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Let's Spread the Risk! (I Mean in Health Care... Not Flu)

By       Message Dominique Lord       (Page 1 of 3 pages)     Permalink

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Reprint from Open Salon.

As you all know by now, how health care in the US should be overhauled has been the subject of intense discussions over the last few months. So far, based on what I've been reading on the interwebs, it seems what everyone's focused on are peripheral topics, like how the US Government is never good at managing anything except for the military (and I'm sure some would argue that they can't even do that); or how a single-payer system would lead to the fall of Western civilization (or at least the United States, which is of course synonymous with Western civilization, depending who you ask). I've yet to read anything about the important concept of spreading the risk, with a few exceptions (see here).

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What's this spreading the risk thing, you ask? As usual, I live to enlighten. This is a concept used in such diverse businesses as the insurance industry and

casinos (among others). Spreading the risk assures that as the number of people in a given group gets larger, a company or governmental agency can more easily spread the risk (that would be the risk of a payout) among the pool of participants. They can therefore better estimate the average cost (or payout) per person in the event that one or even several of the group are victims of a catastrophic event. In other words, even if a few people succumb to a tragic blimping accident, the agency still has enough money or funds (minus administrative expenses) collected from all the participants to cover the costs associated with it. Not just because the agency has more income than expenses, but because the agency has better control or knowledge about disastrous outcomes (like tragic blimping accidents). This concept is based on the
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law of large numbers
: the larger the pool of people, the more accurately the agency can estimate the mean value of the sample population or group. The curious (and possibly masochistic) reader can read more about this subject
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here
, here or here.

My wife has begged me to simplify this, so here goes:

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Say you've got a casino. It's a small, pathetic little casino, so it only has about 100 desperate gamblers in it at any given moment. Now say it's possible for one guy on his last dime to win $10,000. This is a 1% probability. In order for your pathetic little casino to avoid bankruptcy in the case this happens, each of those 100 patrons needs to lose at least $100.00 at the tables (pass the loaded dice).

But, what if two gamblers win $10,000? Well, the casino is still screwed. In order to avoid the casino going under if that happens, each patron needs to shell out at least $200.

But say that you've got one of those really cool, swanky casinos that have tame lions or topless servers or something. This casino has 10,000 gamblers at any given moment, each losing, say $110.00. Now if 100 of them (1%) win $10,000, since the casino has already earned $1,100,000, paying out $1,000,000 isn't a problem. Even if 105 people win $10,000, your casino is sill laughing since the total payout is still below $1,100,000. So, by increasing the number of patrons, the casino can spread the risk of paying out 10 grand in the event more people win than anticipated (a 1% probability).

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Easy, right? Stay tuned for my lectures on the Poisson-gamma and Conway-Maxwell-Poisson distributions.

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Dominique is an Associate Professor in the Zachry Department of Civil Engineering at Texas A&M University. His research work aims at reducing the negative effects associated with motor vehicle crashes. When he's not developing mathematical and (more...)
 

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