Back in 2008, I wrote one of my first pieces for PJM: “Today’s Health Insurance Ain’t Insurance.”  I just re-read it and it stands up pretty well: today’s health insurance still ain’t. Have a look at it, as it has some more detailed explanations for the points I’m going to make in this article, but the point is this: there’s basic mathematics behind all real insurance, and while actuarial math can get pretty hairy, we don’t need it to see the underlying and essential flaw of the whole approach taken by the Affordable Care Act.

At the heart of it, insurance is a bet. You are making a bet with someone else that some bad thing will happen to you, while they’re making a bet that it won’t. If you buy the simplest and cleanest kinds of insurance, like term life, you are betting that you are going to die during the term of the insurance, and the insurance company is betting you won’t. (“Whole life” and “universal life” policies are more complicated things that mathematically act like combining a term life policy with an annuity. This is where the math can get hairy, but you pretty much find out what you need to know when you realize an insurance company would far rather sell you one of these policies than term life and a separate annuity.)

All insurance is based on a really simple equation called expectation value, or more commonly risk. In life insurance, you start by deciding how much money your survivors need if you were to fall over tomorrow. Let’s say it’s \$100,000. (Your spouse can get a job.) So the amount at risk for the insurance company is \$100,000. That’s called the hazard, H. They look at your your age, your sex, your health, and possibly your profession or hobbies (base jumping? Race car driving?) and come up with a probability that you will die during the term of the insurance. That’s a number P where 0 ≤ P ≤ 1. Then they compute the expectation value R of that \$100,000 as

R = P × H

The way to interpret that is: if you sell enough insurance policies to people with the same characteristics, the insurance company can expect to pay out about R dollars for every \$100,000 worth of policies sold. I just went online, and as a 58-year-old man with diabetes, the best rate I found was \$495 a year. That would actually be a little more than the actual risk; insurance companies need to have some room for runs of bad luck, and they need to have some margin over that to pay for all those people running the insurance company and some profits for the stockholders. (Which, contrary to what you hear from the usual suspects, isn’t very large — Aetna, for example has profits between 2 and 6 percent.) So the real premium for a term life insurance policy is a little more than just the expectation value. How much depends on a whole bunch of things, so let’s just say x. Your total premium is going to be R+x and we know x > 0.

When we look at what we call health insurance now, though, that all breaks down, because many of the things that are covered happen — colds and flu, childhood illnesses, and so on — with probability near 1.

Guess what? If P is about 1, that premium is going to be the total cost plus x. Always. No matter what.

We got away with the current scheme for as long as we did because, dating back to Harry Truman’s administration, we let companies buy their group health insurance using pre-tax dollars. In other words, they got a pretty substantial discount for buying health care for their employees instead of paying them more.

Now, when you give people an incentive like that, they’re going to do more of it; what used to be “major medical” starts adding regular doctor visits and such. At the same time, the insurance companies want to control their costs, so they started adding more administration to the whole thing. That increases x but it doesn’t change the relationship.

What does change the relationship is that we start to run into something Milton Friedman called “Gammon’s Law,”  which originated with a study of Britain’s National Health Service done by Dr. Max Gammon. Friedman called it the Theory of Bureaucratic Displacement:

In a bureaucratic system, increases in expenditure are paralleled by a corresponding decrease in production.

Translated from the economist-ese, that means in a bureaucratic system, the more you spend on something, the less you get of it.

Gammon’s original work in which he identified this found the correlation was very nearly perfect: as the number of pounds spent on the National Health System increased, the number of hospital beds declined. The correlation was -0.99.

Aside: for those of you who don’t eat and breathe statistics. Imagine you have a loaf of sliced bread. You weigh the bread, then take out a slice, then weigh it again; keep taking out slices of bread and re-weighing.

The correlation between the number of slices taken out, and the weight of the remaining bread, will be around -0.99.

Why does this happen? There are at least a couple of reasons. As more money goes into the bureaucracy, there’s more pressure to make sure it’s being spent well, which means more forms, more auditors, more independent review boards. All of that takes time and money, and that time and money are being taken away from what used to be the goal.