Hazard, Risk, and Expected Losses | James Howard Hazard, Risk, and Expected Losses | James Howard

James Howard A Mathematician, a Different Kind of Mathematician, and a Statistician

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Hazard, Risk, and Expected Losses

NewHumanist has a great article on the difference between hazard and risk.

Basically, the gist of the article is the hazard is what can go wrong. The risk is how likely it is to go wrong. There’s another important metric they neglected to include is the expected value of the loss (or gain, in other contexts). The expected value is the value of the hazard times the likelihood of it happening.

For instance, I have a tendency to loose my headphones. I go through several pairs per year. So the hazard is losing the headphones and the risk, on any given day, is 1 / 50, assuming I loose a pair every fifty days or so. In this case, assuming I can buy a new pair for $10, my expected loss on any given day is $0.20. That means my expected losses over the year is about $73. That’s for a low-hazard / high-risk scenario.

At the other end of the spectrum is high-hazard / low-risk scenarios. For instance, dying in an airplane accident is high hazard, but very unlikely. So is the risk of terrorism. So the expected losses here are very little, but we spend a lot of money, as a society, protecting against these risks. On the other hand, you are much more likely to die in a random act of gun violence, and while you’re just as dead as from any other cause, the expected loss is substantially higher, and we spend little to counter the risk.

Failure to understand the relationship among hazard, risk, and expected losses are the reasons we make bizarre decisions, as a society.

Image by Ralf Roletschek / Wikimedia Commons.