Luck Versus Skill: The Role of Chance in Economic Success

By James Case

Success and Luck: Good Fortune and the Myth of Meritocracy. By Robert H. Frank. Princeton University Press, Princeton, NJ, April 2016. 208 pages, $26.95.

Robert Frank, professor of economics at Cornell University, is nothing if not prolific. In addition to a host of peer-reviewed publications, contributions to edited volumes, survey articles, book reviews, and opinion pieces, his curriculum vitae lists no fewer than thirteen books. Two are textbooks—one co-authored with Ben Bernanke, former Chairman of the Federal Reserve, and one a treatise on the distributional effects of foreign investment—and ten are mildly iconoclastic examinations of underpublicized aspects of the free market system, intended for popular audiences. Of the latter, the one under review seems destined to become the most controversial, concerning as it does the role of luck, chance, and good fortune—call it what you will—in the attainment of worldly (if not necessarily material) success.

Frank assumes that his latest book will provoke controversy, because he knows from experience how bitterly successful people can resent the merest suggestion that their success could be due—even in part—to something other than their own individual talent and hard work. As E.B. White put it, “Luck is not something you can mention in the presence of self-made men.” Frank learned White’s lesson long ago. Having written a column exploring the influence of seemingly minor chance events on the careers of successful people, and having been surprised by the volume and negativity of the resulting letters to the editor, he had accepted an invitation to appear on Fox Business. Rude awakening!

From the moment the segment began, the show’s host was in high dudgeon, objecting to the mere suggestion that his own celebrity—and that of others like him—could be due to anything other than talent, hard work, and willingness to bear risk! Frank was unable to get a word in edgewise. Only days later did it occur to him that the sputtering host had refuted his own argument. If he had indeed taken risk, his success was—by definition—due in part to random influences entirely beyond his control.

A book of this kind must rely heavily on anecdotal evidence, and Frank makes ample use of “war stories” to demonstrate the impact of seemingly random events on his own and others’ careers. Somewhat dramatically, he describes the misfortune that befell him one morning in 2007. Between sets of tennis, Frank had complained of nausea before losing consciousness and falling to the ground. Doctors later told him that he had suffered an episode of sudden cardiac death, instances of which are almost always fatal; the rare survivors are left severely impaired, both cognitively and otherwise. In Frank’s case, however, an ambulance appeared almost immediately—summoned from the scene of a nearby traffic accident at which it had not been needed—enabling EMTs to administer timely emergency care even as he was being transported (first by ambulance and then by helicopter) to a regional hospital boasting a state-of-the-art cardiac care unit. Had there not been an idle ambulance mere yards from the court, the outcome would likely have been quite different. Because one was on hand, Frank’s career continues!

Even luckier was actor James Doohan, who played Montgomery “Scotty” Scott on Star Trek. As a pilot and captain in combat with the Royal Canadian Artillery Regiment during World War II, he was struck by six bullets from friendly fire. One blew off his middle finger, four hit his leg, and one his chest. He survived for another sixty years, only because the last-named hit the silver cigarette case in his shirt pocket!

Actor Al Pacino, according to Frank, owes much of his Hollywood success to one highly improbable casting decision. Studio executives wanted Robert Redford, Warren Beatty, or Ryan O’Neal for the role of Michael Corleone in Francis Ford Coppola’s adaptation of Mario Puzo’s best-selling novel, The Godfather. But Coppola wanted the unknown Pacino, who actually looked Sicilian. He also wanted Michael Corleone, rather than his father Don, to be the film’s central character. What are the odds, Frank asks, that director Coppola would prevail over studio brass on both counts? And how might Pacino claim credit for either victory? He, one suspects, would be the first to concede that he caught a very lucky break in landing that career-defining role!

Perhaps even luckier was Bryan Cranston, who played the leading role in Breaking Bad, one of the most successful TV dramas of all time. Previously an obscure middle-aged supporting actor, he won four Emmy Awards in the show’s five seasons and is now one of the most sought-after actors in the profession. But he was offered the part only after John Cusack and Matthew Broderick turned it down. Was he not lucky that they did so?

Far more important, in the greater scheme of things, was the stroke of luck by which Microsoft came to own MS-DOS, the operating system designed for the original IBM personal computer. Ownership entitled the firm to collect a royalty on every “plug-compatible” PC sold. Unaware that such a device would soon occupy virtually every office desk in the developed world, IBM negotiators accepted Bill Gates’ offer to acquire, modify, and retain ownership of the “quick and dirty operating system” QDOS, developed by Seattle Computer Products Inc. In accepting that offer, IBM signed away an asset that would end up being worth hundreds of billions of dollars.

Persuasive as such anecdotes are, Frank does not rely on them alone to make his case – he does some modeling as well. In particular, he simulates a winner-take-all tournament in which each of the many contestants receives three component scores between 0 and 100: one for talent, one for effort, and one for luck. Each component score \(CS_?\)is drawn at random from a uniform distribution, and the three are combined into a final score FS as follows:

\[FS=(49 \times CS_\textrm{talent}+49 \times CS_\textrm{effort}+2 \times CS_\textrm{luck}) / 100.\]

Thus, 98% of a contestant’s final score is determined by his effort and skill, while a mere 2% is due to luck. Yet in the presence of many contestants, luck proves instrumental in determining the winner. Frank explains this possibly surprising fact by observing the following: because many of the merit scores \(CS_\textrm{effort}+CS_\textrm{talent}/2\) will fall between 95 and 100 and be tightly spaced, the addition of a small luck component can cause the order of the final scores to differ from that of the merit scores.

In a series of tournaments with 100,000 contestants each, the average luck score of winners was 90.23, and 78.1% of tournament winners did not have the highest merit score; there was usually more than one contestant with a higher merit score than the ultimate winner. The higer-merit contestants’ bad luck, combined with the winner’s good fortune, determined the final outcome. In the book’s appendix, Frank provides the results of various other tournaments in which the number of contestants varied from 1,000 to 10,000 to 100,000, while the weighting of the luck component varied from 1% to 2% to 5% to 10% to 20%, with qualitatively similar results in all cases. The winners always had high merit scores, but seldom the highest one. Most owed their success to a combination of good performance and good fortune!

One can quibble with Frank’s tournament design, which drew component scores from a uniform distribution rather than the normal distributions that ordinarily govern performance scores. But one could easily correct that oversight by replacing each of his component scores with sums of, say, three uniformly-distributed random variables, since the \(n\)-fold convolution of uniform distributions converges rapidly to the normal distribution. Frank’s design also fails to distinguish the one big break actors Pacino, Doohan, and Cranston received from the series of small incremental breaks likely to spur a typical climb to the top of the corporate ladder. But his point is well and clearly made, and lends strong support to his main contention that while a host of individuals exhibit both talent and hard work, relatively few manage to parlay those assets into worldly success. Plenty of equally talented and hardworking people never do manage to grasp the brass ring.

Finally, it should be mentioned that Frank is intimately familiar with so-called “happiness literature,” which seeks to determine how happy people are in various parts of the world and walks of life. In it he finds evidence that people who acknowledge luck as a significant contributor to worldly success, including their own, are on the whole happier than those who deny its influence, and are therefore less reluctant to share their good fortune by paying taxes and engaging in philanthropy.

Success and Luck is an important book, which takes a plausible approach to a difficult problem of genuine significance. It deserves to be widely read and publicly discussed.

James Case writes from Baltimore, Maryland.