Fire your CTO if your company buys cell phone insurance. He’s bad at math.

January 17th, 2014   Tags: , , ,

Ten years ago I was introduced to the game of Texas Hold ‘em. I spent some time reading and studying the game and in most situations can hold my own. A big reason for this is because I understand “pot odds.” It’s a must learn concept for poker players, and it helps explain why insurance is a bad deal.

Some Basic Math

I love math.

Save money with math.

For you poker nuts and statisticians out there, I completely acknowledge the math you’re about to see is an over simplification. But it conveys the point. With that disclaimer out of the way, let’s continue.

Assume you’re sitting at a poker table with four hearts in your hand and one card left to deal. You’re certain that if you get a 5th heart you’ll win the hand. If you don’t get the heart, you’re certain you’ll lose. There’s $100 in the pot and the current bet is $10. Should you stay in the game or get out?

Here’s the math: You have a 25% chance of winning (1 chance in 4 you’ll get a heart) and all you have to do is pay in 10% of the pot. You should make that bet because you’re expected return ($25) is greater than your investment ($10).

Think about it this way, let’s say you had that exact situation 1000 times. 25% of those times you would win and the total of those winnings would be $25,000 (250 * $100). 75% of the time you’ll lose but that will only cost you $7,500 (750 * $10). Profit of $17,500 if you play a 1000 times.

Now change things up. There’s $100 in the pot and you still have those 4 cards for a flush. This time the bet is $50. In other words, you have to put up 50% of the pot with only a 25% chance of winning. In 1000 hands, you’d win that same $25,000 but this time you’re loses would total $37,500 for a net loss of $12,500.

When the pot odds are in your favor, place the bet. If not, fold.

Law of Large Numbers
You can’t say with certainty which hands you’ll win, but you can be confident that if you encounter the above situation 1000 times you’ll come out ahead if you do what the pot odds tell you to. Do it 100,000 times and you’ll be even more confident in the outcome.

This is referred to as the law of large numbers. It doesn’t state that you’ll win or lose any specific hand but, rather, if you play that exact hand a bunch of times you can be extremely accurate in predicting the overall outcome. The more times you play it, the more confident you can be.

It is this mathematical theory that insurance companies use to make money (as well as casinos). They don’t know for sure if they’ll make money on you or not, but they know that if they can find a million people just like you and price things properly, they will win.

Cell Phone Insurance is a Bad Deal
Let’s get out of the world of Texas Hold ‘em and talk about cell phone insurance. We’re going to use Apple’s new iPhone 5S as the example. The 16GB version retails for $649. You might get it for $199 when you sign a two-year contract but if you break it, it will cost you $649 to replace.

This is where the insurance pitch comes in: “Would you like the insurance? It means if you lose or break this phone you won’t have to spend $649 to get it replaced. It’s only $7/mo.”

You think that sounds like a pretty good deal, right? $7/mo and they replace a $650 device if you lose it. Sign me up!

Then you find out there’s also a $199 deductible if you need to file a claim. Well, still, $199 plus $7/mo sounds like a decent offer.

Let’s check the math…

According to Squaretrade, about 13% of iPhone owners will break their iPhone in the first 12 months of ownership. This means your expected cost if you don’t buy the insurance is $649 * 13% = $84. Your required payout to the insurance company is $7 * 12 months = $84. Looks like a wash.

But we haven’t figured in that deductible yet. If there’s a 13% chance you’re going to break your phone, then you can assume 13% of that deductible must also be paid. This brings your total expected cost of using the insurance to $84 + (13% * $199) = $110. In other words, not getting the insurance leaves you with an expected cost of $84 and getting it leaves you an expected cost of $110.

The insurance is a bad deal.

Here’s what you might be thinking. “Well, if I need the deductible then this is a good deal, right? Otherwise I’d be shelling out the entire $649.”

On the surface that seems like a good argument, and that’s probably what the AT&T guy trying to sell you the insurance will say. So let’s think about this another way. Assume you own a company with 1000 employees and you’re going to buy everyone an iPhone 5S. Should you buy the insurance?

Using the law of large numbers we can be fairly certain that about 130 people will break their phone. So the cost of having the insurance is 1000 people * $84/year in insurance + (130 * $199 deductible) = $109,870. That’s what it will cost if you buy the insurance.

What if you don’t buy the insurance? Then you’ll be replacing 130 phones at a retail cost of $649. That comes to a total of $84,370.

If you’re the CTO of your company and you buy the insurance, you should be fired.

If you’re an individual buying cell phone insurance, the odds are you’re wasting money.

What about AppleCare+?
The above numbers come from the insurance offered by Asurion. That’s the plan most cell phone carriers offer. The above math makes it pretty clear it’s not a good deal.

But that’s not the only insurance plan out there. What about Apple’s very own AppleCare+. This costs $99, is good for 2 years, and charges you $79 if you need to use it (it does not cover lost or stolen phones like the Asurion plan does). Let’s do the math again on a 1000 phones. The plan is good for two years so we’ll need to change our possible breakage rate to 26% (bad assumption but it’s a worst case scenario).

With Insurance: (1000 * $99) + ($79 * 1000 * 26%) = $119,540
Without Insurance: 1000 * 26% * $649 = $168,740

Hmmm… In this case it looks like the insurance is a good deal. But there’s a catch.

By far the most common cell phone damage is a cracked screen. There are a lot of third party companies out there that will fix a cracked iPhone screen. Let’s assume that 80% of all smartphone damage is a cracked screen and the rest is something catastrophic – like water damage – that requires a new phone. Let’s also assume the 3rd party cost for an iPhone 5S screen repair is $199.

With Insurance: Still $119,540
Without Insurance: (260 * 80% screen repair * $199) + (260 * 20% total loss * $649) = $75,140

Once again, the insurance turns out to be a bad deal. I’ll go so far as to guarantee that if you do the math, you’ll discover insurance is always a bad deal.

Then why would I ever buy insurance?

There is a simple rule to buying insurance: You should buy it if the cost of the catastrophic event is so great that there’s no way you could cover it but the recurring fees are feasible for you to pay (or if it’s required by law).

Car insurance is something you should always buy. Let’s say you have a $30,000 car and your insurance comes to $100/mo. Many people can afford $100/mo for car insurance if they paid $30,000 for their car. Very few of those people could shell out $30,000 if they totaled the car – or a couple hundred thousand dollars if they totaled the car, someone else’s car, and ended up in the hospital for a week.

The same holds for health insurance, home owner’s insurance, business insurance, and more.

The odds are, you will pay more for that insurance than you’ll get back. That’s why State Farm and Geico are in business. But the fact is, if you smash up your car, your house burns down, or you’re diagnosed with cancer, you will NEED that insurance because you won’t be able to pay for it out of your own pocket.

I would argue that you can afford $649 for a new smartphone. You might not want to, but you could. After all, you can presumably afford the $120+ per month cell phone plan, right? You do not NEED the insurance if your iPhone falls on the ground and the glass cracks or even if it falls in the bathtub and you have to replace the entire thing.

Do the smart thing and say, “No,” the next time that salesperson tries to convince you to buy the insurance plan.

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6 Responses to “Fire your CTO if your company buys cell phone insurance. He’s bad at math.”

  1. Lavee says:

    Great post. I have similar views on insurance in general. I want to add that insurance do have a place and purpose. To use the same analogy with the phone industry, there are cases where insurance can benefit the buyer. Suppose you purchase a new plan with a new network with new phones and you are trying them out before comitting. In this case, it might be a good idea to purchase the insurance for the 30 day term so you are guarantee a way to back out if you find the product/service is not acceptable to your standard.

  2. Lev says:

    How about the mentioned Squaretrade?

    I’ve been using it for my phone and my laptop – items that get carried around a lot and that are relatively fragile electronics (a drop or a good shake could damage them), and the extended warranty in all the cases paid for itself and more… What do you think? What are the odds?

    • JCD Repair says:

      Lev: Once again, it depends on your financial state and how expensive the laptop. As I mention in the article: If the replacement of the device would be financially ruinous to you, then you should definitely get the insurance. However, if it would just be painful but doable to replace the device with your own money, then I’m of the mindset that you shouldn’t get it. Also, if your laptop is a popular brand, there’s a good chance there are companies out there that could do most repairs for not much more than the deductible.

      Obviously, if you lose or completely destroy the laptop in 2 months the insurance would be good to have. But the odds are that you won’t do that.

      Personally, I never get the insurance on electronics.

      • Lev says:

        The big difference here is the fact that there is no deductible. (Ok, I just checked their web site and it seems they have changed up their conditions a bit, there is an option to have a deductible now as well. It’s nowhere near $200, though, which is pretty steep.) Considering that these days the usual warranty period for electronics is a mere one year and the fact that it is more likely for our gadgets to suffer malfunction (on its own or externally caused) in the 2nd year, than in the 1st (and in the 3rd year more, than in the 2nd), assuming there was no failure before, then I say it’s a pretty good ideal to cover your $800 smart phone or your $1500 laptop for extra couple of years with a one time $100 warranty extension (Costco has discounted offers and they also often times have significant promos), because a broken screen or a fried motherboard would cost just as much and then there’s also labor. Don’t forget how much peace of mind and nerves cost ;)

        • JCD Repair says:

          First: If you’re piece of mind is the reason for the insurance, then go for it. But from a financial point of view, it doesn’t make any sense.

          I’m on the SquareTrade website right now and here is what I’m seeing for a $1500-$1999 laptop:

          • 2-Year Plan w/o Deductible: $280
          • 2-Year Plan with $75 deductible: $210

          In other words, the insurance plan on that laptop (with no deductible) will increase the cost of your $1500 laptop by almost 20%.

          A lot of the repairs you might need (cracked screen replacement, new power supply, new hard drive, etc), will probably cost less than $280 to have a third party repair shop fix – and you’re not very likely to need that service.

          Once again, I’ll make the same claim I always do: If it was a good financial decision to buy insurance on electronics, they wouldn’t offer it.

          But again, if it bring a piece of mind, that might be a different issue.

          • Lev says:

            Fair enough.

            Though, like I said I would not get it at these prices. The times I got it, it was significantly cheaper and the cost of repair (usually a screen and usually the lowest found around) at a third party shop was higher than what I paid for the warranty… This is not on one occasion, but on 3 or 4, so it might just be the case that I personally am more prone to getting my electronics damaged, so it does make sense in my particular case :)

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