The Improbability of Success

I heard somebody tell a joke once about chance and the economy. It goes a little something like this.

Suppose an economist and their friend are walking down the street. Suddenly, the friend spots a $20 bill on the sidewalk.

The friend says, “Hey, look! There’s a $20 bill on the ground!”

Without looking, the economist says, “That’s very unlikely.”

As far as I gather, the joke is meant to illustrate the fact that unlikely things (such as finding $20 on the sidewalk, or starting a successful business) happen all the time. It seems to be used as an argument in favor of taking chances and following your dreams, etc. I’m pretty sure I came across it during one of my idea-hope-reality-sadness cycles, which I seem to be cursed to repeat.

Probably in the same thread or video, I heard what I think is a swift and sharp counter-argument:

Well, that’s fine, but when was the last time you found $20 on the sidewalk?

And to really twist the knife:

For that matter, when was the last time anyone you know found $20 on the sidewalk?

Ouch.

It’s true, though, and that’s why it hurts. Having a halfway-original idea and implementing it successfully in a market just isn’t something that’s likely to happen to many folks. The problem I have One of the problems I have is that I take all of the successful businesses I see around me and assume that I’ll be able to replicate their success. That’s what you might call one big ol’ selection bias. And yet I keep having ideas, thinking that this is the one. Stupid, but hard to stop.

I’m trying to wean myself off of this. I’m better than I used to be—there have been some bad times before this where I really thought that this idea was the one that would take off, and other parts of my life were affected unnecessarily—but I still get caught up in things from time to time. (The most recent of these cycles prompted me to write this.) In a sincere effort to get a grip already, I’ve done some math.

Let’s Fermi-estimate that the number of new businesses each year in the United States is on the order of $10^6$. Let’s also assume that about a third are dead after a few years. That leaves about $10^{5.5}$ successful businesses, for a reasonable definition of “successful”. Now, let’s further assume that there are about $10^{8.5}$ people in the United States who could start a business. That means that the chances that I’ll start a successful business this year—all things being equal, whatever that means—are about $\frac{10^{5.5}}{10^{8.5}}=10^{-3}$, or about 1 in 1000. In other words, not great.

According to actuarial tables, I can expect to live about another 50 years. Over a 50-year period, I should therefore expect that my chances of starting a successful business will be about $1-(1-\frac{1}{1000})^{50}$, or about 5%. Even if you account for education, connections, available resources, and other factors, I don’t think any reasonable estimate of this value for me could be higher than 1 in 5 over 50 years.

I’ll admit that that’s higher than I expected. (I calculated all that while writing, instead of calculating and then writing like a good scientist would.) Still, I don’t know if it makes ideas worth pursuing. It hurts when ideas turn out to be bad for some reason, so maybe it would be better to stop? I don’t even know if I can do that. It feels like I’m just going to have ideas forever, no matter what I do. I don’t think this is a unique trait, but it is annoying…

Uhh, so yeah, stay in school, eat your vegetables, and try to stay grounded, I guess? I don’t know, man, just do your thing.