What 80/20 really means

by tomjen August, two thousand and fifteen

I am so bad at understanding exponential numbers that I almost expect it is a flaw that is purposely built in, but of course it is just because humans didn’t grow up in an environment where there was a use for it, so I didn’t inherit the gene to do so.

As a crouch for this, because humans are great at visualisation, I made some pictures. In the first each color takes up 80% of the remaining space, alternating horizontally and vertically.

I have always known that 80% of the results for 20% of the effort means quickly diminishing results, but looking at the picture I now have a much better understanding of why.

Pareto

Pareto distribution: each colored segment takes up 80% of the remaining space.

output-0.6

Pareto-like distribution: each colored segment takes up 60% of the remaining space.

Then I got curious: this is how it looks with each area taken up just 60% of space – doesn’t sound like a lot, but notice how much bigger the small pieces are.

Finally, what happens when each segment takes up 90%?

 

Pareto-like distribution: each colored segment takes up 90% of the remaining space.

Pareto-like distribution: each colored segment takes up 90% of the remaining space.

Not surprising, we care barely see more than the third segment (which also represent < 0.1% of the total area).

Of course the pareto distribution is a theoretical example, I don’t actually know of any situation where you get exactly 80% of the benefit from 20% of the effort.

Economists have a term for the cost of choosing to do something and therefore not choosing to do something else – opportunity cost, which is the benefit you didn’t get by choosing your next best option: going to work means you forgo the opportunity to play with your kids, watch a youtube video, sleep in or spend that day on the beach.

This is interesting in our little experiment because we can visualise the data an other way: given how many efforts, how much benefit do we get? How long is it worth going before diminishing returns means that the marginal utility of one more effort is less than what you would get if you spend your effort elsewhere?

Well I can’t know what your best alternative is, but we can calculate the normalised utility of each unit of effort, and when we do we get the following results:

  1. 1.0
  2. 0.2
  3. 0.04
  4. 0.008
  5. 0.0016

It wasn’t worth computing the rest, because at that point they are basically nothing.