Poisson on startups

startups math

Let’s start with some sage advice.

A lot of curmudgeonly commenters on HN treat viable side-projects as a lottery. If we take that idea seriously, well, your chances of winning a PowerBall per ticket is 1 in 13 983 816. There are around 42620 programmers in Silicon Valley + the other US tech hubs (Seattle, Dallas/Fort Worth, DC, NYC)1. So if every single one of those Y programmers tries to found a startup, the expected number of startups we’ll get is:

$$\frac{1}{13983816} * 42620 = 0.003$$

And clearly, AngelList alone tells me that that number is unrealistically low. So let’s start with more modest assumptions.

Suppose at any given day, the average programmer has a \(1/100\) chance of encountering a viable business idea2. It doesn’t matter how you portion your day to arrive at this number: by reading HN during compile times, by going to the pub with your friends, etc. — I don’t care. What matters is that it’s a consistent number. Let us also assume that no one gets extra lucky and get 2 or more hits in a day.

The question is: how many viable business ideas will you encounter in a year?

Poisson gives us the answer:

$$\begin{align*} P(x) &= e^{-1/100} \frac{(1/100)^{(1)}}{(1)!} \\ & \approx 0.0099 \\ &:= \text{probability of getting a hit per day} \end{align*}$$

$$P(x) \times \text{(365 days)} = 3.61 \text{ viable business ideas}$$

So yeah, that kinda accords with experience. The average coder only gets a handful of hits in a year, and if he’s not the entrepreneurial type he won’t even get any of them off the ground.

But clearly, the world isn’t as bleak. Some people have a nose for this kind of thing, and the banality of serial entrepreneurs in Silicon Valley tells us that there is some element of skill/network/resources involved beyond a mere lottery. Taking for granted that human skill distributions obey power laws, let’s assume our serial entrepreneur is an order of magnitude better than the average. That is, she has a \(1/10\) chance on any given day to sniff out a possible venture.

Then:

$$\begin{align*} P(x) &= e^{-1/10} \frac{(1/10)^{(1)}}{(1)!} \ &\approx 0.0904 \end{align*}$$

$$P(x) \times \text{(365 days)} = 33.02 \text{ viable business ideas}$$

In other words, our super-entrepreneur will get 2-3 viable ideas every month3. I don’t know about you, but that seems to be par for the course for a number of serial entrepreneurs I know. And if you’re uncommon enough to be reading Hacker News for fun I think this number is much more achievable than you think.

What’s the main takeaway from this? Training your nose yields exponential rewards. Going from \(1/100\) to \(1/10\) is a matter of imbibing advice from serial entrepreneurs (you want to listen to people who systematically succeed, not to people who just got lucky), doing small experiments4, placing yourself in a fertile enough environment, and being well-calibrated in general.

Here’s an exercise: for every Show HN post you see, try to guess whether it will fail or not in the next six months. List down all the factors that you think contributes to this number. Then check: if you get it wrong, be a little less confident in the factors that didn’t matter, for they may not be as crucial as you think they are.


  1. Does this number seem too low? Not all people working in tech are devs, and for every full-stack engineer there are probably ten other roles working on the same project. Source.

  2. In my head, “viable” here means an idea that gets at least $500 MRR. Less Silicon Valley and more Indie Hackers.

  3. In retrospect, we could have figured this out without using Poisson, but alas we're already here.

  4. I never got the importance of sales on a gut level until I started selling zines in a zine fair. The difference between just standing there and actively inviting customers is the difference between selling 1-2 zines/hour to selling your entire stock in a frenzy.