When You Hear Hoofbeats, Don’t Expect a Zebra
Mark is a thin man from Germany with glasses who likes to listen to Mozart. Which is more likely? That (a) Mark is a truck driver or (b) he is a professor of literature in Frankfurt. Most will bet on B, which is wrong. Germany has ten thousand times more truck drivers than Frankfurt has literature professors. Therefore, it is more likely that Mark is a truck driver. So what just happened? The detailed description enticed us to overlook the statistical reality. Scientists call this fallacy base-rate neglect: a disregard of fundamental distribution levels. It is one of the most common errors in reasoning. Virtually all journalists, economists, and politicians fall for it on a regular basis.
Here is a second example: A young man is stabbed and fatally injured. Which of these is more likely? (a) The attacker is a Russian immigrant and imports combat knives illegally, or (b) the attacker is a middle-class American. You know the drill now: Option B is much more likely because there are a million times more middle-class Americans than there are Russian knife importers.
In medicine, base-rate neglect plays an important role. For example, migraines can point (among others) to a viral infection or a brain tumor. However, viral infections are much more common (in other words, they have a higher base rate), so doctors assess patients for these first before testing for tumors. This is very reasonable. In medical school, residents spend a lot of time purging base-rate neglect. The motto drummed into any prospective doctor in the United States is: “When you hear hoofbeats behind you, don’t expect to see a zebra,” which means: Investigate the most likely ailments before you start diagnosing exotic diseases, even if you are a specialist in that. Doctors are the only professionals who enjoy this base-rate training.
Regrettably, few people in business are exposed to base-rate training. Now and then I see high-flying entrepreneurs’ business plans and get very excited by their products, ideas, and personalities. I often catch myself thinking: This could be the next Google! But a glance at the base rate brings me back down to earth. The probability that a firm will survive the first five years is 20 percent. So what, then, is the probability that they will grow into a global corporation? Almost zero. Warren Buffett once explained why he does not invest in biotech companies: “How many of these companies make revenues of several hundred million dollars? It simply does not happen. . . . The most likely scenario is that these firms will just hover somewhere in the middle.” This is clear base-rate thinking. For most people, survivorship bias (chapter 1) is one of the causes for their base-rate neglect. They tend to see only the successful individuals and companies because the unsuccessful cases are not reported (or underreported). This makes them neglect the large part of the “invisible” cases.
Imagine you are sampling wine in a restaurant and have to guess from which country it is. The label of the bottle is covered. If, like me, you are not a wine connoisseur, the only lifeline you have is the base rate. You know from experience that about three-quarters of the wines on the menu are of French origin, so reasonably, you guess France, even if you suspect a Chilean or Californian twist.
Sometimes I have the dubious honor of speaking in front of students of elite business schools. When I ask them about their career prospects, most answer that, in the medium term, they see themselves on the boards of global companies. Years ago, both my fellow students and I gave the same answer. The way I see it, my role is to give students a base-rate crash course: “With a degree from this school, your chance of landing a spot on the board of a Fortune 500 company is less than 0.1 percent. No matter how smart and ambitious you are, the most likely scenario is that you will end up in middle management.” With this, I earn shocked looks and tell myself that I have made a small contribution toward mitigating their future midlife crises.