---
title: "An Average Depth of One Meter Can Still Drown You"
author: "Shawn Jiang"
lang: en
date: 2026-09-25
canonical: https://tplog.dev/en/essay/average-depth-wont-get-you-across/
translations:
  ja: https://tplog.dev/ja/essay/average-depth-wont-get-you-across/
  zh: https://tplog.dev/zh/essay/average-depth-wont-get-you-across/
---

# An Average Depth of One Meter Can Still Drown You

A river is one meter deep on average. Can you safely walk across it?

If you cannot swim and there is a three-meter-deep hole along the way, a low average depth will not save you.

Average depth is calculated by combining the depths at many points across the river. But when you cross, you are not standing at every point at once. You follow one particular path, step by step. Whether you make it to the other side depends not only on the average for the river as a whole, but also on what you encounter along that path.

What this example shows directly is that an average cannot represent the risks you will actually face along your path.

It can also help us understand non-ergodicity. The point here is that the average across many possible outcomes may not equal the long-term outcome a single person experiences over time. But variation in the river's depth is not, by itself, a complete explanation of non-ergodicity. What matters more in this analogy is which path you take and whether you encounter a loss that ends the process entirely.

If you fall into the deep hole and drown, you will never get the chance to walk through the half-meter- and eighty-centimeter-deep shallows farther ahead. Those points still count toward the average depth, but they are no longer relevant to you.

Once a single failure can force you out of the entire process, the average result takes on a different meaning. It may describe many points or many possible outcomes, but it cannot guarantee that you will have the chance to continue.

The same problem appears in investing, entrepreneurship, and major life decisions. A strategy may offer a strong average return, but if a single loss is enough to knock you out, you cannot rely on later gains to make up for it. The distinction to make is between a setback you can recover from and a failure that costs you the chance to keep participating.

So before comparing average returns, ask one question:

Will I be out before the good outcomes ever arrive?