5 ms·

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

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 you are in the linear phase (where you are big enough to be treated seriously but your growth rate still looks absurdly high).

withinboredom 1y ago
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.
- jvanderbot 1y ago
  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.
- thaumasiotes 1y ago
  > 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.
  - nis251413 1y ago
    Sigmoid (or the logistic function specifically rather) is exponential until you get close to the "turning point" (or rather, its growth bounded from below by an exponential). It's as you approach that point that it becomes linear, and after that its growth decays. However you are sort of right that "churn" does not necessarily have to do with it being sigmoid because it will be anyway. It may be bring it earlier if the churn rate surpasses the user growth, but that's probably not important here.
    - thaumasiotes 1y ago
      If the churn rate surpasses user growth, you won't go sigmoid, you'll stay exponential. You'll just be shrinking instead of growing. To be sigmoid, you need the growth rate to vary.
  - withinboredom 1y ago
    Growth is not a function of users, though, it is a function of something else that *may* be exponential, for a time. Users don’t beget users (word-of-mouth doesn’t last forever; ad money has diminishing returns), and eventually your market will be saturated, so you can’t grow exponentially forever.
ocean_moist 1y ago
Yeah sigmoid is good. I kind of hint at this when I mention "saturate their TAM at some rate". You can think about it like we are looking at the concave up portion of the sigmoid only. The early growth phase.
mgraczyk 1y ago
They are sigmoids, but for some the plateau is 30 years in the future with a 5T market cap. For example Facebook's revenue is still increasing at an increasing rate, 21 years later
- alangibson 1y ago
  This is an incredibly important thing to understand. Buffet himself said it's better to be an average business in a great market that to be a great business in an average market.
  - ptero 1y ago
    Interesting. Not doubting this, but one of his sayings I saw many times is that "it is better to buy a great company at a good price than a good company at a great price", implying that great companies are worth significant premiums.
godelski 1y ago
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?
- nis251413 1y ago
  Big-O notation is about asymptotics. You have to approach something, and typically there is some infinity involved because if it is not, then you can just compute things instead of giving asymptotic approximations, or else you have 10^10*n and 0.001*n^2-10^20*n and the big-O asymptotics at infinity are useless for smaller numbers. I understand what OP tries to say but that's not really a good framing point for many reasons. If you want to talk about a finite period of time, use a regression model, not asymptotics. But that's probably also a more personal preference around using mathematics colloquially but also in a manner that is not a good metaphor and does not correspond with what the mathematical theory is referring to. And I am not sure at all whether it is very well understood "what part of the graph we're talking about", in the sense that the modern organization of economy is far from acknowledging the fact that resources on earth are actually finite. Talking about O(n) and O(n^2) or O(exp(n)) as if growth can be indefinite comes with a specific kind of mindset, and the frame used reflects this type of mindset.
  - godelski 1y ago
    > Big-O notation is about asymptotics. Excuse me, but what made you believe I do not understand this? I'm not sure what comment you're responding to, but it sure isn't mine. >> I took the author's use of O(n) vs O(n^2) as a framing point rather than a literal model. Honestly, the reason I said this is because from the article | 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). Along with their emphasis on "vaguely". I can forgive the author for bad verbage. It is a personal blog where they're not trying to sell anyone on a fully fledged out idea and appear to be trying to spur conversations. Especially considering it looks like they are an undergrad. Frankly, I can understand them despite the wrong words. Given this, it would require me to operate in bad faith by rejecting the main thing they are attempting to communicate by focusing on the details that ultimately don't matter to their claim. > If you want to talk about a finite period of time, use a regression model, not asymptotics They did. They said "startup". The whole time they bound the conversation to early businesses. I even directly stated this >> Considering startup as context I think we know what part of the graph we're talking about... Maybe you're referring to the preceding line >> Besides, we can approximate sigmoids with linear or quadratic functions when windowing them. Which again, same thing. My point is: you're derailing the conversation You are technically right, but you're derailing the conversation in an effort to prove your intellectual capabilities to a person who were not questioning them in the first place. You're flexing to the wrong group. You just responded to something my comment was never about. > I understand what OP tries to say but that's not really a good framing point for many reasons. So address what the OP tries to say, *and while doing so* you can add additional technical correctness. *This does not derail the conversation.* It continues the conversation and enhances it! You can do both! But as your comment stands (and bee_rider's), you just are moving the conversation away from what OP wanted to discuss and instead hyper-fixating on what they themselves said is not the best language.
danjl 1y ago
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.

withinboredom 1y ago

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.

jvanderbot 1y ago
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.
thaumasiotes 1y ago
> 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.
- nis251413 1y ago
  Sigmoid (or the logistic function specifically rather) is exponential until you get close to the "turning point" (or rather, its growth bounded from below by an exponential). It's as you approach that point that it becomes linear, and after that its growth decays. However you are sort of right that "churn" does not necessarily have to do with it being sigmoid because it will be anyway. It may be bring it earlier if the churn rate surpasses the user growth, but that's probably not important here.
  - thaumasiotes 1y ago
    If the churn rate surpasses user growth, you won't go sigmoid, you'll stay exponential. You'll just be shrinking instead of growing. To be sigmoid, you need the growth rate to vary.
- withinboredom 1y ago
  Growth is not a function of users, though, it is a function of something else that *may* be exponential, for a time. Users don’t beget users (word-of-mouth doesn’t last forever; ad money has diminishing returns), and eventually your market will be saturated, so you can’t grow exponentially forever.

ocean_moist 1y ago

Yeah sigmoid is good. I kind of hint at this when I mention "saturate their TAM at some rate". You can think about it like we are looking at the concave up portion of the sigmoid only. The early growth phase.

mgraczyk 1y ago

They are sigmoids, but for some the plateau is 30 years in the future with a 5T market cap. For example Facebook's revenue is still increasing at an increasing rate, 21 years later

alangibson 1y ago
This is an incredibly important thing to understand. Buffet himself said it's better to be an average business in a great market that to be a great business in an average market.
- ptero 1y ago
  Interesting. Not doubting this, but one of his sayings I saw many times is that "it is better to buy a great company at a good price than a good company at a great price", implying that great companies are worth significant premiums.

godelski 1y ago

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?

nis251413 1y ago
Big-O notation is about asymptotics. You have to approach something, and typically there is some infinity involved because if it is not, then you can just compute things instead of giving asymptotic approximations, or else you have 10^10*n and 0.001*n^2-10^20*n and the big-O asymptotics at infinity are useless for smaller numbers. I understand what OP tries to say but that's not really a good framing point for many reasons. If you want to talk about a finite period of time, use a regression model, not asymptotics. But that's probably also a more personal preference around using mathematics colloquially but also in a manner that is not a good metaphor and does not correspond with what the mathematical theory is referring to. And I am not sure at all whether it is very well understood "what part of the graph we're talking about", in the sense that the modern organization of economy is far from acknowledging the fact that resources on earth are actually finite. Talking about O(n) and O(n^2) or O(exp(n)) as if growth can be indefinite comes with a specific kind of mindset, and the frame used reflects this type of mindset.
- godelski 1y ago
  > Big-O notation is about asymptotics. Excuse me, but what made you believe I do not understand this? I'm not sure what comment you're responding to, but it sure isn't mine. >> I took the author's use of O(n) vs O(n^2) as a framing point rather than a literal model. Honestly, the reason I said this is because from the article | 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). Along with their emphasis on "vaguely". I can forgive the author for bad verbage. It is a personal blog where they're not trying to sell anyone on a fully fledged out idea and appear to be trying to spur conversations. Especially considering it looks like they are an undergrad. Frankly, I can understand them despite the wrong words. Given this, it would require me to operate in bad faith by rejecting the main thing they are attempting to communicate by focusing on the details that ultimately don't matter to their claim. > If you want to talk about a finite period of time, use a regression model, not asymptotics They did. They said "startup". The whole time they bound the conversation to early businesses. I even directly stated this >> Considering startup as context I think we know what part of the graph we're talking about... Maybe you're referring to the preceding line >> Besides, we can approximate sigmoids with linear or quadratic functions when windowing them. Which again, same thing. My point is: you're derailing the conversation You are technically right, but you're derailing the conversation in an effort to prove your intellectual capabilities to a person who were not questioning them in the first place. You're flexing to the wrong group. You just responded to something my comment was never about. > I understand what OP tries to say but that's not really a good framing point for many reasons. So address what the OP tries to say, *and while doing so* you can add additional technical correctness. *This does not derail the conversation.* It continues the conversation and enhances it! You can do both! But as your comment stands (and bee_rider's), you just are moving the conversation away from what OP wanted to discuss and instead hyper-fixating on what they themselves said is not the best language.

danjl 1y ago

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.