Applying Pareto to Pareto, or Math Doesn’t Work That Way

pareto

This article was supposed to be a review of a book. I was contacted by a publisher (one of the big ones), seeking to have an author on the podcast. I suggested I read the book before deciding on whether or not to have the author on the show. So a copy was sent to me.

I made it halfway through the book before I put it aside. (I didn’t throw it, as I felt should happen, because I was reading on my iPad). And each time I picked it up I got more and more irritated. There was a lot in the book that has been suggested over the last 20 years, and a lot of it proven to be ineffective.

But the thing that left me shaking my head was the abuse of the Pareto Principal.

So I’m going to put on my math teacher hat here for a bit.

What is Pareto?

The Pareto Principal states that roughly 80% of the outcomes result from 20% of the inputs.

There are two things to note about this: the word roughly, meaning that this is not an exact measurement. And secondly, that the 80/20 is a ratio.

The Mathematics

Some people have said if 80/20 holds, then it must also hold that 64/4 must hold (because 64 is 80% of 80 and 4 is 20% of 20). And then it must also mean that 51.2/0.8 must hold (because 51.2 is 80% of 64 and .8 is 20% of 20).

Yes. But….it is still the original ratio. But percentages are based on 100. When you make either 64/4 or 51.2/0.8 into a percentage, it is still 80%/20%.

The Power Principle

The Pareto principle is an example of a mathematical power principle. A power principle simply is one where a large proportion of the process variation is associated with a small variation of the process variables.

In other words, a power principle is one where a large change in the output is caused by a small change in the inputs.

Pareto Is Not A Natural Law

There is a difference between an observable set of results with an explanation and a natural law.

Just because it can be observed that 80 percent of the results in some situations can be explained by 20 percent of the actions doesn’t mean that this always holds. There are other power ratios out there that affect our world.

Kepler’s 3rd law of planetary motion is a power ratio. So is the ratio of surface area to volume of a shape. (And neither is 80/20).

But that doesn’t mean that any certain power law applies to every situation. So we can’t take Pareto and apply it to everything in our lives.

For example, putting 20% of a tank of gas in your car is not going to give you the results of 80% of a fuel burn of the tank. It means you will run out of gas.

Please Be Cautious

I have seen recently that it has been suggested that if 64/4 is valid, you should only do 4% of your work.

Um…please don’t.

It’s still 80%/20%. Doing 4% of your work is just going to get you fired.

And The Flip

Remember that if 80% of the positive outcomes comes from a 20% effort, 80% of the negative outcome can also come from a 20% effort.

The Pareto principle is one that allows us to see that there is a power relationship between our input of effort and the output of results. It allows us to see that if we focus on the right 20% we will have exponential results.

But if you hit the wrong 20%? That could be very different.

Conclusion

I know that math is something that most people say they can’t do or aren’t good at. Poppycock. I have never met a single adult who can’t double a recipe or figure out roughly how much change they should get back from a purchase.

But I believe that one of the frustrations people have with math is that there can be a lot of subtleties that are often presented as incontrovertible facts. Pareto is one. But it’s just an observation, not a law.

OK, math lesson is over. You may go about your day.