Matthew, Lindy, and Power laws

Statisticians love the normal distribution; it’s familiar, and reassuring. Its symmetrical bell shape reveals a world where most things are average, and only a small quantity falls outside the norm.

When it applies, Normal distribution — also called Gaussian distribution — makes calculating odds and projections easy and accurate. A Gaussian curve paints a picture where developments are predictable and manageable; it is the statistical tool of choice because of its versatility and intuitive nature. While many phenomena like human height, test scores, and tree leaf sizes are normally distributed; life’s most important elements are not: wealth, natural disasters, wars, and city sizes do not occur on a Gaussian curve.

The normal distribution doesn’t drive the world; the engine of most large-scale phenomena is power laws. In the grand scheme of things it’s fat-tail distributions that matter; they distort and create chaos; they produce a world where the extremes dominate and give us the Matthew and Lindy effects.

The Matthew effect

For to every one who has will more be given, and he will have abundance; but from him who has not, even what he has will be taken away.

— Matthew 25:29.

This Bible verse from the parable of talents has given us what we call today the Matthew effect. In these secular and materialist times we often hear: “The rich get richer and the poor get poorer”. This is the Matthew effect in action.

In athletics the most able and talented kids are selected by the best coaches, hired by the most competitive teams, they get intense and focused training. With this special attention their natural talent increases faster than their less skilled peers. Kids with subpar athletic abilities have to work extra hard to overcome their deficit; they have to close the gap with fewer resources, an extremely difficult feat.

With friends and relationships it’s the same. People with many friends and acquaintances can easily extend their network. Others are naturally pulled into their social orbit, their connections let them meet strangers and bond with other personable folks. Loners on the other hand, gradually lose the few connections they have; people move away, get estranged, or die. Introverts’ social skills atrophy over time, making it harder to break out of their reclusion.

This is especially obvious with wealth. Someone with millions of dollars will get better investment opportunities, and lower costs proportional to their wealth. An investor with a meager fortune will have lower returns and higher fees, fees that will eat a large portion of their smaller returns. The poor have to be more conservative with their money, lest they be wiped out; this, in turn, reduces their upside. Without redistributive policies or financial disasters over time the effects compound and the wealth gap grows.

This is why Matthew effects generate fat tails rather than bell curves. When the rich get richer because wealth compounds, outcomes don’t regress to a mean; they run away from it.

The Lindy effect

Matthew explains accumulation across people; Lindy explains it across time.

Lindy’s was a deli in New York City, unremarkable except for its location near the Broadway theaters. Show business people gathered there to gossip about their peers, and in a 1964 New Republic article, Albert Goldman recorded a folk theorem the comedians had worked out: a performer’s career exposure seemed roughly fixed, so the more TV time a comic had already had, the less future he could expect.

Benoit Mandelbrot later inverted this observation for things that don’t biologically age, like books, technologies, and ideas, arguing that their life expectancy grows with their age. Nassim Taleb popularized this version as the “Lindy effect,” illustrating it with Broadway shows: a production that has already run 100 nights can be expected to run about 100 more, while the youngest shows are the most vulnerable to early closing.

The longer something survived, the longer it’s expected to survive.

The New Testament, Quran, and Torah are more than a thousand years old, and are still the most important books in the world despite the global trend of secularization. The Catholic Church may look outdated, but at 2000 years old it’s likely to survive longer than most modern nation states.

Gold, despite its limited utility in the modern world, is still an important store of value. For five thousand years, gold has been a marker of wealth and status. It is certain that gold will still be valuable long after all the modern fiat currencies have disappeared from circulation.

OpenAI and Anthropic may look formidable in 2026, but their young age doesn’t bode well for their long-term success. According to the Lindy effect, in 50 years Microsoft has a better chance of still being a going concern than today’s AI behemoths.

The Gaussian hammer’s limited power

The world isn’t normally distributed. Despite our desire for stability and predictability, the universe is chaotic, and our best statistical tools can’t help us make complete sense of it. Power laws are everywhere, and they wreak havoc. While Gaussian distribution is a powerful tool, it can mislead us into believing that it’s applicable everywhere.

Years ago I took a statistics class and this was never addressed. The assumption was that central limit theorem was omnipresent, and that variables were generally normally distributed. When results didn’t fit, we were told the measurement must involve multiple underlying variables, all, of course, normally distributed.

When one has a Gaussian hammer everything looks like a normal nail. That’s just not how the world works.