Success stories become cleaner in hindsight.

The uncertain launch becomes a master plan. The chance introduction becomes evidence of superb networking. The employer who happened to say yes disappears from the story, while the person who reached the top can look as though they were always going to get there.

A computer model built by three Italian researchers asks what happens when we put the missing accidents back in.

Alessandro Pluchino, Alessio Emanuele Biondo and Andrea Rapisarda created 1,000 fictional people, followed them through 40-year careers, and allowed lucky and unlucky events to cross their paths. Their study in Advances in Complex Systems produced a result that is easy to repeat too broadly: the highest-talent group supplied the most successful person in only 3 per cent of the simulations examined for that comparison.

That does not make effort pointless, and it does not establish that 97 per cent of success in real life is luck. The experiment was a deliberately stripped-down world designed to expose one mechanism. Under those rules, talent improved people’s average prospects, but it did not reliably identify who would occupy the most extreme peak.

Every fictional career began with the same capital

The model placed 1,000 stationary agents on a square grid. Each began with ten units of capital, the paper’s simplified measure of success. A career lasted 40 years, from age 20 to 60, divided into 80 six-month periods.

The agents differed in one personal quality: talent. The term was intentionally broad, combining traits such as intelligence, skill, effort, perseverance and appetite for risk into a single number between zero and one. Talent remained fixed throughout a career.

Scores followed a bell-shaped distribution centred on 0.6, with a standard deviation of 0.1. Most of the population therefore sat near the middle. Extremely low and extremely high scores were uncommon.

This is an abstraction before it is anything else. Actual people learn, tire, change fields, gain connections, face prejudice, inherit advantages and make choices that alter the opportunities available to them. The model temporarily set those complications aside to ask a narrower question: if talent is distributed normally but success becomes highly unequal, can random encounters help explain the difference?

Luck wandered through the model

The researchers added 500 moving event points to the grid. Half represented good luck and half bad luck. At each six-month step, the events moved randomly and could pass close enough to affect an agent.

When an unlucky event arrived, the agent’s capital was cut in half. When a lucky event arrived, it created an opportunity to double capital, but the person did not automatically benefit. The model generated a random number and compared it with the agent’s talent. An agent with talent of 0.8 had an 80 per cent chance of exploiting that particular opportunity. Someone with talent of 0.4 had a 40 per cent chance.

In other words, ability had a built-in advantage. More talented agents were more likely to convert good fortune into a gain. What talent could not control was whether an opportunity crossed a person’s path in the first place, or whether the next encounter would instead erase half of what had been accumulated.

The distinction matters. The paper did not pit hard work against pure randomness and declare randomness the winner. It modelled success as an interaction: a person needed enough ability to use an opening, and enough openings had to arrive.

What the 3 per cent figure actually describes

In one run, the most successful agent had a talent score of 0.61, almost exactly the population average, and finished with 2,560 units of capital. The most talented agent scored 0.89 but ended with 0.625, below the starting level of ten.

One run might be a curiosity, so the researchers repeated the 1,000-career simulation 100 times. They defined the highest-talent band as scores above 0.8, more than two standard deviations above the mean. A member of that group became the single most successful person in only three of the 100 worlds.

That is the denominator behind the headline’s 3 per cent. It is not a claim that one uniquely most talented person won three times. Nor did the model observe 1,000 real careers. It ran 1,000 artificial careers repeatedly under the same chosen rules.

The researchers later examined 10,000 runs. Winners had an average talent score of about 0.667, above the wider population’s 0.6 average but nowhere near the far end of the scale. The people at the top were generally capable. They were also drawn from the broad, densely populated middle-to-upper range and happened to receive unusually favourable sequences of events.

This is why the wording “moderately talented” needs care. It does not mean mediocre. In the model, the typical winner was more talented than average. The surprising part is that being at the absolute top of the talent distribution was neither necessary nor sufficient for finishing first.

Multiplication turns a good run into a gulf

The model’s arithmetic makes luck unusually consequential.

Begin with ten units of capital. Five converted opportunities in succession produce 20, 40, 80, 160 and then 320. Three more produce 2,560. Each gain enlarges the base on which the next gain acts. An unlucky event works in the opposite direction by cutting the current total in half.

Talent scores, by contrast, occupied a fairly narrow range. A person at 0.8 was substantially better at exploiting a lucky encounter than someone at 0.6, but the difference between them could be overwhelmed if the second person met many more good events. When gains compound, the sequence of encounters matters as well as the conversion rate.

Selecting only the single biggest winner intensifies the effect. The question is no longer who performs well on average, but who reaches the most distant point in the tail. Outliers are often produced by an unusual combination: enough competence to keep converting opportunities and a run of opportunities rare enough that few others receive it.

Silicon Canals recently looked at the broader temptation to read success as a clean reward for merit. The mechanics here sharpen that point. A result can contain real information about ability while still being a noisy measure of it, especially at the very top.

Talent still mattered, just differently

The most talented people did better on average. Across the simulations discussed in the open version of the paper, agents in the highest-talent region finished with average capital of roughly 63 units, compared with about 33 for agents near the population mean.

That is not a small distinction. It says capability increased the expected return from the same kind of fortunate encounter. But an average is not a guarantee for any one person, and it does not determine which individual will become the largest outlier.

The researchers also found that only 32 per cent of agents with talent above 0.7 finished richer than they began. In their artificial world, strong ability without enough usable opportunities could remain largely invisible.

There is a practical difference between saying “talent does not matter” and saying “outcomes do not measure talent cleanly.” The first invites resignation. The second invites better judgement.

A missed promotion may not prove someone lacked ability. A spectacular exit may not prove its founder could reproduce the outcome under different conditions. Results matter, but treating them as a complete audit of character or competence gives chance more credit while pretending to give it none.

The model is an argument, not a census of working life

The paper’s precision can make its world sound more realistic than it is. “Talent” is one fixed number. Agents do not choose where to stand. Lucky and unlucky events arrive from outside. A success doubles capital, a setback halves it, and the same rules apply for four decades.

Real careers contain feedback loops the model does not attempt to reproduce. Money can buy education and time. Status attracts invitations. Networks can be cultivated. Employers discriminate. Illness, caregiving, citizenship and family wealth alter exposure to risk. People sometimes create their own luck by publishing, applying, moving or speaking to more people, although even those actions depend on resources and circumstances.

The simulation therefore cannot tell us that a given billionaire, scientist or artist succeeded mainly because of luck. It cannot estimate a universal percentage of achievement caused by chance. Change the assumptions, and the numerical result can change with them.

What it can do is demonstrate plausibility. A society may begin with talent distributed in a fairly ordinary bell curve and still end with success concentrated among a tiny group, without assuming that the winners are proportionately more capable than everyone else. Multiplicative rewards and uneven exposure to opportunity are enough to create a wide gap.

The work later received the 2022 Ig Nobel Prize in economics. The playful recognition should not obscure the sober question beneath it: how confidently should institutions infer merit from outcomes shaped by chance?

A fairer system gives ability more than one chance to appear

The authors extended the model to research funding. Strategies that spread small grants widely, or retained an element of randomness among eligible candidates, often produced more progress than concentrating all resources on the people who had already done best.

That is not a ready-made policy for every laboratory or workplace. It follows from this model’s rules and should be treated as a prompt for testing, not a universal formula. Still, the underlying institutional question is useful.

If past success partly reflects past opportunity, repeatedly giving the next opportunity only to previous winners can harden an accident into a hierarchy. Organizations can reduce that error by widening early access, judging the quality of decisions as well as outcomes, keeping second chances available and making several modest bets instead of one supposedly certain bet.

For individuals, the conclusion is humbler. Preparation still matters because it raises the chance that an opening becomes something useful. So can increasing one’s exposure to possible openings where that is feasible. Neither action grants control over timing, health, gatekeepers or the random event that changes a career.

Luck is not an excuse to stop developing skill. It is a reason to be cautious about worshipping winners, blaming everyone who falls short, or confusing a rank with a measurement of human worth.

The simulated winners were usually capable people who met an extraordinary run of favourable events. The model’s most credible lesson is not that talent loses. It is that talent and opportunity meet, while the success story usually remembers only one of them.