Population Outcomes Diverge From Individual Outcomes

April 19, 2022

The average outcome across many people doing something once is not the same as one person's outcome doing it many times. This divergence is the signature of non-ergodicity, and confusing the two is one of the most consequential errors in decision-making.

"In ergodic systems, you can use the population outcome to make optimal decisions. In non-ergodic systems, you cannot." Ole Peters

Six people play Russian Roulette once. On average, five survive and collect $6,000 each. The population outcome is $5,000 per player. Now imagine one person playing six rounds. Their expected lifetime outcome collapses toward $0 because each round carries a chance of permanent elimination. The population average looks attractive; the individual trajectory is lethal.

This distinction between the ensemble average (population outcome) and the time average (lifetime outcome) is the foundation of ergodicity economics, pioneered by Ole Peters and Alexander Adamou. In an ergodic system, these two averages converge. A coin flip is ergodic: flip it a million times yourself or have a million people flip once, and you get the same distribution. But most consequential domains in life are non-ergodic. Investing, careers, health, and relationships all contain irreversible events bankruptcy, burnout, death, broken trust that make the time average worse than the ensemble average.

The practical danger is that nearly all conventional advice is built on ensemble averages. "The stock market returns 10% annually" is a population statement. Your individual return depends on sequence of returns, when you need the money, and whether a crash wipes you out before the recovery. Similarly, "most startups fail but the expected value is positive" is true for the venture capital population but potentially ruinous for the individual founder betting their savings.

Whenever you encounter a statistic about average outcomes, ask: is this the population outcome or my lifetime outcome? If the system contains irreversible losses, the two will diverge, and the average is lying to you.

Takeaway: Never make a life decision based on the average outcome of a group ask what happens to one person doing this repeatedly, accounting for the possibility of ruin.