The science of chaos -- in particular the theory of fractal patterns -- is one of the most beautiful discoveries of the last 50 years. So far, business has been rather slow in discovering how to use fractal theory. But now I think there are indications it could possibly make any company large amounts of money.

In my book *The 80/20 Principle*, I explained that 80/20 is very closely related to fractals and chaos theory. I developed the theme in my follow up book, now in a new edition, *The 80/20 Principle* and *92 Other Powerful Laws of Nature*. Perry Marshall, the marketing expert and author of *80/20 Sales and Marketing*, has run with this idea and elaborated it much further, the first person to my knowledge who has combined fractal and marketing theory, and done it to great effect.

In this blog I explain what fractals are, then the link with 80/20, then the reason why this should be a fertile money-making proposition.

**What are fractals?**

Mathematician Benoit Mandlebrot once worked in IBM's pure research lab, using its computers to analyse cotton price data. He showed that there were patterns for daily and monthly price changes that matched perfectly. He coined the word 'fractal' to describe things that are very similar to each other, yet not identical -- such as coastlines, clouds, financial prices, earthquakes or trees. Snowflakes all have the same six-sided shape, but everyone is slightly different.

The fun starts when you look at any large set of data for fractal phenomena. You find strikingly similar patterns regardless of the data being plotted. For example, the year-to-year graph of cotton prices looks eerily like the *shape* -- not the level -- of the month-to-month cotton price variations. Similarly, if you look at coastlines from a plane, it is as though they are spooling through a computer program that endlessly repeats itself -- you recognize almost the same shapes time and time again.

**How do 80/20 and fractals relate to each other?**

As Perry Marshall says, the same mathematics that describes chaos also describes 80/20. And 80/20 is fractal -- meaning that the shape of a curve plotting 80/20 data is almost the same, no matter what the data -- whether it relates to the wealth by rank of person, or the profits from products, or any other plot, regardless of when the data were taken, or the products concerned, or the country to which the data relate. And 80/20 is fractal also in the sense that the whole 80/20 curve is continuous -- there are 80/20 patterns within the 80/20 curve. It's a repeating pattern where the smallest parts resemble the whole. For example, if 20 percent of products give 80 percent of profits, it's likely -- with enough data -- that in the top 20 percent, there will still be a 20 percent giving 80 percent of the profits even within that elite group. So 20 percent of 20 -- 4 percent of products -- will deliver 80 percent of the total 80 percent of results -- that is 4 percent of products will yield 64 of total profits (.8 x .8).

**Can We Make Money Out of This?**

Perry Marshall has developed a really neat tool called the Power Curve, which applies the fractal nature of 80/20 to how much people will spend on a particular product or experience. He shows, for instance, how if 50,000 people will spend at least $100 for a football game ticket, we can calculate with amazing accuracy how many people would spend more than $10,000 -- obviously not for the same ticket, but for something super-high end, such as a skybox. Half the money in the sports industry, Perry says, comes from exploiting this amazing propensity for a tiny percentage of fans to spend outrageous amounts of money. Even a very conservative, frugal elderly gentleman, who drives a six-year-old Crown Victoria even though he could afford the most expensive Mercedes -- even this person, if he *really, really, loves football*, can be sold a skybox. Somehow, he'll find a way to justify it.

The value of individual customers varies enormously, and often firms don't provide a super-premium product to capture what the most fanatical buyers of a product category would pay. With the Power Curve, you can calculate how much money is being left on the table. And since high-priced products are usually very profitable, the amount of profit for a few top-end products can dwarf the profits from the low-end products, even when the revenue from the latter is equal or greater. Any firm can do this analysis, and then develop the right type of product to satisfy the fanatics.

I saw an intuitive application of this idea during my days as a strategy consultant. The eponymous founder of Bain & Company, Bill Bain, realized that you could make a million dollars out of selling a strategy to one firm, but if the firm was the right firm -- basically an extremely large firm with operations around the world and ambitions to take over other firms -- pretty much the same strategy might be worth $10 million or $20 million or $100 million in revenues at much higher profit margins. So I think the Power Curve is useful in high-end service businesses just as much as it is in product businesses.

**Does the Power Curve work the Other Way Round Too?**

Can you also be leaving money on the table by not having a *low-end mass market product?*

Yes.

Consider the luxury goods industry. Fifty years ago, this was all about discreet servicing of a very small, very rich market. Dior, Yves Saint Laurent, Louis Vuitton, Cartier, Hermès -- they really were exclusive purveyors of goods to the privileged few. Many of these brands were founded in the eighteenth and nineteenth century by craftsmen creating beautiful artefacts for the royal court. Later on the market expanded to the upper classes generally, but goods were produced in tiny quantities, often to order. This tradition carried on pretty much until the later twentieth century.

But then the companies discovered that you could democratize luxury. They used the brands on low-priced accessories -- a tube of lipstick, a perfume spray, a T-shirt with their logo, denim handbags. And these items could be sold by the millions. Companies such as LVMH (Louis Vuitton Moӫt Hennessy) have multiplied their profits many times since they started lowering the price points of luxury.

The Power Curve can tell you how much you could expect to sell of any product at a lower price point. Perry Marshall says that if football fan number 50,000 spends $100 per game, then the one millionth most avid fan would spend $7.57 -- so in addition to the $5 million of revenue from the top 50,000 fans, you could have $7.57 million from a lower price product. He says the Curve can be pushed further:

*Fan number 10 million spends $1.04. Maybe all he did was watch a few games and $1.04 is the revenue they generated ... So across 10 million people, the least interested fan spent a buck and the most interested fan spent $1.1 million. The tool says total revenue from all sources equals $67.8 million. That's per game!*

Now, I want to stress that these are theoretical numbers, driven purely by fractal theory and the mathematics of 80/20. The numbers might be off a little bit, even a fair bit. You are still left with the possibility of multiplying current profits if you can use the Power Curve and develop appropriate new products. That must be worth looking at really carefully, for companies large or small.

"The genius of 80/20 is," says Marshall, "it harnesses hidden forces in nature that are far more powerful than you would have suspected." I think he's probably right, and I would like to see research and experimentation to prove it one way or the other. Smart companies should step forward to become Power Curve guinea pigs.