Pick the applicants, pick the slots, then decide how much of the final score is luck. Even when luck counts for almost nothing, watch what it does to who gets in. Drag the luck slider to zero to prove it's fair. You won't like the rest of the range.
Each dot is a strong applicant, placed by skill rank (best on the right) and luck (higher = luckier). The picked ones are colored—notice they're not just the rightmost few.
The model. Each applicant gets a random skill score and a random luck score, both 0–100. Final score = skill weighted by (100 − luck weight) plus luck weighted by the luck weight. The top scorers win. This is the same toy model Derek Muller built for the NASA astronaut class in the Veritasium video on luck—18,300 applicants, 11 chosen. The point isn't that skill doesn't matter; everyone near the cutoff is excellent. The point is that when thousands of excellent people compete for a handful of slots, the margin separating "in" from "out" is thinner than the noise, so luck decides the last yard. Turn the luck weight to zero and the churn vanishes—selection becomes perfectly fair, and also nothing like the world you live in.