“Statistical Notes § Best Student Ever!”, Gwern2014-07-17 (order statistics; similar)⁠:

Miscellaneous statistical stuff

How often could a teacher truthfully say of a student, such as in a letter of recommendation, that the student was their “best student ever”?

This is an instance of the ‘record value’ problem in order statistics, and can be easily solved if we know how many students are taught each year: there are surprisingly many, because the number of best-evers will grow roughly logarithmically in total students, as the initial burst of record-setters fades out into ever-rarer record-breakers.

For example, for the literary critic Harold Bloom’s 64-year-long teaching career, he might observe something like ln(6,400) ≈ 9 best-ever students.

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• Best Student Ever!
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