With its $2 million urinals and other puzzling valuations, the pricing of fine art might seem too arbitrary, too opaque, too wildly jostled by randomness to submit to scientific investigation.

Yet a paper in the journal Science this month promised to explain why some talented artists become rich and famous, and others can’t quit their day jobs.

The answer, which was derived by a collaboration of physicists, social scientists, data experts and an art historian, is a scientific formulation of the old adage that it’s not what you know, but who you know, but also who the people you know, know, and who those people know.

The findings, while not counterintuitive, run counter to that secular American gospel of hard work as the one true road to success.

I soon discovered that one of the paper’s authors, Albert-Laszlo Barabasi, has just published a popular book on success more broadly: “The Formula: The Universal Law of Success.” He told me that people think the Science paper is about art, but it’s really about the way networks separate the stars from the also-rans in many areas. As a physicist, he’d been interested in the science of networks in nature, and eventually became fascinated by human networks and their patterns of well-connected nodes. How, he wondered, do these influence the trajectories of our lives?

What he found was that the less accurately the quality of a person’s performance can be measured, the more position in the network shapes the course of a career. At one end of the spectrum are individual sports, where performance is the key to success (you can’t be a tennis star unless you know how to win matches, no matter how connected you are).

Fine art is at the other end of this spectrum, he said. In the book, he uses the example of the urinal that Marcel Duchamp purchased from a plumbing store, then labeled “Fountain” and sent to an art show. A replica of the work sold for $1.7 million in 1999.

In other endeavors, from pop music to science, quality plays some role in success, but it often follows an asymptotic curve: Some people are much more skilled than others, but at the top, the curve levels off. Experts can tell good wine from bad, he said, but there’s no consensus on ranking within the top tier. Likewise, the differences among highly skilled practitioners in many fields is often infinitesimal, but stars get paid orders of magnitude more money.

Success depends to various degrees on performance and network positioning. The surprise is that the networking part is the more predictable, at least once you have enough data. Barabasi said the art investigation started when one of his colleagues discovered a data set that contained information on exhibits and sales for 500,000 artists, spanning a 35-year stretch. The researchers were able to use something like a Google page-ranking system to see how the different galleries and museums in that data set were connected to one another.

The network effect was so strong that the researchers found they could predict success decades in advance from nothing more than the names of the first five galleries where an artist displayed. The crucial factor of success was for an artist to get connected to one of the central nodes in the network — the Museum of Modern Art, Guggenheim and Metropolitan Museum of Art, among a few other highly selective venues. If you can get into any of these, you can get into the others, and command vast sums for your art. But how to get there?

One way was to start near the top by showing at galleries that had a direct connection to the big ones. Prospects were dimmer for those forced to start at the bottom, but some still attained stardom by displaying at less prestigious galleries that exchanged art with other galleries, that, ultimately, exchanged with the coveted hubs.

The trouble is, nobody knows which lesser galleries have the best path to those hubs, Barabasi said. Many artists will sweat and toil to exhibit their art, but they go around in circles because they don’t realize they are, in network terms, stuck on an island. Those who got off the islands did what Barabasi called “a relentless random search.” That is, they got lucky, but they increased their chances by getting their work placed in diverse galleries.

Quality does matter in art, of course, but since it can’t be measured, Barabasi said curators rarely make independent choices. They instead depend on validation from others. That’s why a painting called “The Man in the Golden Helmet” was the most popular work in the Bode Museum in Berlin when people thought it was painted by Rembrandt, but art professionals and museum-goers lost interest when they realized the painting was, in fact, the work a lesser artist.

With the science of networks, the values assigned to art become a lot less mysterious. For those who have the right connections, almost anything is possible, including the transformation of an ordinary urinal into a $2 million artwork.

Faye Flam is a Bloomberg Opinion columnist. She has written for the Economist, the New York Times, the Washington Post, Psychology Today, Science and other publications. She has a degree in geophysics from the California Institute of Technology.

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