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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 p

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.

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.