We continue our Thanksgiving week of pleasant stories, today with a guest post by Jim Fedako.
“When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’” (Alice in Wonderland)
Ah, the Sports Illustrated (SI) Curse.
Billy Batter has an almost unbroken string of hits late one August. The editors at SI, taking a short break from opining on all things woke, notice his performance and chose him as their next cover story. While stats and story seem to show Billy soaring to epic heights, his hitting slumps, relatively, as soon as the magazine hits the stands.
Fans and commentators alike blame souring slugging on the Curse, the one that seemingly takes down every athlete who graces an SI cover. Some say the Curse is real, others that it has a psychological explanation. The more scientifically-minded observers claim, instead, statistics has the explanation – the regression to the mean. This assumes an existential mean with a gravitational power that pulls deviant series of events back toward that persistent mean.
Select a sample of data. If the sample mean strays far from the actual mean, subsequent samples will likely be be closer to, or less than, the actual mean. So we say the subsequent samples regressed to the mean. This pseudo force is regularly observed in situations where a mean is known or can be closely calculated – series of dice rolls on a craps table, for example. However, means in a sporting context are something completely different.
If asked to defend the regression to the mean explanation of the SI Curse, Humpty Dumpty would likely say, “When I use the word ‘mean,’ it means just what I choose it to mean – neither more nor less.” And that’s a lot of means.
However, what is the mean the regression spies in the distance, pulling athletic performance its way? Is it a never changing, existential attribute of every major league hitter? Sort of like a video game where each player has a halo that blinks their lifetime mean. Or is it a loose concept understood in its looseness – “The mean is simply the expected performance of the hitter based on some recent period of at-bats.” In this, we know what the speaker is saying, or trying to say. But this is far from a rigorous definition of a mean.
Consider an example: Sammy Slugger recently graduated high school with a batting average of .350 during his senior year. He went straight to the minors, struggling his first few months to achieve .245. Was this reduction in hitting prowess a regression to his mean? Or was it the affect of a young professional struggling against other desperate pros? If that is true, and it’s likely, what is his existential mean – the lifetime mean inferred but never defined?
Now, assume Sammy works hard and reaches .290 by the end of the season. Was this a regression back toward his senior year mean, or lifetime mean, or some other mean? What is to be said when his batting average continues improving during his second year in the minors, only to dip after being called up to the majors?
Regressions seem to be going in all directions, searching for a mean that appears to be elusive and ever changing. Means in a sporting context are asserted to be both existential and persistent – an attribute assigned at birth, one that accounts for all at-bats from dust to dust, so to speak. So we would never know a specific player’s mean, nor be able to identify a regression toward it, until a player draws his last breath. Unless, of course, all deviations from recent averages are assumed waiting to be regressed.
But this is neither satisfying nor strict.
The regression to the mean explanation of the Sports illustrated Curse is nothing but a tautology. It is neither real nor distinct. Oh, sure, it’s a concept, but that’s it. Your only challenge is to say, “The mean, and it’s associated regressions, mean what I mean them to mean – neither more nor less.”
Note: None of the above is a refutation of the observed exceptional week followed by a more standard one. It is just calling into question the inexact language used as if it’s a rigorous definition. The use of the regression to the mean in terms of the Curse is analogous to a colloquial use of probability. Both may convey meaning, but both are not technically correct.
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