the accumulation of small risks

a simple plot that informs how i make decisions


December 12, 2023

I like to climb and sometimes when talking with other climbers I get the impression that they are blasé about risk, especially for things that are a little bit dangerous, but not outright scary.

When we take small risks repeatedly, that risk accumulates. Suppose you are setting up an anchor at the top of a climb, and you don’t tether into something secure, so there’s a 2% chance you fall while you work. If you take this risk 20 times, the probability that you fall off a cliff at least once is 33%. That’s really high. Far too high for me.

The numbers above are made up, but the point is that I’m hoping to climb outside for a long time. Climbing is dangerous, and I have a certain risk budget that I am willing to allocate to climbing because I enjoy it. Sometimes I’ll even do big risky things! But it’s important to me that I don’t exceed my risk tolerance, and I suspect I am most likely to that by accumulating small risks without paying attention.

Diatribe aside, I find myself referring back to this figure on a regular basis, and I’m posting it here so that I can point other people to some rough numbers as well.

If you want to toy around with the numbers and make your own figure, you should be able to do that by changing the values in the p_event and time variables below and then hitting the Run Code button.