"This, Like, NEVER Happens!" - Extreme Value Analysis in Everyday Life (#8)

A few days ago, I was playing a late-night round of everyone's favorite social-experiment-pretending-to-be-a-board-game, Settlers of Catan (consider checking my guide to crushing your opponents in Settlers here).  The game, or should I say massacre, had one player building five cities before I got more than 2 roads off the ground.  The number of 10's and 11's rolled defied all reality.  Needless to say, it was a painful game to take part in.  But what interested me most was the sheer unlikelihood of it all.  I was witnessing a 3-standard-deviation event, a blue moon, a 100-year-flood.  And I had no idea how to react without evoking sour grapes.

The first conclusion I reached is that I need to tone down my competitiveness, especially in games that involve luck.  My desperate attempts at trades and persuasive maneuvers in the face of absurd dice rolls more made me crazy than did any good.  It was the equivalent of a mouse writhing and flailing while already in a snake's grasp.  I should have accepted my friend's victory far earlier and focused on enjoying the good company of Emily, JFran, and Alex.

Second point (this is the extreme value analysis one!)
To make a larger point, I've noticed that it's intuitively hard for most people to deal with rare statistical events.  It's a "we'll probably be fine" way of thinking that allowed the New Orleans levees to not be raised or reinforced, young adults to avoid buying even basic health insurance in case of catastrophic illness (pre-ACA I mean, now it's an economic decision), or thousands of financial analysts to disregard the remote possibility of million of simultaneous mortgage defaults in the 2008 housing crisis.  

You may be familiar with the human tendency to assign patterns to random events, especially unlikely ones. I've heard remarks in-game such as "ugh 12's are never rolled" and "4's have been on fire this game".  The former is a small but important rounding error, like saying a piece of paper or a small volume of air weighs nothing, when enough of either would crush a person.  The latter is a clear case of the gambler's fallacy.  We forget that a 100-to-1 odds coincidence is still going to occur more often than not if we have at least 68 rolls of the dice, and if we considered 10 such (independent) 100-to-1 coincidences, one would occur every 7 or so rolls (used my friend binomdist for these).  The point is, if we try something over and over, we would foolish not to expect rare events from time to time.  We should try our best to plan appropriately, devoting 5x more effort to defend against a 10/1 occurrence vs. an equally bad 50/1 occurrence.

But what if the stakes are high?  An extreme event in Settlers only meant that I finished the game with 3 points.  But if you are a government, or an insurance company, or you are gambling with your health, one cataclysmic disaster every few decades is not good enough.  If magnitude-7.5 earthquakes are very likely to occur in LA this century, but an magnitude-8.5 earthquake is only 7% likely, the local government better damn well bite the bullet and require buildings be constructed to withstand an 8.5.  If you are a multibillion-dollar insurance company you cannot allow yourself to be be on the hook for over $440 billion in insurance payouts in the event of a housing collapse (AIG), even if it is quite profitable and you consider the bad case quite unlikely.

Extreme weather indeed.

So, extreme value analysis matters in how we see the world and prepare for the worst, especially as a group.  I am a free-market guy who errs on the side of low regulation, but the long time horizon of the US and the high stakes means I bend my ideology on some issues.  I support inspection for food quality at the federal level because it only takes one great screwup to harm hundreds or thousands of people; pure market forces would allow this to happen in rare cases to increase efficiency, but a government is interested in a society where consumers can trust their businesses.  I accept public policy action to address climate change, even if I think the research is often wasteful and misplaced, because the stakes are high enough and our climate is sensitive enough to the potential actions of crazy people in power.  

I guess you could summarize a practical use of extreme value analysis as:

1. Try to think about risks in a more precise way than "this 'usually' or 'never' happens".

2. The longer your time horizon, and the more intolerable the consequences, the more you must bend your precise thinking to over-prepare for when that remote event occurs.

If you were a big data scientist or a sales forecaster or the FEMA chief, I'd ask you to make models.  For the rest of us, just try to use numbers when thinking about extremes.