3/30/2023 0 Comments Pareto principle![]() ![]() Using the Wins Above Replacement (WAR) metric as an estimate of a player’s value, we can see that MLB players are able to produce wins for their team in a Pareto-distributed fashion. ![]() In most professions it is hard to precisely quantify a worker’s productivity, but Major League Baseball (MLB) teams are experts in exactly this exercise. Perhaps equally profound is the ability to model productivity according to a Pareto distribution (while productivity and wealth are both distributed in the same manner, their correlation at the level of individuals is a matter of dispute and varies by context). Policymakers may not realize that wealth is distributed according to a Pareto distribution rather than a normal distribution, and this gap in understanding could lead to suboptimal policy decisions in countries around the world. The vast majority of the world’s citizens are clustered at a low level of wealth, while a small percentage of the population controls the vast majority of all wealth. Consider its original use case, describing the distribution of wealth across individuals in a society. The Pareto distribution has major implications in our society. For reference, the “80-20 Rule” is represented by a distribution with alpha equal to approximately 1.16.įigure 1: Pareto Distribution (various alpha) This means that the majority of the distribution’s density is concentrated near X m on the left-hand side, with only a small proportion of the density as we move to the right. When we plot this function across a range of x values, we see that the distribution slopes downward as x increases. The probability density function is given by the following formula: The X m parameter is the scale parameter, which represents the minimum possible value for the distribution and helps to determine the distribution’s spread. The α value is the shape parameter of the distribution, which determines how distribution is sloped (see Figure 1). The Pareto distribution is a power-law probability distribution, and has only two parameters to describe the distribution: α (“alpha”) and X m. He famously observed that 80% of society’s wealth was controlled by 20% of its population, a concept now known as the “Pareto Principle” or the “80-20 Rule”. It is named after the Italian economist Vilfredo Pareto (1848-1923), who developed the distribution in the 1890s as a way to describe the allocation of wealth in society. While not as well-known as the bell-shaped Normal (Gaussian) distribution, the Pareto distribution is a powerful tool for modeling a variety of real-life phenomena. ![]()
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