The Geometry of Luck

You are sitting in front of a list of forty-eight songs by bands you have never heard of. You can listen to anything, rate it from one star to five and download what you like. Fourteen thousand people did exactly this in 2006, in what remains one of the cleanest experiments anyone has ever run on success.

Half of them saw only the names of the songs and the bands. The other half saw, beside each song, a small counter showing how many people before them had downloaded it. That was the entire experiment.

The researchers Salganik, Dodds and Watts (2006) did one more clever thing. They split the second half into eight separate "worlds," each starting from zero, each sealed off from the others. Then they let the worlds run. What came back should reshape how we think about success.

Inequality went up sharply when people could see what others were doing. Hits became bigger hits. Flops became bigger flops. The more striking finding was that the worlds disagreed with each other. The same song could top the chart in one world and sink to the bottom in another. Early downloads pulled in more downloads. Leaders fed off being leaders. What decided a song's fate was which one happened to get clicked first.

It remains the sharpest empirical demonstration of how outcomes in any market are shaped by social influence and therefore partly path-dependentPath DependencyEvery decision is the death of a thousand possibilitiesRead the essay↗. The successful song is successful because it caught the early tailwind.

The temptation, once that lands, is to draw a larger conclusion. If the same effort produces wildly different outcomes, we are performing agency inside a process that is already carved out to some degree. Effort and quality do matter, but maybe less than we like to believe.

A different frame

Everyone knows Viktor E. Frankl. One of his closest pupils is far less known. Alfried Längle worked with Frankl for many years and carried many of his ideas forward. In a conversation he once introduced me to his definition of success, which he also lays out in his book Sinnvoll leben (Längle, 2007).

A stone you let go of falls to the ground. Nobody calls that a success. The outcome was fully determined and you contributed nothing to it. Juggling three balls so that one is always in the air involves the same gravity, yet here we do speak of success, because goal-directed action has entered the lawful process and bent it toward an aim. At the other extreme sits pure chance. Running into an old acquaintance on the street is a pleasant event and nobody's achievement.

Success lives between these two poles, on the narrow strip where what you do actually changes what happens. Längle calls it the plane of action. On one side of that strip is Bemühen, deliberate effort, including skill, practice, attention and persistence. On the other side is Glück, the favourable conjunction of circumstance that "falls to" the effort from elsewhere. Every real success is a product of both. The German word Glück, he notes in passing, originally meant to close the gap. Effort reaches up to a certain height. What closes the rest of the distance is what we call luck.

Where effort ends and luck begins

Effort reaches up to a certain height. Whatever closes the remaining distance is luck. As one share grows the other shrinks. After Längle.

Two consequences. Since success requires both halves, neither can carry the full weight of explanation. Crediting yourself entirely for a success is as wrong as blaming yourself entirely for a failure. The depressive who reads every setback as personal incompetence and the narcissist who reads every win as personal genius are making the same error in opposite directions. Längle adds a caveat that keeps the symmetry honest. Repeated failure is not pure bad luck either. At some point the pattern stops being noise and becomes information about the effort.

And since the halves multiply rather than add, more effort raises the distribution of possible outcomes without ever guaranteeing any single one of them. We can prepare the ground. We can't make the seed sprout.

Much of what Längle talks about is what happens when people refuse this structure and chase the outcome directly. In German, the word for success already carries an essential part inside it. Erfolg kann nur er-folgen. Success can only follow.

There is an old joke Längle retells. A rabbi in desperate financial trouble begs God for a win in the lottery. Weeks pass. Nothing. He storms into the temple and accuses God of abandoning him. The voice of God answers. Rabbi, I see your need. But give me a chance. Buy at least a ticket.

Luck needs somewhere to land.

What you can actually do

There is still a practical question. Given that luck is real and partly outside our reach, are there ways to raise the probability of favourable luck events?

The answer is yes. Luck has a surface area. The larger the surface, the more opportunities pass through it.

Sam Matla (2024), building on Jason Roberts (2010), frames it as a multiplication. Luck is the product of three things. Surface area, the size of the target you present to the world. Position, the part of the world you are in. And staying power, the duration over which the previous two are sustained. Each factor has zero as a possible value. Any zero collapses the product. A large surface in a poor location is wasted. A perfect location with no staying power produces nothing.

The three factors of luck

Luck is surface area times position times staying power. Each factor can fall to zero. A single zero collapses the whole product.

Surface area is built primarily through what Roberts called doing-and-telling. Doing alone is not enough. The world cannot find work it does not know exists. Telling alone is not enough. There is nothing for the world to find. The product of the two scales the probability that the right person sees the right thing at the right time.

The mechanism behind this is the same one that drove the Music Lab cascades. Networks reward existing visibility with more visibility. The implication is that volume matters in a way that intuition resists. Skill compounds with reps. Signal emerges from variance. The single best video, post or product typically outperforms the next-best by an order of magnitude. Strategy cannot identify in advance which one it will be. Volume is how that lottery is run.

Position is built through environment and agency. The high-agency person, in George Mack's phrasing, treats the story given to them about what is possible as a story rather than a fact. They court rejection. They ask for unreasonable things. They follow up. They fly to meet someone in person when the meeting matters. They assume what looks fixed is in fact learnable. None of these moves looks dramatic in isolation. Aggregated over years, they shift the social and geographic region in which luck can find them.

Staying power is the simplest of the three to articulate and the hardest to live. Most people abandon a project at article ten, video twenty or year three, just before the regime that would have rewarded their persistence kicks in. Endurance over long horizons is the price of admission for any non-linear payoff. Curiosity is what makes the endurance bearable. Energy is what makes the curiosity sustainable. The three feed each other. None substitutes for the others.

What the luck is worth

Jim Collins ran a different kind of experiment. He and Morten Hansen (Collins & Hansen, 2011) studied pairs of public companies in volatile industries. One member of each pair was an outlier success. The other was a similar peer that failed to thrive. The hypothesis was that the outliers had been luckier. The data did not support it. When they coded discrete luck events across each pair's history, both members had received roughly comparable numbers of good and bad ones.

What separated the winners was something Collins called Return on Luck. The outliers got a higher return on every event of luck they encountered, both by extracting more upside from the good ones and by absorbing more of the impact of the bad ones.

Same luck, different return

Two people meet the same run of good and bad events. What differs is how much each one draws from the good and how much each absorbs from the bad.

Bill Gates and the IBM contract is the classic case. Several other people in 1980 had access to the same configuration of circumstances. Few had Gates's combination of preparation, paranoia and execution speed. The luck was widely distributed. The capacity to convert it was not.

If outcomes are partly random, the relevant skill is not the elimination of randomness, which is impossible. It is the conversion of randomness into outcome. Discipline, financial conservatism, what Collins calls productive paranoia, the readiness to act decisively at the moments that matter.

Two implications follow. The value of preparation is measured at the points of inflection rather than continuously. Most preparation looks wasted most of the time. It earns its keep in the rare moments when an opportunity arrives that the unprepared cannot capitalise on and the underprepared cannot survive. And surviving a bad luck event that destroys your peers is itself a high return on negative luck. Antifragility, in Taleb's vocabulary (2012), is the same idea seen from a different angle.

How to decide

The Music Lab tells us the world is path-dependent. The same starting point does not produce the same destination. Längle tells us the right orientation for a life lived inside such a world is values rather than outcomes, since outcomes are partly outside our reach but values are not. Surface area tells us we can shift the probability distribution of outcomes by widening our exposure to favourable ones. Return on Luck tells us that the same widening is wasted without the discipline to convert what arrives.

The decision-maker who measures themselves on outcomes in a path-dependent world will be either crushed by negative variance they did not deserve or inflated by positive variance they did not earn. The decision-maker who measures themselves on the quality of their inputs, which are within reach, has an evaluable signal that is independent of whether any single bet pays off. This is the operational meaning of Längle's redefinition of fulfilment. It is also what good poker players do. They keep making the right bets and trust the long run. Bad players make the right bet, lose the hand and conclude the bet was wrong. Act in ways that increase the probability that good luck finds you, while staying honest about the fact that you cannot make it find you.

Längle's line captures it. Ich kann nur das mir Mögliche tun, dies aber ganz. I can only do what is possible for me. And that, completely. The rest is the suspense of being alive.