1/
Get a cup of coffee.
In this thread, I'll walk you through some key concepts related to Survival, Resilience, and Aging:
- Conditional Lifetime Probabilities,
- The Force of Mortality,
- The Lindy Effect, and
- Taleb's Turkey.
(h/t @nntaleb)
Get a cup of coffee.
In this thread, I'll walk you through some key concepts related to Survival, Resilience, and Aging:
- Conditional Lifetime Probabilities,
- The Force of Mortality,
- The Lindy Effect, and
- Taleb's Turkey.
(h/t @nntaleb)
2/
Suppose a restaurant, on average, stays open for 8 years before shutting down.
And suppose Bob has a restaurant -- that has been open for 3 years now.
How much longer should we expect Bob's restaurant to stay in business?
Suppose a restaurant, on average, stays open for 8 years before shutting down.
And suppose Bob has a restaurant -- that has been open for 3 years now.
How much longer should we expect Bob's restaurant to stay in business?
3/
We may be tempted to answer: 5 years.
After all, restaurants last 8 years on average. And Bob is already 3 years in. So, on average, he has 8 - 3 = 5 years left, right?
Not necessarily.
This 8 - 3 = 5 logic may lead us very far off the mark.
We may be tempted to answer: 5 years.
After all, restaurants last 8 years on average. And Bob is already 3 years in. So, on average, he has 8 - 3 = 5 years left, right?
Not necessarily.
This 8 - 3 = 5 logic may lead us very far off the mark.
4/
Why?
Because 8 years is the average lifetime across ALL restaurants -- those that survived their first 3 years AND those that didn't.
The statistics of these two groups may be VERY different.
Why?
Because 8 years is the average lifetime across ALL restaurants -- those that survived their first 3 years AND those that didn't.
The statistics of these two groups may be VERY different.
5/
Lots of new restaurants open their doors each year.
But the restaurant business is tough. Failure rates are high. Many new restaurants may not even survive 1 year.
Just the fact that Bob has survived 3 years in this environment may mean he's doing something right.
Lots of new restaurants open their doors each year.
But the restaurant business is tough. Failure rates are high. Many new restaurants may not even survive 1 year.
Just the fact that Bob has survived 3 years in this environment may mean he's doing something right.
6/
Maybe people like Bob's food.
Or maybe Bob is unusually talented as a restaurant operator.
So, the key question to ask is: what's the average lifetime AMONG restaurants that have survived 3 years?
Maybe people like Bob's food.
Or maybe Bob is unusually talented as a restaurant operator.
So, the key question to ask is: what's the average lifetime AMONG restaurants that have survived 3 years?
7/
This is a *CONDITIONAL* probability question.
We DON'T want the average lifetime across ALL restaurants. That's misleading.
We ONLY want the average of restaurants that meet a *specific* condition -- namely, surviving 3 years. That's far more representative of Bob.
This is a *CONDITIONAL* probability question.
We DON'T want the average lifetime across ALL restaurants. That's misleading.
We ONLY want the average of restaurants that meet a *specific* condition -- namely, surviving 3 years. That's far more representative of Bob.
8/
For this, we need to have a *model* for how restaurants tend to fail over time.
How many restaurants don't make it past Year 1, how many fail in Year 2, etc.
For example, here's one such model:
For this, we need to have a *model* for how restaurants tend to fail over time.
How many restaurants don't make it past Year 1, how many fail in Year 2, etc.
For example, here's one such model:
9/
According to this model:
We open a restaurant. It has a 50% chance of dying in Year 1.
IF we make it past Year 1, it has a 25% chance of dying in Year 2.
And beyond Year 2, there's a 5% chance of dying in any subsequent year.
According to this model:
We open a restaurant. It has a 50% chance of dying in Year 1.
IF we make it past Year 1, it has a 25% chance of dying in Year 2.
And beyond Year 2, there's a 5% chance of dying in any subsequent year.
10/
This is a simple model. But it has several useful features.
First, it's a "Markov Chain". We start at a particular "state". And each year, we move to a possibly different state -- based on the outcome of a random, coin-flip type event.
For more:
This is a simple model. But it has several useful features.
First, it's a "Markov Chain". We start at a particular "state". And each year, we move to a possibly different state -- based on the outcome of a random, coin-flip type event.
For more:
https://twitter.com/10kdiver/status/1383471136868995079
11/
Second, this Markov Chain has exactly one "absorbing state" -- namely, death.
That is, once our restaurant dies, we stay in this dead state forever. There's no coming back from death. Because death is "absorbing".
Second, this Markov Chain has exactly one "absorbing state" -- namely, death.
That is, once our restaurant dies, we stay in this dead state forever. There's no coming back from death. Because death is "absorbing".
12/
Third, our restaurant gets *harder* to kill with each surviving year: 50% chance of death in Year 1 --> 25% in Year 2 --> 5% in Years 3 and beyond.
This is called "aging in reverse".
It's the *opposite* of how humans and other living beings work for the most part.
Third, our restaurant gets *harder* to kill with each surviving year: 50% chance of death in Year 1 --> 25% in Year 2 --> 5% in Years 3 and beyond.
This is called "aging in reverse".
It's the *opposite* of how humans and other living beings work for the most part.
13/
As living things get older, they usually become *more* (not *less*) prone to death.
80 year old humans are generally *more* likely to die before they turn 81, than 40 year old humans are before they turn 41.
But *restaurants* may work differently.
As living things get older, they usually become *more* (not *less*) prone to death.
80 year old humans are generally *more* likely to die before they turn 81, than 40 year old humans are before they turn 41.
But *restaurants* may work differently.
14/
In fact, even with humans, many societies/countries have high *infant mortality*.
That is, infants tend to be more prone to death. But past a certain age (5 years or so), this "prone-ness to death" starts decreasing. And then it picks up again in old age.
Like so:
In fact, even with humans, many societies/countries have high *infant mortality*.
That is, infants tend to be more prone to death. But past a certain age (5 years or so), this "prone-ness to death" starts decreasing. And then it picks up again in old age.
Like so:
15/
This "prone-ness to death" has another name: the Force of Mortality.
It's the probability of encountering death within a short time interval, at any given age.
The "Force of Mortality" vs "Age" graph tells us what kind of *aging* a particular system exhibits:
This "prone-ness to death" has another name: the Force of Mortality.
It's the probability of encountering death within a short time interval, at any given age.
The "Force of Mortality" vs "Age" graph tells us what kind of *aging* a particular system exhibits:
16/
If we apply the basics of probability to our restaurant aging model, we can calculate both the expected life of a restaurant (8 years) and the *conditional* expected life left for Bob's restaurant.
Note: The latter is NOT 8 - 3 = 5 years.
It's actually 19 years!
If we apply the basics of probability to our restaurant aging model, we can calculate both the expected life of a restaurant (8 years) and the *conditional* expected life left for Bob's restaurant.
Note: The latter is NOT 8 - 3 = 5 years.
It's actually 19 years!
17/
Thus, aging in reverse is wonderful.
With each surviving year, the expected remaining life of a business that exhibits this type of aging gets longer and longer.
Such businesses tend to have "moats". Over time, competitors tend to find them harder and harder to destroy.
Thus, aging in reverse is wonderful.
With each surviving year, the expected remaining life of a business that exhibits this type of aging gets longer and longer.
Such businesses tend to have "moats". Over time, competitors tend to find them harder and harder to destroy.
18/
For investors, businesses that "age in reverse" are likely to generate future cash flows that, a) last longer, and b) are more certain.
This in turn means investors can pay a bit more for such businesses, and still do reasonably well in the long run.
For investors, businesses that "age in reverse" are likely to generate future cash flows that, a) last longer, and b) are more certain.
This in turn means investors can pay a bit more for such businesses, and still do reasonably well in the long run.
19/
The Lindy Effect, popularized by @nntaleb in his wonderful book "Antifragile", is a particular kind of "aging in reverse".
Here, it's not enough if expected future life just *increases* with each surviving year. It has to be *proportional* to the number of years survived.
The Lindy Effect, popularized by @nntaleb in his wonderful book "Antifragile", is a particular kind of "aging in reverse".
Here, it's not enough if expected future life just *increases* with each surviving year. It has to be *proportional* to the number of years survived.
20/
And for the mathematically inclined, here's a wonderful paper highlighting several interesting Lindy-related factoids.
For example, if a system obeys the Lindy Effect, its lifetime has to follow an 80/64 Fat Tailed Pareto Distribution.
doi.org/10.1016/j.phys…
And for the mathematically inclined, here's a wonderful paper highlighting several interesting Lindy-related factoids.
For example, if a system obeys the Lindy Effect, its lifetime has to follow an 80/64 Fat Tailed Pareto Distribution.
doi.org/10.1016/j.phys…
21/
Another @nntaleb book, The Black Swan, contains a thoughtful cautionary example: Taleb's Turkey.
This parable highlights the dangers of extrapolating past data without understanding its root cause.
In business terms: mere *survival* may not imply a *moat*.
Another @nntaleb book, The Black Swan, contains a thoughtful cautionary example: Taleb's Turkey.
This parable highlights the dangers of extrapolating past data without understanding its root cause.
In business terms: mere *survival* may not imply a *moat*.
22/
So, how do we tell whether our portfolio companies are Lindys or Turkeys?
Lindys keep expanding their moats. Over time, they get harder and harder to kill.
Turkeys are just temporarily lucky. They're not harder to kill just because they've been in existence for a while.
So, how do we tell whether our portfolio companies are Lindys or Turkeys?
Lindys keep expanding their moats. Over time, they get harder and harder to kill.
Turkeys are just temporarily lucky. They're not harder to kill just because they've been in existence for a while.
23/
A final thought:
This thread contained many concepts in *conditional* probability -- restaurant lifetimes, the Force of Mortality, the Lindy Effect, etc.
Conditional probability is often un-intuitive.
But it pays to learn how to do it correctly.
A final thought:
This thread contained many concepts in *conditional* probability -- restaurant lifetimes, the Force of Mortality, the Lindy Effect, etc.
Conditional probability is often un-intuitive.
But it pays to learn how to do it correctly.
https://twitter.com/ProbFact/status/1250816982536110080?s=20
24/
Thank you very much for reading all the way to the end.
You've survived this long. So, I confidently expect you to survive several more long threads in the coming weeks and months.
Please stay safe. Enjoy your weekend!
/End
Thank you very much for reading all the way to the end.
You've survived this long. So, I confidently expect you to survive several more long threads in the coming weeks and months.
Please stay safe. Enjoy your weekend!
/End
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