Standard deviation matters

I was recently reviewing two health plans which I could join.  One was a typical HMO-type plan and the other a high deductible plan.  High deductible plans have been pushed pretty heavily lately, what with the focus on rising health care costs, the recent legislation, etc.  I don’t want to jump into the fray on the political aspects, but I do want to share with you an observation on being risk adverse.

The way that a high deductible plan keeps premiums down is by requiring the policy holder to pay everything out of pocket until you reach some limit.  For that reason, high deductible plans are often called catastrophic coverage plans, since they only become helpful if you incur massive costs.  In exchange, you pay very low premiums.  And that’s because you get very little benefit most of the time.  These plans, from everything I’ve read online, are great for young and healthy people, but not so good (obviously) for people with chronic conditions or families.

I am married and have two kids, but I was willing to run the numbers and look at the odds to see whether I should go with a traditional plan or a high deductible plan.  First you have the premiums to pay.  If you use no care than a high deductible plan beats a traditional plan hands down in premiums.  The rest is an odds game.  How many times will you have to visit the doctor?  How many prescriptions will you need?  What are your odds of having a catastrophic illness?  For a traditional plan, each one of these events costs you just a copay – typically $20.  For a high deductible plan, you have to pay the full amount until you reach the yearly limit.  (Never mind the fact that if you have a chronic condition you’ll reach that limit year after year after year).

Because I’m a data person, I happen to have tons of data on how often we visit the doctor and my current insurer was kind enough to send me a complete history of all charges so I had a reasonable idea of what various things would cost me.  Then, I built two models, one using a traditional plan and the other using a high deductible plan.

Guess what, in the end, odds were that even with my family (and we make our fair share of doctor visits), I’d likely pay less with the high deductible plan than with a traditional plan.  It wasn’t true in every situation, the potential cost to me of the high deductible plan overlaps with the potential costs of the traditional plan, but the premiums for a traditional plan are so much higher that it was difficult to overcome them.

But, there was something else I observed.  Not only did my models calculate the average result, but they also calculated the range of possible results.  And not surprisingly, the high deductible plan had a much, much higher standard deviation.  This isn’t surprising, since each medical event in a high deductible plan costs a lot more, and so the variability in the result is potentially much greater.

Ultimately, that’s why I stuck with a traditional plan.  Yes, I’m very likely to pay more, but the result is predictable, and I like predictable outcomes.  (I also like not having to concern myself with whether its worthwhile to go to the doctor).  If you’re a risk adverse person, and if studies about investing are to be believed you are more risk adverse than you think you are, then a traditional plan produces a more comfortable financial result.  It’s like buying bonds instead of stocks.  You may not come out way ahead, but it’s much more unlikely that you’ll come out far behind.

Consider that when designing a process as well.  Consistency is important.  You can end up with a software development process that sometimes produces perfect code, but sometimes produces awful code, or you could have a process which produces consistently average code.  Which one is easier to deal with for continuous improvement?

2 thoughts on “Standard deviation matters”

  1. My situation is almost the same as yours (2 kids) and I did the same calculations as you. I actually choose to put the difference in premiums into the HSA and to let it ride a bit. My wife was actually against it because she didn’t want to have to think about going to the doctor. Well, we were reasonably healthy and it worked well in 2009 and in 2010 my company forced us into an HSA so I’m happy we piloted it so we were used to it.

    My main issue in general with the HSA is that anyone of us could at anytime develop a chronic illness in our family…and in those cases…we are basically making the sick pay the vast majority of healthcare costs. Some would say this is a fair result because they are the users…but I prefer a result that takes into account that most people are not the cause of their major illness. I guess that is where the politics diverge.

    Interesting note. We are talking about having another child. We’ll be maxing out our out of pocket to the tune of around 6000 if that happens and that’s going to hurt in that year. Perhaps this is a place where it’s appropriate I pay more…because it’s the only major health cost that feels like a true choice rather than bad luck.

  2. I can see the “users should pay” mentality, but by that vein, victims of crime should pay for the police services they receive. As I believe you’d agree from your comments, there’s a social value to everyone being healthy, just as there is to everyone being safe.

    It’s true that you’ll face a significant financial burden as the result of having a child. My son’s birth, just the birth, not all the services leading up to it, cost more than $15,000 and it was a routine birth with no particularly special intervention. Do we really want to discourage people having children by making it a significant financial decision? A geriatric population would be quite a burden on an ever shrinking younger population. I’m inclined to think the answer lies not in who does or does not get insurance or how much they pay for it, but to discover ways to make care cheaper to begin with, such that insurance is truly serving the purpose it was designed for – catastrophic events, not routine care.

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