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Many professions practice certifications as a way to establish that a person practicing this profession has reached a certain skills level. At first glance, it may sound like several years of practice should help a person pass the corresponding certification test, but in reality, even after several years of practice, most people are not able to pass the test, while after a few weeks of intensive training, most people pass it successfully. This sounds counterintuitive, since the overall number of problems that a person solves during several years of practice is much larger than the number of problems solved during a few weeks of intensive training. In this paper, we show that Zipf’s law explains this seemingly counterintuitive phenomenon. 1 Formulation of the Problem The more years a person works on a job, the more skilled this person becomes. This is true for medical doctors, this is true for software developers, this true for college instructors. One may expect that eventually, many years of practical experience would make a person a well-qualified specialist. However, in reality, often people with as many years of practice cannot pass the corresponding qualifying exam (such as a software exam; see, e.g. [1]) – while as little as a few weeks of comprehensive training enables them to pass this exam. Why is that? It is, to many people, a mystery. It is not that during the previous several years people did not work hard – they did; at times, they make

Several years of practice may not be as good as comprehensive training: Zipf’s law explains why