# Pareto principle

The Pareto Principle asserts that only a "vital few" peapods produce the majority of peas.

The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity)[1][2] states that, for many events, roughly 80% of the effects come from 20% of the causes.[3] Management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896, as published in his first work, Cours d'économie politique. Essentially, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population.

It is an axiom of business management that "80% of sales come from 20% of clients".[4] Richard Koch authored the book, The 80/20 Principle, which illustrated some practical applications of the Pareto principle in business management and life.[5]

Mathematically, the 80/20 rule is roughly followed by a power law distribution (also known as a Pareto distribution) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution.[6]

The Pareto principle is only tangentially related to Pareto efficiency. Pareto developed both concepts in the context of the distribution of income and wealth among the population.

## In economics

The original observation was in connection with population and wealth. Pareto noticed that 80% of Italy's land was owned by 20% of the population.[7] He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.

A chart that gave the inequality a very visible and comprehensible form, the so-called "champagne glass" effect,[8] was contained in the 1992 United Nations Development Program Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income.[9]

Distribution of world GDP, 1989[10]
Quintile of population Income
Richest 20% 82.70%
Second 20% 11.75%
Third 20% 2.30%
Fourth 20% 1.85%
Poorest 20% 1.40%

The Pareto principle also applies to taxation. In the US, the top 20% of earners have paid roughly 80% of Federal income taxes in 2000 and 2006,[11] and again in 2018.[12]

## In software

In computer science the Pareto principle can be applied to optimization efforts.[13] For example, Microsoft noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated.[14] Lowell Arthur expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!"[15] It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of COCOMO estimating for software coding.

In load testing, it is also common practice to estimate that 80% of the traffic will occur during a particular 20% of the total time period.[citation needed]

## In sports

It has been inferred the Pareto principle applies to athletic training, where roughly 20% of the exercises and habits have 80% of the impact and the trainee should not focus so much on a varied training.[16] This does not necessarily mean that having a healthy diet or going to the gym are not important, but they are not as significant as the key activities. It is also important to note this 80/20 rule has yet to be scientifically tested in controlled studies with regards to athletic training.

In baseball, the Pareto principle has been observed in Wins Above Replacement (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of the all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto Principle holds up pretty soundly when it is applied to baseball..."[17]

## Occupational health and safety

Occupational health and safety professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.[18]

Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order as the technique ensures the resources used are best used to prevent the most accidents.[19]

## Other applications

In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.[13]

The law of the few can be also seen in betting, where it is said that with 20% effort you can match the accuracy of 80% of the bettors.[20]

In the systems science discipline, Epstein and Axtell created an agent-based simulation model called Sugarscape, from a decentralized modeling approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle became emergent in their results, which suggests the principle is a collective consequence of these individual rules.[21]

The Pareto principle has many applications in quality control.[22][citation needed] It is the basis for the Pareto chart, one of the key tools used in total quality control and Six Sigma techniques. The Pareto principle serves as a baseline for ABC-analysis and XYZ-analysis, widely used in logistics and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.[23]

In health care in the United States, 20% of patients have been found to use 80% of health care resources.[24]

Some cases of super-spreading conform to the 20/80 rule,[25] where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions.[26] In epidemics with super-spreading, the majority of individuals infect relatively few secondary contacts.

The Dunedin Study has found 80% of crimes are committed by 20% of criminals.[27] This statistic is used to support both stop-and-frisk policies and broken windows policing, as catching those criminals committing minor crimes will likely net many criminals wanted for (or who would normally commit) larger ones.

## Mathematical notes

The idea has a rule of thumb application in many places, but it is commonly misused. For example, it is a misuse to state a solution to a problem "fits the 80/20 rule" just because it fits 80% of the cases; it must also be that the solution requires only 20% of the resources that would be needed to solve all cases. Additionally, it is a misuse of the 80/20 rule to interpret a small number of categories or observations.

This is a special case of the wider phenomenon of Pareto distributions. If the Pareto index α, which is one of the parameters characterizing a Pareto distribution, is chosen as α = log45 ≈ 1.16, then one has 80% of effects coming from 20% of causes.

It follows that one also has 80% of that top 80% of effects coming from 20% of that top 20% of causes, and so on. Eighty percent of 80% is 64%; 20% of 20% is 4%, so this implies a "64/4" law; and similarly implies a "51.2/0.8" law. Similarly for the bottom 80% of causes and bottom 20% of effects, the bottom 80% of the bottom 80% only cause 20% of the remaining 20%. This is broadly in line with the world population/wealth table above, where the bottom 60% of the people own 5.5% of the wealth, approximating to a 64/4 connection.

The 64/4 correlation also implies a 32% 'fair' area between the 4% and 64%, where the lower 80% of the top 20% (16%) and upper 20% of the bottom 80% (also 16%) relates to the corresponding lower top and upper bottom of effects (32%). This is also broadly in line with the world population table above, where the second 20% control 12% of the wealth, and the bottom of the top 20% (presumably) control 16% of the wealth.

The term 80/20 is only a shorthand for the general principle at work. In individual cases, the distribution could just as well be, say, nearer to 80/10 or 80/30. There is no need for the two numbers to add up to the number 100, as they are measures of different things, (e.g., 'number of customers' vs 'amount spent'). However, each case in which they do not add up to 100%, is equivalent to one in which they do. For example, as noted above, the "64/4 law" (in which the two numbers do not add up to 100%) is equivalent to the "80/20 law" (in which they do add up to 100%). Thus, specifying two percentages independently does not lead to a broader class of distributions than what one gets by specifying the larger one and letting the smaller one be its complement relative to 100%. Thus, there is only one degree of freedom in the choice of that parameter.

Adding up to 100 leads to a nice symmetry. For example, if 80% of effects come from the top 20% of sources, then the remaining 20% of effects come from the lower 80% of sources. This is called the "joint ratio", and can be used to measure the degree of imbalance: a joint ratio of 96:4 is very imbalanced, 80:20 is significantly imbalanced (Gini index: 60%), 70:30 is moderately imbalanced (Gini index: 40%), and 55:45 is just slightly imbalanced.

The Pareto principle is an illustration of a "power law" relationship, which also occurs in phenomena such as brush fires and earthquakes.[28] Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from Normal or Gaussian distribution phenomena. This fact explains the frequent breakdowns of sophisticated financial instruments, which are modeled on the assumption that a Gaussian relationship is appropriate to, for example, stock price movements.[29]

## Equality measures

### Gini coefficient and Hoover index

Using the "A : B" notation (for example, 0.8:0.2) and with A + B = 1, inequality measures like the Gini index (G) and the Hoover index (H) can be computed. In this case both are the same.

${\displaystyle H=G=|2A-1|=|1-2B|\,}$
${\displaystyle A:B=\left({\frac {1+H}{2}}\right):\left({\frac {1-H}{2}}\right)}$

### Theil index

The Theil index is an entropy measure used to quantify inequalities. The measure is 0 for 50:50 distributions and reaches 1 at a Pareto distribution of 82:18. Higher inequalities yield Theil indices above 1.[30]

${\displaystyle T_{T}=T_{L}=T_{s}=2H\,\operatorname {artanh} (H).\,}$

## References

1. ^ Bunkley, Nick (March 3, 2008). "Joseph Juran, 103, Pioneer in Quality Control, Dies". New York Times. Archived from the original on September 6, 2017. Retrieved 25 January 2018.
2. ^ Box, George E.P.; Meyer, R. Daniel (1986). "An Analysis for Unreplicated Fractional Factorials". Technometrics. 28 (1). doi:10.1080/00401706.1986.10488093.
3. ^ Bunkley, Nick (March 3, 2008). "Joseph Juran, 103, Pioneer in Quality Control, Dies". The New York Times.
4. ^ Marshall, Perry (2013-10-09). "The 80/20 Rule of Sales: How to Find Your Best Customers". Entrepreneur. Retrieved 2018-01-05.
5. ^ Koch, Richard (1998). The 80/20 Principle : the Secret of Achieving More with Less. New York: Doubleday. ISBN 9780385491747.
6. ^ Newman, MEJ. "Power laws, Pareto Distributions, and Zipf's law" (PDF). p. 11. Retrieved 10 April 2011.
7. ^ Pareto, Vilfredo; Page, Alfred N. (1971), Translation of Manuale di economia politica ("Manual of political economy"), A.M. Kelley, ISBN 978-0-678-00881-2
8. ^ Gorostiaga, Xabier (January 27, 1995), "World has become a 'champagne glass' globalization will fill it fuller for a wealthy few", National Catholic Reporter
9. ^ United Nations Development Program (1992), 1992 Human Development Report, New York: Oxford University Press
10. ^ Human Development Report 1992, Chapter 3, retrieved 2007-07-08
11. ^ Curtis Dubay (May 4, 2009) The Rich Pay More Taxes: Top 20 Percent Pay Record Share of Income Taxes, Heritage.org, accessed 12 April 2018
12. ^ Laura Sanders (April 6, 2018) Top 20% of Americans Will Pay 87% of Income Tax, Wall Street Journal, accessed 12 April 2018
13. ^ a b Gen, M.; Cheng, R. (2002), Genetic Algorithms and Engineering Optimization, New York: Wiley
14. ^ Rooney, Paula (October 3, 2002), Microsoft's CEO: 80–20 Rule Applies To Bugs, Not Just Features, ChannelWeb
15. ^ Pressman, Roger S. (2010). Software Engineering: A Practitioner's Approach (7th ed.). Boston, Mass: McGraw-Hill, 2010. ISBN 978-0-07-337597-7.
16. ^
17. ^ Jeff Zimmerman (Jun 4, 2010). Applying the Pareto Principle (80-20 Rule) to Baseball, BeyondTheBoxScore.com, accessed 12 April 2018
18. ^ Woodcock, Kathryn (2010). Safety Evaluation Techniques. Toronto, ON: Ryerson University. p. 86.
19. ^ "Introduction to Risk-based Decision-Making" (PDF). USCG Safety Program. United States Coast Guard. Retrieved 14 January 2012.
20. ^
21. ^ Epstein, Joshua; Axtell, Robert (1996), Growing Artificial Societies: Social Science from the Bottom-Up, MIT Press, p. 208, ISBN 0-262-55025-3
22. ^ 50MINUTES.COM (2015-08-17). The Pareto Principle for Business Management: Expand your business with the 80/20 rule. 50 Minutes. ISBN 9782806265869.
23. ^ Rushton, Oxley & Croucher (2000), pp. 107–108.
24. ^
25. ^ Galvani, Alison P.; May, Robert M. "Epidemiology: Dimensions of superspreading". Nature. 438: 293–295. doi:10.1038/438293a. PMID 16292292.
26. ^ Lloyd-Smith, JO; Schreiber, SJ; Kopp, PE; Getz, WM (2005). "Superspreading and the effect of individual variation on disease emergence". Nature. 438: 355–359. doi:10.1038/nature04153. PMID 16292310.
27. ^ Nicola, Davis (2016), 'High social cost' adults can be predicted from as young as three, says study, The Guardian
28. ^ Bak, Per (1999), How Nature Works: the science of self-organized criticality, Springer, p. 89, ISBN 0-387-94791-4
29. ^ Taleb, Nassim (2007), The Black Swan, pp. 229–252, 274–285
30. ^ On Line Calculator: Inequality