Distribution, minimum, or tail

Evaluate how outcomes vary across people, cases, or scenarios, with special attention to the worst-served and the rare severe tail.

Your retirement spreadsheet says you're fine: average market returns, average lifespan, average costs, comfortable outcome. But you don't get to live the average. You get one draw, and the draws that ruin people, a long life plus low returns plus a late-life care bill, are invisible in a projection built on medians.

Distribution, minimum, or tail is the reference shape that looks past the mean: it evaluates how outcomes vary across people, cases, or scenarios, with special attention to the worst-served, the minimum, and the rare severe tail. Use it when reliability, fairness, or rare catastrophic outcomes matter and averages conceal the decision-relevant variation. For the retirement plan: stress it under the low-return, long-life, high-inflation, and care-cost scenarios, and judge it by whether the plan survives those, not by the median projection. A plan that's slightly worse on average but robust in the tails is often the right buy. What changes: you start designing for the outcomes that would actually break you. Two cautions from the spec: optimizing only the worst case can sacrifice large benefits everywhere else, and tail estimates are data-hungry, so state whose tail matters, why, and what tradeoff you'll permit rather than chasing impossible certainty.