# Max R. P. Grossmann

## The Rule of 13

Posted: 2024-04-28 · Last updated: 2024-05-04

### Statement

For any incidence $x$ per year and 100,000 persons, calculate $x/13$ to obtain the approximate percent chance of having the event happen at least once in your life.

This rule of thumb works well for incidences up until approximately 390.

### Example

At the time of writing, the intentional homicide rate in Saint Pierre and Miquelon was 16.5 per 100,000 people and year. This means that there is an approximate $\frac{16.5}{13} = 1.27\%$ chance of getting intentionally homicided over the course of one's life in Saint Pierre and Miquelon.

(The true value is that there is a 1.23% chance.)

### Proof

Let $z$ be the literal percent chance of some event, $z \in [0, 100]$. (Yes, I am violating conventions for the sake of applicability here.) Assume that some event has a constant incidence of $g$ per 100,000 persons and year, and that lifespan is 75 years. Years are independent. Then, $$z = 100 \left( 1 - \left[ 1 - \frac{g}{100000} \right]^{75} \right).$$ Take the first-degree Maclaurin series of $z$, $$z \approx \frac{3}{40} x \approx \frac{x}{13}.$$