The Improbability of Success

2019-09-25

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.