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
0.3660323412732292
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
0.60500606713753635
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
0.13261955589475294
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.

2 comments:

  1. Very interesting. Thanks for this.

    ReplyDelete