Nine More Applications of Price's Law

I just learned about Price's Law a few days ago and it intrigued me. Because I've been thinking about city issues like safety and law & order, I wondered how Price's Law might apply to crime, which I wrote about yesterday. But after sleeping on it and considering its implications, I explored additional ways to apply Price's Law.

Derek J. de Solla Price came up with what's now called “Price’s Law” after noticing that half of all published research is produced by the square root of the total number of authors working in that domain It's deceptively simple idea that seems to pop up everywhere once you start looking for it. 

In its classic form, it says that the square root of the participants in a domain produce roughly half the output. So in a company of 100 people, about 10 people do half the meaningful work. In a city of 1 million, about 1,000 people may generate much of the innovation or influence. Or in a city the size of Duluth (86,000) 293 generate half the innovation or influence. In short, game-changing leadership is not a crowded field.

The really fascinating part is how universal the pattern feels. The more you think about it, the more applications there seem to be.

Churches and Volunteerism
In many churches, the square root of the congregation often handles most of the ministry, fundraising, cleanup, and organizing. A congregation of 400 may function largely because 20 people quietly carry the institution on their backs.

Family Dynamics

In extended families, one or two individuals often become the “memory keepers,” organizers, peacemakers, and caretakers for dozens of relatives. The entire emotional architecture of a clan may rest on surprisingly few shoulders.

Civilization Itself

One could argue that a tiny fraction of humans created the majority of the ideas that shaped civilization—Newton, Maxwell, Gutenberg, Shakespeare, Plato, Edison, etc. Most people inherit culture; very few materially alter it.

Internet Comment Sections

A tiny number of users generate most online discourse. One percent of users may produce half the posts, arguments, outrage, and memes that define a platform’s “culture.” My guess is that most people simply "lurk" to see what everyone's talking about..

Conspiracy Theories
Price’s Law may explain why a handful of highly motivated activists or ideologues can disproportionately shape public narratives. Most people are passive consumers; a small energetic minority drives movements.

Entropy in Organizations
As organizations grow, the productive core does not scale linearly. Bureaucracy expands faster than contribution. This may partially explain why large institutions often become sluggish despite employing thousands. 

Marriage and Friendships

In many social networks, a few people initiate most gatherings, phone calls, and emotional labor. Remove them, and entire friend groups dissolve. I've seen this happen

Historical Turning Points

Many revolutions, reformations, and renaissances may have hinged on an astonishingly small number of determined individuals operating at precisely the right moment. In the American Civil War, the Battles of Vicksburg and Gettysburg turned the tide of the war, with a devastating outcome for the South. (Both happened the same week.)

Decay of Institutions

A frightening inverse version of Price’s Law: when the most competent square root burns out, retires, or disengages, the whole structure can suddenly wobble. The institution looked massive and stable, but its true load-bearing beams were few.

Price's Law as Applied to Crime and Safety

Price's Law (also known as Price's Square Root Law) is a principle in productivity and scientometrics that describes extreme inequality in output within groups. (Keep reading and you'll understand how that plays out.)

The concept was proposed by a British physicist and historian of science named Derek J. de Solla Price in the 1960s, who originally observed patterns in scientific publishing. It states that in any given field, approximately half of all published research is produced by the square root of the total number of authors working in that domain.

For example, if a scientific field has 100 researchers, then √100 = 10 researchers will account for roughly 50% of all papers published. In a company of 10,000 employees, about 100 people (√10,000) will produce half the total output or value.

This makes Price's Law more extreme than the better-known Pareto Principle (commonly referred to as the 80/20 rule). As group size grows, the proportion of top producers shrinks dramatically relative to the whole.

Why It Matters

Price's Law shows how productivity follows a power-law distribution rather than a normal one. A small elite drives the majority of results in research, sales teams, creative fields, companies, and even open-source projects. While controversial and not universally precise, it explains why superstar performers, top scientists, or key employees often contribute disproportionately.

Understanding Price's Law encourages organizations to identify, nurture, and retain high-impact talent — and individuals to strive to be among that critical square-root group.

New Applications

Stumbling across Price's Law got me thinking about an application I'd not considered before: fighting crime. Is it possible that if there a x number of violent criminals in a city, that the square root of that number is committing half the violent crimes? If this were the case, an overtaxed police force could make a big impact by narrowing their focus on these "most productive" criminals. Are there 100 such violent felons in your medium-sized city? This would suggest that ten are doing half of the violent crime, and your city could become much safer by placing them behind bars. And maybe there are only 25. This would suggest five are the really bad dudes that should be behind bars.

Corollary: The square root of all criminals does half of all crime.

I haven't tested this theory yet, but I've an inkling that there's something to it.

What do you think?