New Proof: Relying on Averages Can Lead You to Terrible Decisions

Imagine two stores with identical monthly sales figures: same average, same spread, same every summary number. In one store, most days are steady and a few are huge. In the other, most days are dead and a handful are enormous. To a spreadsheet, they look the same. But how many extra T-shirts you should stock is completely different. That's the heart of a new mathematical paper from researchers Andrés Cristi, Matteo Russo, and Jiechen Zhang.

The team built a formal proof showing that when you only know the "moments" of a situation — that's math-speak for averages and similar summary stats — you cannot reliably pick the best action. They constructed pairs of scenarios that share every summary number but demand opposite decisions. In plain terms: identical dashboards, opposite right answers.

They then showed how badly this breaks real problems. In the classic "newsvendor" puzzle — how many newspapers or fresh sandwiches to order each day — any fixed order amount can fail badly. In setting prices, no pricing strategy can guarantee anything close to the best possible outcome. And in hiring or dating-style "best candidate" problems, knowing only averages caps your success at about 37% instead of the 58% you'd get with full information.

The takeaway isn't that data is useless. It's that summaries hide shape. The same average can mean a calm week or a rollercoaster. If you're making decisions where being wrong is expensive — inventory, staffing, pricing, insurance — you need the actual spread and pattern of outcomes, not just the headline number. Ask for the full picture, not the average.