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🤏Lecture 17 - Small samples and shrinkage

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📅 Last Review7 Dec 2025

Rank anything by a rate and the top and bottom fill up with small samples. The ranking is measuring size.
Shrinkage: pull each estimate toward the group average in proportion to how little data it rests on.
It makes every individual estimate slightly biased and the whole set far more accurate. That trade is worth it almost every time.
For a scorecard: a carrier with six loads should be shown mostly as an average carrier we know little about, with a wide range, and not ranked at all.

small samples produce the extremes. best AND worst. always
the best hospital, school, bakery in any league table is usually a small one. so is the worst
that is not quality. that is n
fix: shrink each estimate toward the overall average, more when there is less data
big sample → keeps its own number. tiny sample → mostly the average
it is regression to the mean (week 1) done on purpose, in advance
this is the answer to Gideon. THIS IS THE ANSWER TO GIDEON. wrote that in the margin and Rasmus looked over
shrinking is Bayes: the overall average is the prior

Bring shrinkage to 📌 Analyse scorecard weightings with Bao
Sketch what a shrunk score looks like on the prototype for Tomasz
Work out how many loads a carrier needs before its own number counts for more than half
Write to Gideon Asante with the idea, in plain words, no formula
Capture 🔍 Show carrier scores as ranges, not ranks

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