Vikings. Adofo-Mensah was hired in 2022 to replace Rick Spielman.
Photo from the team website – https://www.vikings.com/team/front-office-roster/kwesi-adofo-mensah

The sports analytics movement has proven time and again to help teams win games, across sports and leagues, and so unsurprisingly essentially every team in every major sport employs an analytics department. I in fact find it very annoying that there are still statheads that act like they’re David and not Goliath for this reason. I also think that the impact of analytics on baseball has been a disaster from an entertainment standpoint. There’s a whole lot one could say about the general topic. (I frequently think about the fact that Moneyball helped advance the course of analytics, and analytics is fundamentally correct in its claims, and yet the fundamental narrative of the book was wrong.*) But while the predictive claims of analytics continue to evolve, they’ve been wildly successful.

I want to address one particular bugaboo I have with the way analytical concepts are discussed. It was inevitable that popularizing these concepts was going to lead to some distortion. One topic that I see misused all the time is regression/reversion to the mean, or the tendency of outlier performances to be followed up by performances that are closer to the average (mean) performance for that player or league. (I may use reversion and regression interchangeably here, mostly because I’m too forgetful to keep one in my head at a time.) A guy plays pro baseball for five years, he hits around 10 or 12 homeruns a year, then he has a year where he hits 30, then he goes back to hitting in the low 10s again in following seasons – that’s an example of regression to the mean. After deviation from trends we tend (tend) to see returns to trend. Similarly, if the NFL has a league average of about 4.3 yards per carry for a decade, and then the next year the league average is 4.8 without a rule change or other obvious candidate for differences in underlying conditions, that’s a good candidate for regression to the mean the next year, trending back towards that lower average. It certainly doesn’t have to happen, but it’s likely to happen for reasons we’ll talk about.

Intuitively, the actual tendency isn’t hard to understand. But I find that people talk about it in a way that suggests a misunderstanding of why regression to the mean happens, and I want to work through that here.

So. We have a system, like “major league baseball” or “K-12 public education in Baltimore” or “the world”. Within those systems we have quantitative phenomena (like on-base percentage, test scores, or the price of oil) that are explainable by multiple variables, AKA the conditions in which the observed phenomena occur. Over time, we observe trends in those phenomena, which can be in the system as a whole (leaguewide batting average), in subgroups (team batting average), or individuals (a player’s batting average). Those trends are the result of underlying variables/conditions, which include internal factors like an athlete’s level of ability, as well as elements of chance and unaccounted-for variability. (We could go into a big thing about what “chance” really refers to in a complex system, but … let’s not.) The more time goes on, and the more data is collected, the more confidently we can say that a trend is an accurate representation of some underlying reality, again like an athlete’s level of ability. When we say a baseball player is a good hitter, it’s because we’ve observed over time that he has produced good statistics in hitting, and we feel confident that this consistency is the product of his skill and attributes rather than exogenous factors.

However, we know that good hitters have bad games, just as bad hitters have good games. We know that good hitters have slumps where they have bad three or five or ten etc game stretches. We even acknowledge that someone can be a good hitter and have a bad season, or at least a season that’s below their usual standards. However, if a hitter has two or three bad seasons, we’re likely to stop seeing poor performance as an outlier and change our overall perception of the player. The outlier becomes the trend. There is no certain or objective place where that transition happens.

Here’s the really essential point I want to make: outliers tend to revert to the mean because the initial outlier performance was statistically unlikely; a repeat of that outlier performance is statistically unlikely for the same reasons, but not because of the previous outlier. For ease of understanding let’s pretend underlying conditions stay exactly the same, which of course will never happen in a real-world scenario. If that’s true, then the chance of having an equally unlikely outcome is exactly as likely as the first time; repetition of outliers is not made any less likely by the fact that the initial outlier happened. That is, there’s no inherent reason why a repetition of the outlier becomes more unlikely, given consistent underlying conditions. I think it’s really important to avoid the Gambler’s Fallacy here, thinking that a roulette wheel is somehow more likely to come up red because it’s come up black a hundred times in a row. Statistically unlikely outcomes in the past don’t make statistically unlikely outcomes any less likely in the future. The universe doesn’t “remember” that there’s been an outlier before. Reversion to the mean is not a force in the universe. It’s not a matter of results being bent back into the previous trend by the gods. Rather, if underlying conditions are similar (if a player is about as good as he was the previous year and the role of variability and chance remains the same), and he had an unlikely level of success/failure the prior year, he’s unlikely to repeat that performance because reaching that level of performance was unlikely in the first place.

* – the A’s not only were not a uniquely bad franchise, they had won the most games of any team in major league baseball in the ten years prior to the Moneyball season
– major league baseball had entered an era of unusual parity at that time, belying Michael Lewis’s implication that it was a game of haves and have-nots
– readers come away from the book convinced that the A’s won so many games because of Scott Hatteberg and Chad Bradford, the players that epitomize the Moneyball ethos, but the numbers tell us they were so successful because of a remarkably effective rotation in Tim Hudson, Barry Zito, and Mark Mulder, and the offensive skill of shortstop Miguel Tejada – all of whom were very highly regarded players according to the old-school scouting approach that the book has such disdain for.
– Art Howe was not an obstructionist asshole.