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O(n) vs. O(n^2) Startups

rohan.ga

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Re: O(n) vs. O(n^2) Startups

#21

Post by wavemode »

> 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.

Kind of a strange formulation to have n represent the key metric. In algorithm analysis, we would typically have n represent time (or some other cost). So we would say that the startup whose key metrics accelerate exponentially with time is actually an O(log n) startup - they only have to spend (log n) time to get n results.

Re: O(n) vs. O(n^2) Startups

#22

Post by ryandrake »

danjl wrote: post #7

> O(n) companies can’t afford to hire the absolute best talent. O(n) companies tend to have more experienced founders and engineers in my experience. This is partly why they have "nice deadlines, clear SoW" and "understand their customers" enough to have PMF. The strength of their talent, experience and job networks often greatly outweighs the cash incentives, allowing them to hire top candidates. They do not just hi…

The vast, vast majority of companies don't need "the absolute best talent." Their product is a JSON interface to someone else's service. You don't need John Carmack to write that. Companies comically overestimate the level of talent they actually need, and let positions stay open for months, sometimes years, looking for that unicorn programmer they don't actually need, and passing up hundreds of candidates who would work out fine.

Re: O(n) vs. O(n^2) Startups

#23

Post by ridiculous_leke »

I wonder what's optimal for me as an employee. I am working in a O(n) startup where colleagues are nice, work is streamlined yet challenging, and I do see growth potential in the long term. Several O(n^2) founders have reached out recently and the pay is attractive(even after accounting for a move to an HCOL area).

Re: O(n) vs. O(n^2) Startups

#24

Post by jvanderbot »

withinboredom wrote: post #15
bee_rider wrote: post #11

Huh. Not working in the field, I assumed startups went like sigmoids (everything is a sigmoid after all). Exponential at first as word of mouth spreads, then linear as your users start bumping into each other and word of mouth stops working, and then you eventually start leveling off near carrying capacity (you’ve hit your addressable market). I thought the game was to try to get bought by some massive company while…

This is actually a better model and one that more closely reflects reality. You can see it on revenue as well, since even if growth is exponential, churn is a percentage of your total paying users. Thus, it produces a sigmoid curve unless you can get churn to 0% (pro-tip: you can’t). But, these are the two basic levers for a SaaS: growth and churn.

The first thing I learned when I joined my first business was covered in orientation with leadership: every product or business unit is a sigmoid, and to maintain growth you must add new products or business units without spending too much to do so. Then the overall company profit can grow linearly or whatever by being a sum of sigmoid functions that spawn over time.

Good leadership knows when the flattening will happen and pivots.

This is called "innovation". That really stuck with me as a mental model.

Re: O(n) vs. O(n^2) Startups

#25

Post by thaumasiotes »

wavemode wrote: post #21

> 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. Kind of a strange formulation to have n represent the key metric. In algorithm analysis, we would typically have n represent time (or some other cost). So we would say that the startup whose key metrics accelerate…

>> 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.

> Kind of a strange formulation to have n represent the key metric. In algorithm analysis, we would typically have n represent time

In the quote you pulled, n is time. If n were the key metric, everything would be ϴ(n).

> So we would say that the startup whose key metrics accelerate exponentially with time is actually an O(log n) startup - they only have to spend (log n) time to get n results.

No, you don't know how the notation is used.

Re: O(n) vs. O(n^2) Startups

#26

Post by danjl »

wavemode wrote: post #21

> 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. Kind of a strange formulation to have n represent the key metric. In algorithm analysis, we would typically have n represent time (or some other cost). So we would say that the startup whose key metrics accelerate…

Normally, with big-O notation, the goal is to reduce complexity. The author's wording kinda reverses that assumption only to "surprise" you in the end? A somewhat forced irony.

Re: O(n) vs. O(n^2) Startups

#28

Post by thaumasiotes »

withinboredom wrote: post #15
bee_rider wrote: post #11

Huh. Not working in the field, I assumed startups went like sigmoids (everything is a sigmoid after all). Exponential at first as word of mouth spreads, then linear as your users start bumping into each other and word of mouth stops working, and then you eventually start leveling off near carrying capacity (you’ve hit your addressable market). I thought the game was to try to get bought by some massive company while…

This is actually a better model and one that more closely reflects reality. You can see it on revenue as well, since even if growth is exponential, churn is a percentage of your total paying users. Thus, it produces a sigmoid curve unless you can get churn to 0% (pro-tip: you can’t). But, these are the two basic levers for a SaaS: growth and churn.

> You can see it on revenue as well, since even if growth is exponential, churn is a percentage of your total paying users. Thus, it produces a sigmoid curve unless you can get churn to 0% (pro-tip: you can’t).

Exponential growth means that additional users are a percentage of your total users.

It is trivial to see that adding a source of exponential decay will give you another exponential function. All churn (as you've defined it) does is lower the exponent. It will never take you from exponential to sigmoid.

Re: O(n) vs. O(n^2) Startups

#29

Post by [deleted] »

ridiculous_leke wrote: post #23

I wonder what's optimal for me as an employee. I am working in a O(n) startup where colleagues are nice, work is streamlined yet challenging, and I do see growth potential in the long term. Several O(n^2) founders have reached out recently and the pay is attractive(even after accounting for a move to an HCOL area).

[deleted]

Re: O(n) vs. O(n^2) Startups

#30

Post by neilv »

> O(n) companies can't afford to hire the absolute best talent. [...]

> O(n^2) companies hire high agency people. [...] People are generally given a lot of equity to join and as a reward.

O(n^2) is often a matter of ZIRP-VC-powered artificial-growth (e.g., their example of Uber). That also includes hiring a large quantity of people.

For factors in genuine O(n^2) growth, you might be onto something: with structuring culture to leverage employee agency, and for using meaningful equity to help align employees with business success.

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