H056
If no player’s skill ever changes, why does their “best season ever” almost never happen twice?
Athletes who land on a magazine cover after a career-best season often follow it with a quieter one — a predictable pattern, not a jinx.
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There's no jinx anywhere in this code — just a fixed skill number and a fresh random draw each season. The top performers are still above the league average next season; they just aren't as spectacular as their record season made them look.
The same thing happens anywhere you select for an extreme result — a hot sales quarter, a breakout test score, a viral post. Expect the next measurement to look more ordinary. That's a statistical pattern, not a jinx, a slump, or a sign that something changed.
Try it somewhere else
A city put speed cameras at the intersections that had the most crashes last year, and crashes there dropped.
How much of that drop might have happened with no cameras at all?
Why does the top group specifically fall back?
Every simulated player has one fixed true skill level for their entire career. Each season's score is just that fixed skill plus random noise — good luck or bad luck, drawn fresh every time. Nothing decays, nothing is cursed, and nothing "knows" it was on a cover. Pick the top 5% of one season's scores and you've mostly picked the players who got lucky that year, not just the most skilled ones. Next season, that luck resets, so their scores fall back toward their true skill, which was always a bit closer to average than their peak season made it look.
It is the same selection effect as our Survivorship Bias exhibit, pointed the other way: that one hides the cases filtered out entirely, while this one over-weights whichever case happened to land on the extreme end of ordinary luck. Both make a data set look like it is telling a different story than the noise it is actually built from.
A real-world case: a river divided during a wet streak
In 1922, seven states divided the Colorado River using the flows measured from 1905 to 1922: about 16.4 million acre-feet a year. (One acre-foot covers a football field 1 ft (0.3 m) deep, about 326,000 gallons.) Counting Mexico's later share, 16.5 million acre-feet a year was promised. Every measurement was accurate. But tree-ring studies later showed that 1905–1922 was one of the wettest stretches in centuries: the baseline came from an extreme stretch, just like a career-best season.
The river's long-term average, 1906–2024, is about 14.6 million acre-feet a year. Since 2000, drought and warmer temperatures have pushed it lower still, to about 12.4 million. So today's shortfall has two causes: a promise based on a lucky stretch, and a river that has since become drier. The same caution applies to a budget built on boom years or a contract signed after a hot streak.
Related exhibits
Sources: the "Sports Illustrated cover jinx" is a long-documented piece of sports folklore (see Sports Illustrated's own reporting and Psychology Today, "The Sports Illustrated Cover Jinx," October 2016) that statisticians commonly cite as a real-world illustration of regression to the mean — the same effect Francis Galton first identified in 1886 comparing parents' and children's heights. Rather than rely on unverified real cover statistics, this exhibit simulates the underlying mechanism directly (fixed skill + random noise per season) with a seeded random-number generator. The first numbers shown are exactly reproducible from this page's own code; the "Run a new simulation" button draws fresh random players each time. Colorado River figures: Congressional Research Service, "Management of the Colorado River" (R45546), for the Compact allocations, the 16.4 million acre-foot flow assumed in 1922, and natural-flow averages of 14.6 million (1906–2024) and 12.4 million (2000–2024); tree-ring evidence on the wet 1905–1922 period from Stockton and Jacoby (1976) and later reconstructions.