The Prevalence Of The Pareto Distribution

‘For to every one who has will more be given, and he will have abundance; but from him who has not, even what he has will be taken away.’ 

The slightly eerie statement from the Book of Matthew below essentially dictates that from those who have much, more will be given. And for those who have little, more will be taken. The Bible, riddled with predictions of apocalypse and the fiery consequences of sin isn’t well-known for its cheeriness. But this one quote, commonly referred to as The Matthew Principle has been mathematically analysed to become the Pareto distribution. And it’s presence in our everyday lives is abundant.

The Pareto Distribution

Named after the economist and sociologist Vilfredo Pareto, the Pareto distribution is a power-law probability distribution that can be seen throughout nature, humanity, and even geography.

The mathematical representation of the Pareto distribution
The mathematical representation of the Pareto distribution.

A simpler way to consider the distribution is to conceptualise it as the ’80/20′ rule. This rule, by contrast, determines that 80% of x is consumed by 20% of y. For example, 80% of a particular economic market may be dominated by just 20% of businesses. Incremented again, this tends to mean that 80% of the wealth is owned by 20% of civilians (though, in modern times, this figure is far more radical).

Prime Examples

Tom Brady

Any NFL fan worth his salt knows that Tom Brady is the man of the hour, and has been for approximately the last 15 years. 5 Super Bowl wins, 4 Super Bowl MVP’s, and he’s thrown touchdowns to 71 different receivers. These stats are impressive on their own merit but especially compelling in comparison to other quarterbacks.

Tom Brady Pareto Distribution

Tom Brady has an astonishing 202 regular season wins. Out of all the other quarterbacks in NFL history, there have only been 13 who have won at least HALF that amount. Brady is an exceptional case study for the Pareto distribution, that determines that those who begin to win, keep winning exponentially.

Kanye West

Another individual of considerable talent (he will tell you himself) is Kanye West. West’s musical success is undoubted as far as sales go. But it’s his astonishing number of Grammy nominations and wins that see the Pareto distribution at work. The rapper has 68 nominations and 21 wins, compared to other popular music artists’ average of about… 0.

But the Pareto distribution works with Kanye on a more molecular level, within his own music. Kanye’s 2005 album Late Registration, is an undeniable classic. However, a fun and relevant fact is that, according to Spotify, the breakout single Gold Digger has approximately 30 million more streams than the 20 other tracks on the album COMBINED. So not only does the Pareto Distribution work across populations but also within individuals’ creations.

Geography

A simple final example of the Pareto distribution is the congregation of human settlements in urban environments. For example, 90% of Australians live in and around urban areas. However, there are exceptions to this rule such as China, where only 60% of residences occupy urban spaces.

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Why It Matters

There is a slew of obvious reasons why the above examples work the way they do.

Tom Brady has had incredible discipline and athletic ability throughout his career, not to mention to coaching expertise of Bill Belichick.

Kanye West is a talented beat-maker and lyricist, whose charisma and solid connections have seen him rise to the top of his game. Plus, Gold Digger is an undisputed banger.

Finally, inner-Australia is a mostly barren wasteland, and it’s understandable why the masses would choose to live in some of the world’s most liveable cities.

But wouldn’t you assume that most quarterback’s careers are fairly even? Or most songs get similar play? Or even that land receives the same number of occupants? Obviously not.

The simple truth is that the Pareto distribution is a commonality across all human and natural domains. Communist dictatorships such as Stalin’s Russia tried to snuff out this phenomenon. And even through murder and political deceit, the USSR failed. Instead of money flowing to the top small fraction, power was the currency of choice. Those who had power lived.

This is a dire yet important example because according to the mathematical and somewhat Machiavellian Pareto distribution, humanity isn’t going to change any time soon.