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 you are in the linear phase (where you are big enough to be treated seriously but your growth rate still looks absurdly high).
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.
I took the author's use of O(n) vs O(n^2) as a framing point rather than a literal model. It just seems to be missing the forest for the trees. Besides, we can approximate sigmoids with linear or quadratic functions when windowing them. Considering startup as context I think we know what part of the graph we're talking about... Do we see that exponential explosion or is the sigmoid much more flat. Replace the x in your sigmoid with (ax) and is a <1 or >=1?
If only it was exponential in the beginning, as word-of-mouth spreads. Sigh. The reality is that you need to claw and scrape your way to your first customers. The numbers vary depending on whether your product is b2b, consumer, or more niche, but the first customers are the hardest. You rarely get word-of-mouth in the beginning. Instead, it comes much later, typically after a long period of slow growth as you learn more about your customer's workflows and problems and adjust the product to get closer to PMF.
> 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 hire "to fit a job description" because, since money was tighter, they are super conservative about hiring, have always done the job they are hiring for themselves for a long time, and know exactly what they need. It is the O(n^2) companies that hire for job descriptions that fit the positions the VCs tell them they need. I think your experiential datapoints may be too sparse.
In my experience the heavily VC funded companies have a lot of very talented and experienced people, too.
But they have so much money and pressure to hire that they start dipping deeper and deeper into their candidate pipeline. They start lowering their standards to keep the employee count growing. This results in a mix of talented people trying to get work done and a lot of people who are good at interviewing and stretching the truth about their experience.
Every time I’ve been at a company like this, they tell themselves they’ll hire fast and fire fast to compensate. Then they never fire fast or at all, because nobody wants their little empire to shrink.
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.
Experience != talent. Perhaps a better way to phrase it is that they hire the minimum needing to succeed in a well defined role. Startups aren't afforded this comfort as the roles are not well defined.
To quote a private equity investor friend: “I’ve known startup CEOs of billion-dollar companies that are flat broke. Meanwhile people with $50mm/ARR dating sites from Europe live like kings.”
A good reminder that it’s worth deeply understanding venture portfolio economics before you get on the ride. Not that it’s a bad ride. But it’s a ride.
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).
Or, really, to say the unsaid bit out loud: there are lots of important considerations when taking a job. The author seems to assume that money is the only driver, when, for many top candidates, money is not their primary motivation. The ability to plan well and thereby reduce stress is a good measure of the management experience. Other non-cash incentives tend to be given out more readily at well-run non-enterprise companies, including remote work, longer vacations, and more strategic control, to name just a few.
Modern society tends to severely overemphasize money as the optimisation goal. This is an emergent behaviour of our good capitalist system.
Your time is precious. You spend it once and you can't predictably get any more of it.
I suggest you choose your optimisation goal function very very carefully to suit the outcomes you want (money is only an intermediate step). It's hard to decide what we really want. Money is the default game that we see our peers playing (and it's easy to gain moderate success at the money game). It requires more attention to find and learn from people that have had success playing less common games.
Cynically (or even conspiratorially) investigate the suggested life defaults for you by your society as though they were dark patterns designed to mislead you.
I like what Naval wrote about status games (money is only one aspect of status). Paraphrased:
Status is a zero-sum game, not a positive-sum game. There’s always a subtle competition going on between status and wealth. For example, when journalists attack rich people or the tech industry, they’re really bidding for status. The problem is, to win at a status game you have to put somebody else down. That’s why you should avoid status games in your life – because they make you into an angry combative person. You’re always fighting to put other people down and elevate yourself and the people you like. Status games are always going to exist; there’s no way around it. Realize when you’re getting attacked by someone else and they’re trying to look like a goody-two shoes. They’re trying to up their own status at your expense. They’re playing a different game. And it’s a worse game.
Disclaimer: I've had moderate success at chasing money. I've had less success at optimizing for other goals (work in progress in my 50s).
Money has no maximum so it's a weird goal to try and reach. I wonder why Warren Buffett waited until 95 to decide to retire? He would easily be the richest man in the world if he hadn't charitably given so much away.
Another relevant paraphrased snippet from an interview about better lives for the elite: https://archive.ph/kF0YR
There’s this study called the American Freshman Survey [edit:snip] In the 1960s, 50% of students said making as much money as possible was a really important goal. Today, that’s 80% to 90%. That change shows that this is not human nature. It is culture.
I actually passed my discrete math class and final a few days ago and got the big O vs Theta vs Omega question right.
The reality is that companies often underperform their best case possible growth rate. O(n) and O(n^2) are meant to represent the best possible growth rate which may be practically be underperformed.
You may be thinking about algorithmic analysis where the term "worst case" is used for the upper bound, but here, the upper bound represents the best case. Sort of counter-intuitive but the underlying mathematical notation is properly defined.
Since O(n^2) is used as a proxy for “something superlinear, but don’t get hung up on how much”, you might also choose O(n^(1+ε)), an upper bound characterised by some arbitrarily superlinear function.
There's an interesting misunderstanding in this article.
The argument for O(n) is well formed here.
O(n^2) is not, the core argument is that these grow faster because of compounding. Compounding is fundamentally an exponential process, far larger asymptotically than a quadratic.
The article clearly isn't meant to be mathematically correct: you are being over-rigorous in your criticism. From the article:
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(n²). 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 n² 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.
Article would be better using something like O(linear) and O(≫linear). The big O notation is a useful and memorable metaphor, but the n squared is really confusing. The article also doesn't use Unicode for the notation - which fucks usability (e.g. I used screenshot OCR and reedited).
True exponential growth is possible, but I suspect is rare, because the expenses can also compound, so a polynomial growth may be an acceptable approximation. It's also important to remember that "every exponential growth curve is a sigmoid in real life" (can't remember the source of the quotation).
> [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.
It is interesting that YC started as being more Founder friendly ... and I guess "Founder's Fund" did too
But there is still some divergence in interests ... i.e. if you have to make a choice between a safer O(n) path and a riskier O(n^2) path, then the investor prefers the riskier path
Or I'd be very interested in an argument that they don't
> I think many prospective founders, if their goal is money, should optimize for O(n) businesses from day 1.
Honestly, I don't think anyone "picks" the kind of business they want to run. You just kind of go with the flow. If you raise VC money, you follow their lead, if you're running a small bakery, you'll do whatever makes sense there.
So while this is a fun intellectual exercise, it's an exercise in hindsight. In the moment, you're really just trying to survive the day-to-day and not really "optimizing" for a specific growth pattern.
> 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.
>> 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.
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.
> In algorithm analysis, we would typically have n represent time (or some other cost).
No, n is never time in any kind of algorithmic analysis. n is a function of the size of the input and the output is some measure of the cost related to the input.
In O(n^2), the size of the input is n and the amount of time, or space, or some measure of the cost has an upper bound that is proportional to n^2.
> [The conclusion is that] 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 O(n^2) company.
It's a bit like getting a regular job vs playing a lottery: the former gives you better financial results on average, while the latter gives you a chance to make it really big.
(I also wish it were "linear companies" and "quadratic / exponential companies", or maybe "snooker-cue companies" vs "hockey-stick companies".)
VC-land is a strange place with strange laws. If you stay in it for too long, you forget that most of the world doesn't follow the power law, and that most of the VC-reasoning just does not help.
> 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.
Or, O(n^2) companies are founded and run by people motivated solely by making lots of money, while O(n) companies are there for multiple reasons: passion for the topic, making employee's lives better, and helping their customers solve problems. Though those motivations exist at O(n^2) companies too, they are in the shadow of making money. While, at O(n) companies, money is also essential, but it exists to support the other goals. A slight shift in priorities can make all the difference.
I wonder about the cultural effects at large getting the O(n²) most of the funding. That expansive, aggressive and not always safe behavior is promoted, while the slow but solid approach is not. That shapes the ecosystem and the people in it, in and out those companies.
Maybe it is a good way for short term profits, but that is just one metric. That kind of dynamic may be harmful in the long term, and in a really big scale.
If it grows at O(n) it is not a startup in the way "startup" is used in Silicon Valley. It is just an ordinary new business.
It's worth noting that starting an ordinary new business is hard. Probably as hard as starting a startup for anyone who has not started a new business a few times before. And maybe harder because most new businesses are undercapitalized and therefore likely to suck up personal capital while startups get to use other people's money.
I use business, startup, and company interchangeably. Generally I tried to use business for O(n), startup for O(n^2), but I guess I wasn't strict with my usage...
Perhaps they are harder to start, but they are also vastly more likely to succeed to their O(n^2), and this is not only due to the increased barrier to entry.
That's what I mean when I say, founders are more likely to succeed at O(n) companies.
Story applies to most people in regular life: the average return of working a regular job is far higher than playing the lottery. But for a rare few, playing the lottery works out.
Uber exploits drivers (car cost, maintenance, and depreciation) for illusionary freedom as a substitute for taxis. Not really groundbreaking except screwing people.
Counter hypothesis: fast but linearly growing early stage startup acquire good early funding and enter into a growth loop dominated by the ability to invest these fund in marketing, which increase valuation and allow for further funding, fueling more growth etc.
After all cost of customer acquisition is largely dominated by external factors and cost per user mostly linear until close to market saturation.
Now there might be economy of scale intervening at some point increasing the margin per user, which feed back into growth, but on average fast growing startup are cash negative until much later in life.
TLDR I think the implications in the article is inverting cause and effect
What ever happened to providing a good service? Why does everything have to be a "unicorn"? You greedy capitalists, and billionaires have sucked out the life of everything — tech, food, airlines.
VC culture, private equity, and "hyper-growth" mentality has screwed over many good companies that once provided good services to the community. Good paying jobs with excellent benefits and providing upward mobility.
Now the labor benefits are shrinking, company loyalty is gone, customers screwed over, labor exploited with minimal in return, rising cost of living, increasing wage disparity, abuse of powers.
One can argue the neoclassical/neoliberal economic theory and "Reagan-omics" that birthed PE/VC culture gave power to the idiocracy we see today.
I'm getting an impression it's just not profitable enough. For many years I get a feeling that business is considered sound only if it is superprofitable (not exactly the right term, but still) in order to cover all losses.
Probably it's because of market competition required to be at least noticed. Some companies' spendings for marketing are greater than for R&D, production and operations combined. Maybe we got ourselves into a situation where everywhere competing for low-hanging fruits or trying to make customer believe it's the service they need while all of it doesn't really overlap with real society needs.
bee_rider|9 months ago
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 you are in the linear phase (where you are big enough to be treated seriously but your growth rate still looks absurdly high).
withinboredom|9 months ago
But, these are the two basic levers for a SaaS: growth and churn.
godelski|9 months ago
danjl|9 months ago
mgraczyk|9 months ago
For example Facebook's revenue is still increasing at an increasing rate, 21 years later
ocean_moist|9 months ago
You can think about it like we are looking at the concave up portion of the sigmoid only. The early growth phase.
danjl|9 months ago
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 hire "to fit a job description" because, since money was tighter, they are super conservative about hiring, have always done the job they are hiring for themselves for a long time, and know exactly what they need. It is the O(n^2) companies that hire for job descriptions that fit the positions the VCs tell them they need. I think your experiential datapoints may be too sparse.
Aurornis|9 months ago
But they have so much money and pressure to hire that they start dipping deeper and deeper into their candidate pipeline. They start lowering their standards to keep the employee count growing. This results in a mix of talented people trying to get work done and a lot of people who are good at interviewing and stretching the truth about their experience.
Every time I’ve been at a company like this, they tell themselves they’ll hire fast and fire fast to compensate. Then they never fire fast or at all, because nobody wants their little empire to shrink.
ryandrake|9 months ago
jbmsf|9 months ago
ocean_moist|9 months ago
vessenes|9 months ago
A good reminder that it’s worth deeply understanding venture portfolio economics before you get on the ride. Not that it’s a bad ride. But it’s a ride.
ridiculous_leke|9 months ago
danjl|9 months ago
unknown|9 months ago
[deleted]
robocat|9 months ago
Your time is precious. You spend it once and you can't predictably get any more of it.
I suggest you choose your optimisation goal function very very carefully to suit the outcomes you want (money is only an intermediate step). It's hard to decide what we really want. Money is the default game that we see our peers playing (and it's easy to gain moderate success at the money game). It requires more attention to find and learn from people that have had success playing less common games.
Cynically (or even conspiratorially) investigate the suggested life defaults for you by your society as though they were dark patterns designed to mislead you.
I like what Naval wrote about status games (money is only one aspect of status). Paraphrased:
Disclaimer: I've had moderate success at chasing money. I've had less success at optimizing for other goals (work in progress in my 50s).Money has no maximum so it's a weird goal to try and reach. I wonder why Warren Buffett waited until 95 to decide to retire? He would easily be the richest man in the world if he hadn't charitably given so much away.
Another relevant paraphrased snippet from an interview about better lives for the elite: https://archive.ph/kF0YR
curiousgibbon|9 months ago
ocean_moist|9 months ago
The reality is that companies often underperform their best case possible growth rate. O(n) and O(n^2) are meant to represent the best possible growth rate which may be practically be underperformed.
You may be thinking about algorithmic analysis where the term "worst case" is used for the upper bound, but here, the upper bound represents the best case. Sort of counter-intuitive but the underlying mathematical notation is properly defined.
TypingOutBugs|9 months ago
ccppurcell|9 months ago
sshine|9 months ago
ocean_moist|9 months ago
brap|9 months ago
fooker|9 months ago
The argument for O(n) is well formed here.
O(n^2) is not, the core argument is that these grow faster because of compounding. Compounding is fundamentally an exponential process, far larger asymptotically than a quadratic.
robocat|9 months ago
nine_k|9 months ago
ocean_moist|9 months ago
> [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.
chubot|9 months ago
https://news.ycombinator.com/item?id=4497461
https://paulgraham.com/swan.html
It is interesting that YC started as being more Founder friendly ... and I guess "Founder's Fund" did too
But there is still some divergence in interests ... i.e. if you have to make a choice between a safer O(n) path and a riskier O(n^2) path, then the investor prefers the riskier path
Or I'd be very interested in an argument that they don't
dvt|9 months ago
Honestly, I don't think anyone "picks" the kind of business they want to run. You just kind of go with the flow. If you raise VC money, you follow their lead, if you're running a small bakery, you'll do whatever makes sense there.
So while this is a fun intellectual exercise, it's an exercise in hindsight. In the moment, you're really just trying to survive the day-to-day and not really "optimizing" for a specific growth pattern.
ocean_moist|9 months ago
Generally if you have some sort of idea of what you want to do, you'll be more successful at it.
wavemode|9 months ago
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.
thaumasiotes|9 months ago
> 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.
danjl|9 months ago
Maxatar|9 months ago
No, n is never time in any kind of algorithmic analysis. n is a function of the size of the input and the output is some measure of the cost related to the input.
In O(n^2), the size of the input is n and the amount of time, or space, or some measure of the cost has an upper bound that is proportional to n^2.
mperham|9 months ago
wavemode|9 months ago
smahs|9 months ago
nine_k|9 months ago
It's a bit like getting a regular job vs playing a lottery: the former gives you better financial results on average, while the latter gives you a chance to make it really big.
(I also wish it were "linear companies" and "quadratic / exponential companies", or maybe "snooker-cue companies" vs "hockey-stick companies".)
ark296|9 months ago
neilv|9 months ago
> 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.
danjl|9 months ago
gmuslera|9 months ago
Maybe it is a good way for short term profits, but that is just one metric. That kind of dynamic may be harmful in the long term, and in a really big scale.
brudgers|9 months ago
If it grows at O(n) it is not a startup in the way "startup" is used in Silicon Valley. It is just an ordinary new business.
It's worth noting that starting an ordinary new business is hard. Probably as hard as starting a startup for anyone who has not started a new business a few times before. And maybe harder because most new businesses are undercapitalized and therefore likely to suck up personal capital while startups get to use other people's money.
ocean_moist|9 months ago
Perhaps they are harder to start, but they are also vastly more likely to succeed to their O(n^2), and this is not only due to the increased barrier to entry.
That's what I mean when I say, founders are more likely to succeed at O(n) companies.
unknown|9 months ago
[deleted]
unknown|9 months ago
[deleted]
SoftTalker|9 months ago
burnt-resistor|9 months ago
adityamwagh|9 months ago
I’m assuming there are similar problems with Lyft.
kristopolous|9 months ago
avereveard|9 months ago
After all cost of customer acquisition is largely dominated by external factors and cost per user mostly linear until close to market saturation.
Now there might be economy of scale intervening at some point increasing the margin per user, which feed back into growth, but on average fast growing startup are cash negative until much later in life.
TLDR I think the implications in the article is inverting cause and effect
xyst|9 months ago
VC culture, private equity, and "hyper-growth" mentality has screwed over many good companies that once provided good services to the community. Good paying jobs with excellent benefits and providing upward mobility.
Now the labor benefits are shrinking, company loyalty is gone, customers screwed over, labor exploited with minimal in return, rising cost of living, increasing wage disparity, abuse of powers.
One can argue the neoclassical/neoliberal economic theory and "Reagan-omics" that birthed PE/VC culture gave power to the idiocracy we see today.
Snawoot|9 months ago
I'm getting an impression it's just not profitable enough. For many years I get a feeling that business is considered sound only if it is superprofitable (not exactly the right term, but still) in order to cover all losses.
Probably it's because of market competition required to be at least noticed. Some companies' spendings for marketing are greater than for R&D, production and operations combined. Maybe we got ourselves into a situation where everywhere competing for low-hanging fruits or trying to make customer believe it's the service they need while all of it doesn't really overlap with real society needs.