Some Thoughts on “Expected Value”

In the middle of last year, I wrote an article on playing the lottery in which I talked about the “expected value” of winning a lottery ticket. In that article, I gave an example of a typical Powerball jackpot and spelled out how the average return you would get on a $1 lottery ticket is $0.36.

The idea of “expected value” isn’t a new one to me. It was one I used to employ when I was heavily into buying and trading sports cards and other collectible cards. One could, with some calculations, figure out the odds of opening a particularly valuable card in a given pack. Then, one could multiply the odds by the value of the card, and repeat that calculation for each valuable card one might get, then add together the results. That would get you the “expected value” of the pack.

Most of the time, the packs weren’t worth it. Still, I kept an electronic spreadsheet for many types of packs and I had a strong sense as to the value of some of the packs one might find. Every once in a while, I’d hit the figurative jackpot and find some store or some individual selling off packs far below their “expected value,” and I would clean up.

The thing is, I find the idea of “expected value” popping up over and over again in my life. Whenever I’m considering a non-essential purchase, the concept of “expected value” is always on my mind.

So, here’s my humble proposal for shopping for the non-essential: have some idea of the expected value of the item you’re receiving, and make sure it exceeds the cash value that you’re spending for it.

What does that imply?

The first step is to know the value of certain things in your life. How much value does an hour’s worth of entertainment have for you? How much value does an hour’s worth of entertaining a friend have for you? What value does a good meal have beyond a normal meal? What value does an hour of completely free time have for you?

This requires a fair amount of thought in advance. For example, I’m pretty hesitant to spend more than $1 per hour of entertainment that will be extracted from an item, whether by myself or by my friends. That’s why I usually wait until computer games are on sale before I buy them and I research other entertainment items heavily before I’ll spend my money on them. I want to be pretty confident that I’m going to get that level of use out of the item.

I value my free time pretty heavily, so if something is proposing that it’s actually going to save me time, it’s got my attention, but I want to be sure that it’s going to save me that time. That leads me to my second principle: you need to have a strong understanding of what it is that you’re buying. If it’s a film you’ve never seen and have little idea as to what it’s about, it’s going to be incredibly hard to judge the value you’re going to get out of it. Are you going to watch it ten times? Are you going to watch it once and then it gathers dust?

You need to know what you’re buying before you put your money down.

Another principle is to simply wait for sales. Almost every item you might want will eventually go on sale if you’re patient enough. Let go of the idea of paying a premium price just to have the newest and greatest thing.

Whenever I want an item, I usually figure out an approximate expected value for it. For example, if a computer game that I play regularly has a sequel coming out, I might figure that I’ll get twenty hours of play out of it on the conservative side. If that’s the case, and I value my entertainment at $1 per hour, I’ll be willing to pay $20 for that game. However, when it comes out, it’s $50. That means I wait for a sale. When it drops to $20 or below, I’ll buy it, because I know I’m getting value for my dollar.

This leads into a final tactic: estimate low. All of this is estimation, anyway. When you’re estimating the expected value of something, estimate on the low side. That way, if you’re still getting a positive estimated value out of your purchase, you’re really getting a bargain, because there’s a good chance the actual value you get out of the item will exceed even your estimates.

The idea of “estimated value” is one that will guide you well with your non-essential purchases. It requires you to think more carefully about what you’re buying and sets a standard for which you’ll be richly rewarded.

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