Success has no ceiling

Eight hundredths of a second

On 14 August 2016, in Rio de Janeiro, eight men ran the Olympic 100-meter final. Usain Bolt won in 9.81 seconds. Justin Gatlin was second in 9.89 and Andre De Grasse third in 9.91. The gap between gold and silver was 0.08 seconds, about 0.8 meters at the finish line. Everyone in the stadium, and everyone watching, agreed on who was fastest, and nobody could say the result was a matter of taste: performance in a race is as well measured as anything in life can be. But look at how little separated them. The slowest of the eight finished in 10.06 seconds, only about 2.5 percent behind the winner.

The gaps are small at every Games, and they vary. The winning margin over the runner-up was 2.1 percent when Bolt won in Beijing in 2008, 1.2 percent when he won in London in 2012, and 0.8 percent in Rio. In Tokyo in 2021 it was 0.4 percent, and in Paris in 2024 the first two runners were separated by five thousandths of a second, about five centimeters. Bolt’s world record of 9.58 seconds, set in Berlin in 2009, is only 3.7 percent less time than the 9.95 seconds of the first fully electronic sub-ten-second race, run at altitude at the 1968 Olympics in Mexico City, 41 years earlier. Human bodies have limits, and the people at the top of a measured field are packed against them. This is the third of the lectures’ ten rules: performance is bounded. Where performance can be measured, the best differ from the next best by a sliver.

A week on the bestseller list

Now look at the rewards. In the week of 15 to 19 September 2009, Dan Brown’s novel The Lost Symbol went on sale, and sold about 1.16 million copies in the United States in its first week, according to the sales tracker Nielsen BookScan. (The publisher’s “over two million” counted the United States, Britain, and Canada, and all formats.) On the New York Times hardcover fiction list dated 4 October, which by our reckoning covered sales through 19 September (the list is dated about two weeks after the sales it reports), The Lost Symbol was number one and The Last Song, a novel by Nicholas Sparks, was number two. Sparks’s book had itself been number one the week before. Readers can argue about which is the better book, and neither author is an unknown. Yet the sales of number one were enormous, and the lectures put the sales of number two at about a tenth as much. We cannot confirm that figure for Sparks’s book, and the lectures’ rules of thumb about how many copies it takes to reach the list (three or four thousand a week, ten thousand for the top) are folklore: nobody publishes the threshold, and it changes from week to week.

Better documented is a week in May 2013, when Dan Brown’s next novel, Inferno, sold 369,000 copies in the United States while the second-best-selling hardcover in the country sold 43,000, a ratio of about 9 to 1, according to Publishers Weekly. More generally, an economist studying 1,217 hardcover novels published in 2001 and 2002 found that the top 12 titles, 1 percent of the sample, took a quarter of all the sales in their first six months; the 205 titles that made the Times list took 84 percent. The typical novel peaked at 486 copies a week. Compare that with the 18,438 copies sold in its best week by the median novel that made the list, and with the 1.16 million copies of The Lost Symbol in its first week.

That is the fourth rule: success is unbounded. The runners finished within a few percent of one another; the books sold hundreds of times more than the typical title, and the gap between first and second was a multiple, not a percentage. The contrast is not a paradox. Performance is limited by the person: a writer can write only so many words, a runner can run only so fast. Success is not a property of the person at all. It is what a community gives, and a community can give a thousand times more to the one it prefers, because a reader’s choice costs the reader almost nothing and one popular book can be printed for millions at a small extra cost. The economist Sherwin Rosen worked out this logic in 1981 in a paper called “The economics of superstars”: when buyers will not accept two mediocre performances in place of one excellent one, and one performer can serve a huge market, small differences in talent turn into large differences in reward, and a few people dominate a field.

Success breeds success

If the world rewards a near-equal a hundred times more, how does it pick the one? A fifth rule offers the beginning of an answer: success breeds success. A person who is already noticed is more likely to be noticed again, whether or not they are better. The sociologist Robert Merton gave this a name in 1968, after a verse of the Gospel of Matthew (“unto every one that hath shall be given”), and called it the Matthew effect. Drawing on interviews with American Nobel laureates, he argued that famous scientists tended to get the credit for joint work and unknown scientists tended to be overlooked. In 1976 the information scientist Derek de Solla Price modeled a process in which each new citation of a paper is more likely to go to papers that already have many, and called it cumulative advantage. This is the “rich get richer” mechanism of Course 16, in which new links attach to nodes that already have many.

Plausible, but how would you test it? The trouble is that famous people may simply be better. To separate the two, you must hand out early success at random to people who are otherwise alike, and watch what happens. That is a randomized experiment, and several have been done.

In the first, in 2012, the sociologists Michael Restivo and Arnout van de Rijt took the most active 1 percent of editors of the English-language online encyclopedia, picked 200 of them at random, and split them into two groups of 100. Editors can give one another a small digital award, called a barnstar, to thank them for work. The researchers gave a barnstar to the people in one group and nothing to the other. The two groups were alike in everything else, including how much they had edited before. Three months later, 12 of the 100 who had received a barnstar had been given further barnstars by other editors (14 awards in all), against only 2 of the 100 who had received nothing (3 awards). The difference was statistically significant, and the people who were awarded were also a little more likely to keep editing. A single early token of status made later tokens more likely.

In 2014 the same group published a larger test of the idea, in four places at once: crowdfunding projects on Kickstarter (293 of them), reviews of products on a review site (481), the encyclopedia editors again (521), and petitions on a petition site (200). In each, they gave a random sample of ordinary cases an early success: a small donation, a “very helpful” rating, an award, twelve signatures. Everywhere, the cases that got a push were more likely to get more later. On Kickstarter, 70 percent of the projects that received a small early donation got later donations from other people, against 39 percent of those that did not. For the reviews it was 90 percent against 77. The effects did not fade by the end of the observation periods.

But the authors drew a more careful conclusion than the slogan. Where a random early success gave a clear boost, a bigger boost gave almost nothing more: a donation of 1 percent of a project’s goal worked about as well as a donation of 10 percent, and four early ratings did hardly better than one. They called it decreasing marginal returns: the first success matters, the fourth adds little. Some of the totals were borderline, and a later replication on petitions, with 400 of them, found the effect small. The authors concluded that cumulative advantage plays a “more modest role” in explaining inequality than often thought. In the language of this course: success does breed success, but a lucky start by itself does not produce runaway winners.

A different experiment looked at votes. In 2013 Lev Muchnik, Sinan Aral, and Sean Taylor gave each new comment on a news-sharing website a random “up” vote, a random “down” vote, or nothing. Over five months and 101,281 comments, those that began with one up vote were 32 percent more likely to get an up vote from their first viewer, and ended with a final average score 25 percent higher than the comments left alone. A random down vote was corrected by the crowd, which up-voted those comments back to normal. One site and one kind of vote, but it showed that a single unearned tick could grow.

Eight worlds, eight winners

The most famous experiment of this kind built a small music market. In 2004 and 2005, Matthew Salganik, Peter Dodds, and Duncan Watts invited 14,341 visitors to a website popular with teenagers to listen to 48 songs by unknown bands, rate them, and download any they liked for free. The visitors were split at random. Some, the “independent” group, saw only the titles and made up their own minds. The rest were sent into one of eight separate “worlds,” in each of which they could also see how many times each song had been downloaded by earlier visitors in that world. Each world began empty and developed on its own, like eight parallel universes in which the same 48 songs competed.

In all eight worlds, a few songs took a much larger share of the downloads than in the independent group, so inequality was higher. And the worlds disagreed: a song that became the hit of one world might sit in the middle of another. So the results were less predictable too, and the stronger the social signal (in the second experiment the songs were ranked in a list), the more unequal and the more unpredictable. In the authors’ words, paraphrased: the best songs were never failures and the worst were never hits, but nearly anything in between could happen. “Best,” here, means popular in the independent group, which is a weaker definition than it sounds, and the participants were mostly American teenagers.

A follow-up, in 2008, asked whether a false signal could lock in a bad outcome. For a new batch of 12,207 participants the researchers swapped the download counts, so that the most popular song looked like the least popular and the reverse. Most songs showed a self-fulfilling prophecy: a song that appeared popular got more downloads. But the market did not stay inverted. The very best songs recovered their popularity in the long run. Quality did not decide everything, and it did not count for nothing.

Luck, persistence, and what the winners don’t show

If early luck matters, should you simply keep trying? The popular answer is yes, and it comes with stories. J. K. Rowling’s first Harry Potter manuscript was turned down by about a dozen publishers, according to a 2003 newspaper profile, before Bloomsbury paid an advance of £2,500. But these are stories about people who eventually succeeded, and we do not hear from the others. Two studies tried to do better than anecdotes.

The first, in 2019, looked at young scientists who applied for their first major grant from the US National Institutes of Health. It compared those who just missed the funding line with those who just made it, 623 near-misses and 561 narrow wins, who were nearly identical at the time of the decision. In the next ten years the near-misses were more likely to publish a highly cited paper (16 percent of their papers, against 13 percent for narrow winners in the first five years). It was a striking finding: a setback made some people stronger. But the study also found that the near-misses were more likely to drop out of the system altogether, so that those who remained were a selected group, and a 2025 re-analysis across 14 funding programs found that the setback effect was not robust across funders, though the Matthew effect itself, the advantage of winning, replicated well. A second 2019 study, of grants, start-ups, and terrorist attacks, found that the number of failed attempts did not separate those who eventually succeeded from those who did not. What differed was whether each new attempt built on the best of the earlier ones. Persistence is not a strategy by itself: trying again helps if you learn from the last try.