I’ve been sitting in on our introductory Decision Science course for MBAs, which I’m planning to teach for the first time next year. One recent topic was the “flaw of averages” (a nice catchphrase due to Sam Savage, introduced into our course by Nabil Al-Najjar.) In mathematical terms, letting X be an exogenous random variable, a be a decision parameter, and f be any function not linear in X, this says

{{\rm argmax}_a E[f(a,X)] \neq {\rm argmax}_a f(a,E[X])}

In plain English, this just means that when you make a decision, do not assume that uncertainty will always take on its average, or “expected,” value. This leads me to a related point, and to my own catchphrase (see title) which I hope the students will find useful. “Expected Value” is an awful piece of terminology, as judged by its (very weak) relationship to the English word “expected.” I’m certainly not one of the first to point this out: It is possible, of course, for X to never come close to its “expected” value. The real question is why the term persists, when we have the perfectly clear term “average value” available. No better reason than our QWERTY keyboard, I suppose; once everyone is used to writing E for expectation, it’s hard to shake. Anyway, I think I’ll be showing a slide with the motto in the title next year; hopefully the students will find that memorable. It will be tempting, I suppose, to reinforce this with a brief clip from Monty Python: “No one expects the Spanish Inquisition!”