Pareto’s Fractal

I’ve decided that Pareto’s Rule is fractal in nature.

mandelbrot

A “fractal” is – for the purposes of this discussion – a pattern that is the same no matter what the magnification. In other words, it looks the same from far off as it does from up close.

For instance – if you look at a dirt clod, or if you magnify a mote from inside that dirt clod, they will present many of the same surface patterns.

You can’t tell by the surface patterns, when you are looking at a water surface, if you are seeing it from an airplane or under a magnifying glass. A pattern of ice crystalized on a window looks remarkably the same as a snowflake.

The idea is one of repeating patterns, and that the patterns repeat until the scale is too small to support them (or too large).

Pareto’s Rule is the 80/20 rule, which keeps showing up in all types of applications. It was initially named for Italian economist Vilfredo Pareto, who observed that 80% of the land in Italy was owned by 20% of the people.

It shows up again and again – “80% of your sales come from 20% of your clients”, “80% of the service work is done by 20% of the congregation”, “80% of the Nat’l Championships in the country come from the 20% of the teams that are in the SEC” (sorry about that : ).

I’m currently on a largish project at work, and I noticed early on that I got 80% of the work done in 20% of the time, and that the other 20% of the work is taking 80% of the time. This is so true in software development that nobody even ever has to say it; it’s just the way things are. 80% of the bugs take 20% of the effort, and the other 20% of the bugs take 80% of the effort.

But I’m starting to think that this rule is a fractal – that, when you get the first 80% done in 20% of the time, that then that last 20% has its own Pareto rule – that 80% of the last 20% will be done in 20% of the last 80% of the time, and that that 20% of the last 20% will take 80% of that time.

Let’s see how this looks – let’s say that there are 625 tasks that take 625 hours (numbers I chose after I made the following table🙂 :

          Total 80% 20%
1st Tasks 625 500 125
Hours 625 125 500
2nd Tasks 125 100 25
Hours 500 100 400
3rd Tasks 25 20 5
Hours 400 80 320
4th Tasks 5 4 1
Hours 320 64 256

So we’d knock out 500 of those 625 tasks in 125 hours, but the other 125 tasks would take 500 hours.

And of that last 125 tasks, 100 would take 100 hours total, but the other 25 would take 400 hours – see where this is going?

Of that last 25 tasks, 20 would take only 80 hours, but the other 25 would take 320 hours –

And that last, most difficult task of all would take 256 hours by itself.

Right now, I’m thinking that I’m on the last row – the last 5 of the 625 tasks that are taking 320 hours, or more than half of all of the time.

And I’ve wasted about 20 minutes of that doing this stupid post : )

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