I recently saw a tweet[1] about how people should go about starting startups/businesses, and it caused me to formalize my intuitions around two distinct types of tech businesses I am familiar with. I’ll call them $O(n)$ startups and $O(n^{2})$ startups.

Throughout this essay, let n represent the time elapsed since launch. An $O(n)$ startup grows its key metric (revenue, users, etc.) roughly linearly with time—double the time, double the metric. An $O(n^{2})$ startup accelerates, with growth compounding super-linearly over time.

Here are a few popular examples:

• $O(n)$: Mailchimp, 37signals -> steady ARR, high margins, no outside capital.
• $O(n^{2})$: Slack (pre-acq), Uber -> heavy spend, but every user fuels ecosystem/network effects.

what do i mean?

Businesses generally grow following a few patterns. They generally have some TAM to saturate and saturate the TAM at some rate. This rate can be vaguely linear, what I call $O(n)$, or vaguely superlinear, what I call $O(n^{2})$.

The reason I borrow the asymptotic notation is because it implies the growth rate is an upper bound (best case scenario) and generalizes away specific constant factors and sums. The analogy breaks down when you force $n$ or $n^{2}$ imply something numerically specific about your growth rate, or introduce functions with different growth rates like logs or exponentials. For now we will (somewhat unprincipledly) stick with two sole classes: $O(n)$ and $O(n^{2})$.[2]

I think businesses aim to improve their growth rate via constant factors (eg $O(n^{2})$ -> $O(2*n^{2})$)[3] but fundamentally can’t change them. Some businesses are doomed to grow linearly (lifestyle businesses) and some are able to grow superlinearly.

implications

VCs generally only invest in $O(n^{2})$ companies. While $O(n)$ businesses are far more common. $O(n)$ businesses can’t be fund returners.

Notice how this growth rate is an upper bound and ignores intercepts? This essentially means a company could underperform their growth rate in some cases and that an $O(n)$ company could be valued higher than an $O(n^{2})$ company at some non-asymptotic time.

differences (people)

The $O(n)$ companies I am familiar with are generally 100% bootstrapped, B2B SaaS or tech adjacent, and have between 10–50m in revenue. The $O(n^{2})$ companies I am familiar with are pre series B consumer/B2B SaaS.

The way these two companies operate are completely different from day 1. I think one of the biggest ways is talent/people.

$O(n)$ companies can’t afford to hire the absolute best talent. At the top, the founder(s) are generally very smart, but they don’t have the budget for the best growth/product people. They hire and value sales people to butter up their clients who are generally execs at super big publicly traded companies. They hire people who fit a job description.

$O(n^{2})$ companies hire high agency people. People who can just go in under constrained environments. People are generally given a lot of equity to join and as a reward.

differences (economics)

Another difference is the economics.

For $O(n)$ companies the biggest stressor is making payroll. Invoices are paid net 30 or even net 90, but people expect to get paid twice a week. You either need excellent lines of credit, or a lot cash reserved, something which can be hard to do from scratch.

For $O(n^{2})$ companies the biggest stressor is growth and retention. Sure you have a runway, but generally PMF can solve all your problems so you can become default alive or raise your next round.

differences (PMF)

Now we have come to another key difference. PMF is practically assumed, almost a certainty, for $O(n)$ companies. You understand your customer, and it’s very easy to build for them. You are capitalizing on your networking/sales to become the default for clients while ensuring you keep them happy by running a tight, operationally efficient ship.

Because of this $O(n)$ companies have nice deadlines, clear SoW (statement of work), and are easy to reason about.

$O(n^{2})$ businesses sacrifice all this. The future is much less promised. All for the possibility of “hyperscale”.

conclusion

This brings us to perhaps the most important part of the essay: $O(n)$ companies are higher EV than $O(n^{2})$ companies.

I mean that, on average, a founder will make more money pursuing an $O(n)$ company than an $O(n^{2})$ company. And not an insignificant amount, the amount of liquidity and networth a 20m ARR $O(n)$ company is extremely hard to match by a traditional VC backed company.

People don’t really tell you this because it is in VCs best interest people keep filling out lottery tickets, and it’s in the $O(n)$ business owners best interest to keep their moat a secret.

$O(n)$ businesses (and founders), since they don’t need to raise money or do much marketing, can keep an extremely low profile. It’s very hard to access them simply because of obscurity.

I think many prospective founders, if their goal is money, should optimize for $O(n)$ businesses from day 1.

[1] https://x.com/oceanmoist/status/1921751004938465347

[2] Perhaps choosing a better two functions could more closely explain the growth dynamics of network effects, which could be more exponential. I think the analogy diminishes in value if you try to directly numerically match it to some growth metric.

[3] $\Theta(n^{2})$ technically.