Probability, Insurance, Statistics, and Cameras

So I'm probably going to buy a new camera very soon. I'm imagining what it would be like to say "no" to my co-workers about all the add-ons and stuff, when I know how bad it looks for them if they fail to sell me all that crap.

I'm sure I'll be asked if I want to buy a warranty. And I'm sure I'll say No. Why not? Here's the deep dark secret: Because it's not worth it. Like, mathematically.

We're always being pushed to sell more damage-protection warranties with cameras (which is when, if anything happens to the camera, anything short of theft or loss, we'll fix it or replace it for free, even if YOU broke it being stupid. It does buy you some peace of mind, and is cheaper than what it would cost to fix the camera).

If we're always being pushed to sell them, they must be very profitable.

If they're very profitable (or, really, profitable at all), then on average most people do not get their warranties'-money's worth in camera repairs. Which means that you're better off not getting it, because you're so unlikely to use it. In other words, the warranty costs less than a camera repair, but the warranty cost divided by the probablility of you actually breaking the camera is NOT less money than the cost of the camera repair. Otherwise we wouldn't be selling them. This means not getting a warranty is a gamble, but one in your favor. (If that's probabilistically obvious to you, you can skip the rest of the post. If not, read on. I think it's actually pretty interesting).

It's like insurance. From years of looking at what people need their insurance to pay for what, hey know how much to charge people so that, when people do need the insurance money, the insurance company still makes money from them in the long run. Even when people need tons of insurance money - like if their car is destroyed or something - then those people, and everyone else, is charged just a tad more so that the insurance company makes money in the end. So if people just put away as much money as you would pay the insurance company, then on average most people would find that this money is enough for them to pay for doctors and car repair and whatnot. But for SOME people - the ones who do crash their cars irreparably, the ones whose house burns down, then ones who for no reason catch an expensive disease - they DO make money off the insurance company. And if, tragically, you end up being one of those people, then you want insurance!

How many people profit from insurance in the long run, versus how many people don't, can be guessed at by how profitable insurance is. Which is: marginally. So the gamble of whether or not to get insurance is a pretty even one. Of course, the small probability of a catastrophically strong need for being insured is what leads most people (and the law) to decide (quite rightfully) that it's a good idea. But in the end, all that insurance is, is: either you're paying for someone else's car accident/disease, or they're paying for yours. Which is great, in an idealistic, socialist kinda way.

(Wow, that was longer than I expected). Why is it important for me to lay all that down clearly? Because that's what allows me to see that warranties on electronics, as much as they buy you peace of mind, are most often not worth it.

Say 90 people buy cameras this month. Say that half of them buy a warranty, and that the chance of you breaking your camera over its first couple years is one third (I'm just making up numbers, but hang on). That means that 45 people buy a warranty, and that 15 of those will have the camera repairs paid for by the warranty. (Or, rather, 15 camera repairs, not 15 people: If you need it repaired twice, that counts as two, and you need to stop carrying your camera in your pocket when you go snowboarding). That means that everyone who buys the warranty has to pay one-third of a camera repair cost, in order for the warranty system to pay for itself, as far as the store is concerned. If that were the case, then the system would break even (if they charged you the fraction of a camera repair cost (one third in this case) that corresponds to the fraction of insured camera repairs per camera purchases, 15/45). For it to be profitable, they need to charge you MORE than that. If they charge, say, 40% of the repair cost, then, on average, seven fortieths of your warranty cost goes to the company, and 33/40 goes to paying for repairs (because, remember, one in three people use it, in our example).

This means that the chances of you needing a camera repair are 1/3, so on average the money you will be spending on camera repairs is 1/3 the cost of one repair... but you just paid that and a little bit to the store, which is more than the expected cost of getting it repaired if and when it breaks.

In other words, if 1/X of the people who buy warranties actually use them to pay for camera repairs, and if all those camera repairs put together cost Y, then the warranties must cost Y/X to break even, and MORE than Y/X to make money. However, each person on average will spend Y/X on camera repairs, which means that, if the warranty system is profitable for the store, than on average it is not profitable to the customer. It IS a little profitable to the people whose cameras break, but it is very much unprofitable to the people whose cameras don't, so in the end, it's actually not a good gamble, statistically. Just as gambling is just slightly unprofitable for most people, and quite profitable to very few, but not enough to make it a good deal (which is why casinos make money).

So don't buy camera warranties. Unless you buy a camera from ME of course...

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