The Success Equation. Michael J. Mauboussin

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      Where an activity lies on the continuum has important implications for making decisions. So our initial goal is to place activities properly on the continuum between skill and luck. Naturally, there are variables that make this an elusive task. For example, the skills of athletes shift as they age, and most companies lose their competitive advantages as new technologies emerge. But having some sense of where an activity falls on the continuum is of great value. Here are some ways that untangling skill and luck can be very useful in guiding our thinking and in evaluating events.

      Take Sample Size into Account

      To assess past events properly, consider the relationship between where the activity is on the luck-skill continuum and the size of the sample you are measuring. One common mistake is to read more into an outcome than is justified. Howard Wainer, a distinguished research scientist for the National Board of Medical Examiners and an adjunct professor of statistics at the University of Pennsylvania, makes this point by identifying what he calls, “the most dangerous equation.” Derived by Abraham de Moivre, a renowned French mathematician, the equation states that the variation of the mean (average) is inversely proportional to the size of the sample. This says that small samples display much larger variation (measured by standard deviation) than large samples in activities that involve a large dose of luck.²⁴ You can visualize the mean and standard deviation with the bell curve, the shape that traces the distribution. The largest number of observations is close to the top of the bell, near the mean, or average. From the top of the bell, the curve slopes down the sides symmetrically with an equal number of observations on each side. Standard deviation is a measure of how far the sides of the bell curve are from the average. A skinny bell curve has a small standard deviation, and a fat bell curve has a large standard deviation.

      A small number of results tell you very little about what's going on when luck dominates, because the bell curve will look fatter for the small sample than it will for the overall population. Wainer deems this the most dangerous equation because ignorance of its lessons has misled people in a wide range of fields for a long time and has had serious consequences.

      Wainer offers an example to illustrate the point: the rate at which people contract cancer of the kidney in the United States. He provides a map showing that the counties in the United States with the lowest rates tend to be rural, small, and in the Midwest, South, and West. He then shows a map of the counties with the highest rates. They tend to be rural, small, and in the Midwest, South, and West. This is simply de Moivre's equation at work: if you're closer to the luck side of the luck-skill continuum, small sample sizes will exhibit large variations and will lead to unreliable conclusions. Wainer then shows the rate at which people contract cancer of the kidney as a function of the population of any given county, and it is visually clear that small counties have the highest and lowest rates of incidence of cancer while large counties have rates that are closely clustered. A small population equals a small sample and therefore a wide variation.²⁵

      Failing to understand de Moivre's equation has led to some significant blunders in making policy. One example is the effort to improve the education of children. Seeking reform, policy makers proceeded in a seemingly sensible way by asking what kinds of schools had children who scored well on tests. The next step was to restructure other schools to look like the ones producing the outstanding students. As you would guess by now, small schools are substantially overrepresented among the schools that scored the highest. This led to a movement toward reducing the size of schools. In fact, the private and public sectors spent billions of dollars to implement a policy aimed at reducing the size of schools.

      A closer look at the data shows that small schools were not only overrepresented among the schools that scored the highest, they were also overrepresented among the schools that scored the lowest. Further, Wainer offers evidence that, toward the end of their secondary education, students at larger schools actually score better on average than those at small schools, because larger schools have the resources to offer a richer curriculum, with teachers who can specialize in a subject.²⁶

      Here's the main point: if you have an activity where the results are nearly all skill, you don't need a large sample to draw reasonable conclusions. A world-class sprinter will beat an amateur every time, and it doesn't take a long time to figure that out. But as you move left on the continuum between skill and luck, you need an ever-larger sample to understand the contributions of skill (the causal factors) and luck.²⁷ In a game of poker, a lucky amateur may beat a pro in a few hands but the pro's edge would become clear as they played more hands. If finding skill is like finding gold, the skill side of the continuum is like walking into Fort Knox: the gold is right there for you to see. The luck side of the continuum is similar to the tedious work of panning for gold in the American River in California; you have to do a lot of sifting if you want to find the nuggets of gold.

      Most business executives try to improve the performance of their companies. One way to do that is to observe successful companies and do what they do. So it comes as no surprise that there are a large number of books based on studies of success. Each work has a similar formula: find companies that have been successful, identify what they did to achieve that success, and share those СКАЧАТЬ