Patrick T. Hoffman

Habit 4: Live by Pareto’s Law

In the late nineteenth century, Vilfredo Pareto, an Italian economist and sociologist, observed remarkable similarity in the distribution of income and wealth in different countries. Everywhere he looked, these monetary measures were unequally distributed, and the patterns of distribution appeared nearly identical. This was not a chance event, in Pareto’s view. He posited that the distribution of income and wealth in every society follows a specific mathematical function, a function now termed a Pareto distribution.
There’s no need to concern ourselves with the mathematical details of Pareto’s work. What’s important for our purposes is to understand the gist of a Pareto distribution, and that can be easily done without recourse to equations. In a Pareto distribution, the frequency of a quantity is inversely related to its size: small quantities appear frequently, while large quantities are rare. If we’re looking at the distribution of wealth, as Pareto did, we’ll find a handful of billionaires, a modest number of millionaires, and a whole lot of folks who are flat broke. Subsequent to Pareto, others noticed that many things besides income and wealth seemed to fit a Pareto distribution. There are a few big cities, but many small towns; a few major earthquakes, but many minor temblors. People also began to focus on a particular implication of a Pareto distribution’ that a small proportion of items constitutes a large share of the cumulative distribution. For example, the most active 10 percent of burglars are responsible for the majority of housebreaking. In the movie industry, a few blockbuster films dominate studio revenues. A few wardrobe items account for most visits to a clothes closet (creating the annoyance that closets are stuffed with clothes that are rarely worn). This type of imbalance is often called ‘Pareto’s Law,’ a term generally traced to quality control expert J. M. Juran, who in 1950 referenced Pareto in describing how relatively few types of manufacturing defects accounted for the bulk of quality losses. All good quantitative thinkers are Paretians. That’s because Paretian thinking is crucial to understanding many numbers. For instance, you’ve no doubt heard that about half of all marriages in America will fail. That statistic is often interpreted to mean that every other person who ties the knot will suffer a divorce. But Elizabeth Taylor’s Law (the marital version of Pareto’s Law) reminds us that a small fraction of the population accounts for a disproportionate share of divorces, which leads to the conclusion that the majority of people who marry never divorce. Suppose we observed the marital careers of five individuals. One married and divorced three times, another wed twice and split up once, and each of the remaining three had a single, lasting marriage. Overall, four of the eight marriages (50 percent) ended in divorce. But three of the five people (60 percent) had lifelong unions. Juran also referred to Pareto’s Law as the rule of the ‘vital few and trivial many.’ * The latter phrase proved less catchy, but it highlights what Juran considered the key lesson of Pareto’s Law: Pay attention to the vital few. It is estimated that 10 percent of cars on the road generate more than half of auto-related pollution. Pareto’s Law suggests that pollution can be reduced more cheaply by identifying these cars and getting them repaired or junked’ as opposed to requiring stricter emissions standards on new vehicles, an approach that doesn’t target the heaviest polluters. In fact, if pollution regulations raise the cost of new cars, many car owners will hold on to their older (and more polluting) vehicles for longer than they otherwise would. There’s a counterargument to Pareto’s Law, and we’ve all heard it. ‘Little things add up.’ Business lore holds that American Airlines saved $100,000 by eliminating one olive from every salad served in first class. But for American Airlines, $100,000 is peanuts. When Pareto distributions are involved, little things usually add up to little numbers. Big things’ such as what American spends on jet fuel’ are often big all by themselves. That’s not to say that the little-things adage is useless, but its main value lies in fostering an economizing spirit that brings savings on big-ticket items. Pareto’s Law teaches us that numbers have to be prioritized. Whether we’re looking at a spreadsheet of financial data, a page of sports stats, or a nutritional label on a cereal box, some numbers are invariably more important than others. A useful technique when looking at a group of numbers is to ask yourself which number, or set of numbers, is the most important. In our experience, asking this question often leads to the discovery that we’ve been looking at numbers aimlessly, without any game plan. Asking what the most important number is forces us to figure out *The most common synonyms are the ‘Pareto Principle’ and the ‘80/ 20 Principle.’ We prefer ‘Pareto’s Law’ to these alternatives, since a law suggests a natural regularity while a principle suggests a maxim of choice. Why we looked at the numbers in the first place, what we are trying to learn from them, and which number or numbers can (and can’t) tell us what we want to know. Pareto’s Law is just as important at home as it is at work. According to surveys, working Americans save much less for retirement every year than they think they should. The annual gap between desired and actual saving is, on average, about 10 percent of household income. This is why family discussions so often include such lines as, ‘You paid WHAT to get your hair colored’’ or, ‘Just because your best friend has titanium golf clubs doesn’t mean you need them.’ Hairstyling and golf equipment are not trivial expenses for most people, but unless you have little income, or a passion for changing your hair color or your golf clubs, they don’t come close to 10 percent of income. Personal spending, like corporate spending, is governed by Pareto’s Law. While writing this chapter, one of us looked at a year’s worth of his credit card charges, a frightening research exercise. Five percent of charges accounted for 46 percent of total expenses. Had your author included his check writing, by which he pays for most major outlays, 5 percent of items would have easily accounted for more than half of total expenses. Tightening your belt by 10 percent is difficult. If you try to buck Pareto’s Law, it’s that much harder. According to data from the federal government’s Consumer Expenditure Survey, 32.4 percent of household expenditures go for housing and 19.5 percent for transportation. That’s a total of 51.9 percent, which means that if you don’t cut back on housing or car expenses, you have to rein in everything else by more than 20 percent. More than that actually, since outlays for health care, education, and pension and Social Security contributions account for 14.9 percent of expenditures, and you don’t want to pare those. So you’d really have to reduce your spending on everything else by 30 percent to meet the 10 percent target. Let’s face up to Pareto’s Law: Most Americans need to take a hard look at their housing and car expenses. Illuminating Numbers: When skilled quantitative thinkers daydream, they imagine a world where numbers are always accompanied by a critical analysis of their significance. The fantasy takes them away from the reality of planet Earth, where trying to comprehend quantitative information is a never-ending struggle. Fortunately, good quantitative thinkers have developed a couple of habits that make it easier to understand numbers.