Friday, August 31, 2012

The myth of the 100-year flood

Casual handling of statistics make me cranky.  So we take a break from job-seeking and a SQL tutorial for this public service announcement about the so-called 100-year flood.

WaPost's Five myths about Hurricane Katrina included this tidbit:
4. New Orleans’s levees are fixed and could withstand another Katrina.
After Katrina, Washington committed $14.5 billion to flood-protection improvements that are supposed to survive a 100-year storm — a term of art that refers to storms that have a 1 percent chance of striking in any given year.
Kudos to writer Jed Horne for using "term of art" to emphasize that the term has a specific actuarial and regulatory definition.

Unfortunately, most people are not so careful.

If an area has a 1% chance of flooding each year, it does NOT mean that it will flood once per century.

I fired up python in an OS X terminal, but you can use any calculator or programming language you like to replicate these results.

Assuming each year is independent of every other year, you have a 99% chance of NOT being flooded in any given year.  Over a 100 years,

>>> .99**100
you have a 36.6% chance of escaping flooding.
You also have a 1 - 0.3660323412732292 = 63.4% chance of being flooded at least once per century.

Over 50 years,
>>> .99**50
you have a 60.5% chance of escaping flooding.
Conversely, you have a 1 - 0.60500606713753635 = 39.5% chance of being flooded at least once.

Suppose you have a 2% chance of flooding each year.  Over 100 years, 
>>> .98**100
you have only a 13.3% chance of escaping flooding.

Hey, that doesn't scale (linearly)!  ;-)

The power of powers never ceases to amaze.

You may also want to read What planet are they on? for another illustration of nonlinear phenomena.


  1. Very interesting. Thanks for this.