Superlinear Returns

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| October 2023One of the most important things I didn't understand about the world
when I was a child is the degree to which the returns for performance
are superlinear.Teachers and coaches implicitly told us the returns were linear.
"You get out," I heard a thousand times, "what you put in." They
meant well, but this is rarely true. If your product is only half
as good as your competitor's, you don't get half as many customers.
You get no customers, and you go out of business.It's obviously true that the returns for performance are superlinear
in business. Some think this is a flaw of capitalism, and that if
we changed the rules it would stop being true. But superlinear
returns for performance are a feature of the world, not an artifact
of rules we've invented. We see the same pattern in fame, power,
military victories, knowledge, and even benefit to humanity. In all
of these, the rich get richer.
[1]You can't understand the world without understanding the concept
of superlinear returns. And if you're ambitious you definitely
should, because this will be the wave you surf on.It may seem as if there are a lot of different situations with
superlinear returns, but as far as I can tell they reduce to two
fundamental causes: exponential growth and thresholds.The most obvious case of superlinear returns is when you're working
on something that grows exponentially. For example, growing bacterial
cultures. When they grow at all, they grow exponentially. But they're
tricky to grow. Which means the difference in outcome between someone
who's adept at it and someone who's not is very great.Startups can also grow exponentially, and we see the same pattern
there. Some manage to achieve high growth rates. Most don't. And
as a result you get qualitatively different outcomes: the companies
with high growth rates tend to become immensely valuable, while the
ones with lower growth rates may not even survive.Y Combinator encourages founders to focus on growth rate rather
than absolute numbers. It prevents them from being discouraged early
on, when the absolute numbers are still low. It also helps them
decide what to focus on: you can use growth rate as a compass to
tell you how to evolve the company. But the main advantage is that
by focusing on growth rate you tend to get something that grows
exponentially.YC doesn't explicitly tell founders that with growth rate "you get
out what you put in," but it's not far from the truth. And if growth
rate were proportional to performance, then the reward for performance
p over time t would be proportional to pt.Even after decades of thinking about this, I find that sentence
startling.Whenever how well you do depends on how well you've done, you'll
get exponential growth. But neither our DNA nor our customs prepare
us for it. No one finds exponential growth natural; every child is
surprised, the first time they hear it, by the story of the man who
asks the king for a single grain of rice the first day and double
the amount each successive day.What we don't understand naturally we develop customs to deal with,
but we don't have many customs about exponential growth either,
because there have been so few instances of it in human history.
In principle herding should have been one: the more animals you
had, the more offspring they'd have. But in practice grazing land
was the limiting factor, and there was no plan for growing that
exponentially.Or more precisely, no generally applicable plan. There was a way
to grow one's territory exponentially: by conquest. The more territory
you control, the more powerful your army becomes, and the easier
it is to conquer new territory. This is why history is full of
empires. But so few people created or ran empires that their
experiences didn't affect customs very much. The emperor was a
remote and terrifying figure, not a source of lessons one could use
in one's own life.The most common case of exponential growth in preindustrial times
was probably scholarship. The more you know, the easier it is to
learn new things. The result, then as now, was that some people
were startlingly more knowledgeable than the rest about certain
topics. But this didn't affect customs much either. Although empires
of ideas can overlap and there can thus be far more emperors, in
preindustrial times this type of empire had little practical effect.
[2]That has changed in the last few centuries. Now the emperors of
ideas can design bombs that defeat the emperors of territory. But
this phenomenon is still so new that we haven't fully assimilated
it. Few even of the participants realize they're benefitting from
exponential growth or ask what they can learn from other instances
of it.The other source of superlinear returns is embodied in the expression
"winner take all." In a sports match the relationship between
performance and return is a step function: the winning team gets
one win whether they do much better or just slightly better.
[3]The source of the step function is not competition per se, however.
It's that there are thresholds in the outcome. You don't need
competition to get those. There can be thresholds in situations
where you're the only participant, like proving a theorem or hitting
a target.It's remarkable how often a situation with one source of superlinear
returns also has the other. Crossing thresholds leads to exponential
growth: the winning side in a battle usually suffers less damage,
which makes them more likely to win in the future. And exponential
growth helps you cross thresholds: in a market with network effects,
a company that grows fast enough can shut out potential competitors.Fame is an interesting example of a phenomenon that combines both
sources of superlinear returns. Fame grows exponentially because
existing fans bring you new ones. But the fundamental reason it's
so concentrated is thresholds: there's only so much room on the
A-list in the average person's head.The most important case combining both sources of superlinear returns
may be learning. Knowledge grows exponentially, but there are also
thresholds in it. Learning to ride a bicycle, for example. Some of
these thresholds are akin to machine tools: once you learn to read,
you're able to learn anything else much faster. But the most important
thresholds of all are those representing new discoveries. Knowledge
seems to be fractal in the sense that if you push hard at the
boundary of one area of knowledge, you sometimes discover a whole
new field. And if you do, you get first crack at all the new
discoveries to be made in it. Newton did this, and so did Durer and
Darwin.
Are there general rules for finding situations with superlinear
returns? The most obvious one is to seek work that compounds.There are two ways work can compound. It can compound directly, in
the sense that doing well in one cycle causes you to do better in
the next. That happens for example when you're building infrastructure,
or growing an audience or brand. Or work can compound by teaching
you, since learning compounds. This second case is an interesting
one because you may feel you're doing badly as it's happening. You
may be failing to achieve your immediate goal. But if you're learning
a lot, then you're getting exponential growth nonetheless.This is one reason Silicon Valley is so tolerant of failure. People
in Silicon Valley aren't blindly tolerant of failure. They'll only
continue to bet on you if you're learning from your failures. But
if you are, you are in fact a good bet: maybe your company didn't
grow the way you wanted, but you yourself have, and that should
yield results eventually.Indeed, the forms of exponential growth that don't consist of
learning are so often intermixed with it that we should probably
treat this as the rule rather than the exception. Which yields
another heuristic: always be learning. If you're not learning,

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