Statistics Matter September 14, 2023
Regression to the mean
Laws of Randomness
Any variable that cannot be accurately predicted is a random variable.
The performance of an athlete or of a sports team can be a random variable. This is what makes athletics enjoyable to watch because on any given event, you cannot be certain of the outcome.
Part of the reason is that skill and teamwork is not always a constant; and there is consider-able luck (or mishap). The soccer ball slams off the post and hits off the back of your team’s defender to score the game-losing goal. The referee does not see that the player’s foot was out of bounds on the game-winning shot or goal. Sports is filled with random variables.
Regression to the Mean
While any given performance or game of skill can be considerably random due to luck; many games over time is a truer measure of an athlete or team. So if a very talented team that is predicted to win gets “blown out” by a lesser team; the “law of averages” will predict that their next performance will be greatly improved because they will perform closer to their average performance.
Conversely, if they win the event or game they were predicted to lose; or they become world champions in a highly competitive field; the next game or next season they will sta-tistically play closer to their “average” performance—and not win the next game or the next season. They will “regress to the mean.” In sports, “regression to the mean” is not about “bad performance” or “determination and will”; it is simply a mathematically truer perfor-mance over time. (this was part of the story behind the movie “Money Ball” —of using sta-tistics instead of the story that comes from “your gut.”
The Narrative Fallacy
The narrative fallacy is taking bits of data that may be random or even correlated; but con-necting them in a way that is emotively causative. By threading a story through random-ness; it graphs the data and gives it will, meaning, and purpose. The numbers “care”!
Keeping with the sports theme, I will offer two examples of the narrative fallacy and regres-sion to the mean. March Madness: a 12th seeded team wins their first three games making
it to the elite eight. Due to skill and some randomness; they have won their first three games against teams most predicted they would lose to. The country holds their breath that “Cinderella” might make it to the big dance. Their next game they get beat soundly. Statisti-cally, this is nothing more than regression to the mean— they finally played closer to their average level that earned them the 12th seed.
But the narrative is that “this tough underdog team just couldn’t hang in with the big dogs”. “The big arena, the pressure, the lights, the not-so-big program with the not-so-paid-as-much coach just couldn’t handle it when it gets to this level of the competition”….But wait! They handled it last game in the same arena, the same pressure, lights, and coach—and won! This narrative fallacy which is preached every year during March Madness is an emo-tional story of the heart that isn’t much more than a math problem.
Another example is a “World Championship” team that makes it on the cover of Sports Il-lustrated (because they were World Champions) and are then “cursed”. This is not just heart and guts; now the heavens and gods have gotten involved in the game. The narrative goes something like this: “They were too over-confident” “Thought they had it in the bag this year” “They lost their edge.” “Lost focus as a team.” “Trouble in the locker room” “Trouble in the business office.”….But wait! All these accusations were thrown at them last year; and they won! This is the narrative fallacy; the drama instead of the data. Regardless of the tal-ent, coach, “drive and will” of the team; very few teams win back-to-back championships because they “regress to the mean” and play closer to the average of their skill.