# Statistics and Preparedness

Being part of the amateur radio world, and being predisposed to preparedness on my own anyway, I rub shoulders with a lot of people for whom preparedness’ ranges from the Boy Scouts sort of Be Prepared” to the end of the spectrum where it’s about being prepared for the Zombie Apocalypse and the downfall of civilization as we know it.

I see a lot of people spending a lot of resources preparing for things where the probability is so low that it vastly outweighs the costs incurred, and I see many of those people being unprepared for events that are very likely to happen.

So I’d like to introduce a concept from the world of mathematical statistics and show how it bears on the decisions of what to prepare for and how much ought to be spent on those preparations.

The concept is expected value”. This is the sum of the payoffs of all outcomes (either a win or loss, as a positive or negative number) times the probability of the relevant outcomes. Suppose we can make a wager where if a coin flip comes up heads we win a dollar, and if it comes up tails, we lose 50 cents. The expected value of that wager is (.5 * \$1) + (.5 * -\$0.50) = \$0.50.

If we play this game for many turns, we can expect that on average we will win \$0.50 per turn.

Now let’s examine preparedness through that lens. Is it worth preparing for a massive earthquake? If we spend, say, \$1000 on earthquake preparedness, but the earthquake never happens, we’re out \$1000. If we spend \$1000 on earthquake preparedness, and the earthquake happens and our preparedness means we evade the destruction of our house worth \$500,000, we’re up \$500,000 - 1000 or \$499,000.

Now, which side do we want to take in this wager? Do we spend the \$1k, or do we not spend it and risk destruction of our house in the event of an earthquake?

The expected value of this wager is the utility times the probability of both outcomes, added together. If we say the probability of the earthquake occurring is 1% over some time period (say, the time we will live in this house), then the expected value is (.99 * -1000) + (.01 * 499,000) or \$1000. So assuming the probability of the earthquake really is 1%, then it makes sense to spend \$1000 to protect our house from an earthquake even though the event is unlikely to happen.

Alternatively we can calculate how unlikely the earthquake has to be for it to make more sense for us to keep the \$1000 and risk destruction of our house. That will happen when the expected value of one side of the wager is equal to the expected value of the other side, so that we’re indifferent as to which outcome we get. In our case that would be ((1-P) * -1000) + (P * 499,000) = 0. Solving that equation for P tells us that P = .002, so if the odds are higher than 2 in 1000, we should spend the \$1000 and prepare.

So two things factor into our preparedness decisions: how likely the event is, and the expected value of the sum of the outcomes. It’s worth preparing to prevent massive losses even if the event is fairly unlikely.

It’s also worth preparing for very likely events where the expected value of the event is only slightly negative, but the event is very likely and the cost of the preparation is low.

Let me offer up three practical examples that come to mind right away.

Suppose you need some medication to survive. If some event occurs which separates you from your supply of this medication for even a short time, you will die.

Suppose the probability of an event where you’re separated from the supply is modestly unlikely - an earthquake, a bad storm, being forced to flee a wildfire, etc. The expected value of carrying enough of these meds to last you two weeks (long enough to reconnect with a supply) is modestly negative - the cost of the meds plus the hassle of carrying it on your body at all times times the high probability that they will never be needed. The expected value of not carrying is massively negative, because dying is worst possible loss, times the admittedly low probability you will need the meds to survive.

The massive loss if there’s an event and you don’t have the meds, along with what is a very modest cost of carrying the meds on your body at all times, means that as long as the probability is not zero, it makes great sense to carry a small vial with the meds you need to stay alive for two weeks in it, in your pocket, all the time.

Another example, this time carrying a flashlight. In the dark, a flashlight is highly useful. The benefit of having a flashlight in the dark is modest in some cases and life-saving in others, the cost is low, and the probability is 100% that it will become dark in the next 24 hours. It makes sense to always carry a flashlight. (decent flashlights are now so small and cheap that for years I’ve given friends and loved ones keychain flashlights just for the peace of mind it gives me to know they have it)

Knives are cheap and easy to carry but useful even in everyday life as well as vital in many emergencies (imagine: you are in an auto accident, must get out of the car quickly before it burns, and your seatbelt is jammed). The probability that you’ll need to cut something (e.g. open a package) in the next 24 hours is close to 100% The math is obvious: carry a knife, all the time.