Monday, 13 October 2014

Pleasing 80% Of People 20% Of The Time

Some years ago I noticed that I had a few patients who spent a lot of time with me and had various complex issues which took a while to resolve, and lots of patients who were in and out of the door very quickly because their health improved rapidly.  For quite a while, I worried about this and thought I ought to be able to increase the size of one or the other lot.  I put quite a lot of work into trying to arrive at an approach which would do this, to no avail.  The numbers of patients fluctuated but the proportions never did.
Then I came across something called the "80:20 rule", also known as the "log-normal distribution".  I am neither a mathematician nor a statistician, although I am a logician so I'm vaguely aware of certain things.  This is no longer an exercise in losing readership.  Nonetheless, I'm about to show you a couple of graphs, the first of which shows a bell curve, thus:

If you took four dozen pennies and flipped them a few gross times, recording the proportion of heads in each, then plotted it on a graph, or recorded popcorn popping and tried to find the peak and pattern of distribution, you'd probably end up with a graph which was roughly this shape.  I doubt I have to tell anyone reading this that these are called Gaussian or normal distributions or bell curves.

You could actually apply this to something like the quality of items coming off a production line, or so I imagine.  The Friday afternoon cars are down near zero in quality, most of them are in the middle and there are a few super-duper wonderful cars at the top.  I experienced this a couple of years ago when I bought a £60 mini-tablet and it went on and on for more than a year while everyone else's went wonky very fast.  That was also probably part of the charmed life we lead of course.

The another phenomenon which is equally interesting although, for me at least, harder to understand, is "log-normal", also known as 80:20.  It looks like this:

To quote Eddie Izzard, as you can see from my diagram there's a big hump on one side, then a long tail on the other.  Eighty percent is somewhere around the 1.5 mark, I reckon, then that tail accounts for the rest.  This is the log-normal - something seen in all sorts of things, roughly.  There are different shapes but they all have a majority on one side consisting of relatively few of something and a minority consisting of relatively many.  For instance, taking this blog entry as an example, there are relatively few words like "the", "and" or "is", but after you've got about twenty percent of the types of words like that out of the text, you'd be left with approximately eighty percent which are more like the word "approximately" and occur at most a couple of times.  The same applies to letters, or is likely to.

For some reason I don't understand, "everything" is like this, and I will now illustrate it in two ways using my herbal practice.

Around twenty percent of my patient notes consist of great thick folders stuffed full of paper, representing clients whose recalcitrant or recurrent problems have led to the need for a great deal of attention from yours truly.  Their health improves, but slowly, or their initial problems are replaced by others, and I scribble endlessly in my impenetrable combination of Blissymbolics, Elizabethan handwriting and modal logic that I playfully call my "writing" for side after side for a decade or more, on and off.  About eighty percent consist of a couple of sides of sparsely covered A4 recording their rapid departure as happy bunnies now devoid of eczema or migraines, off oxygen or whatever, after a couple of weeks.  This is not a specific failure on my part with that twenty percent - they keep coming back and I do help them, but their problems are deep and complex, as they often are.  The conclusion we can reach from this is that the majority of health problems resolve quickly but a minority of them don't.  Also, though, probably the majority of our health problems as individuals resolve quickly but a minority of them won't, but that minority will eventually come to dominate our lives.  One particular health problem will of course take infinitely long to resolve for every one of us!

The other aspect of this, although there are several and I've forgotten some, shows up in the herbs I use.  Again, a minority of herbs are in the majority of prescriptions but a majority are in a minority.  This means that most people's health is improved by a relatively small list of herbs, but there will always be a minority of people each of whom needs a relatively obscure herb.  Eighty percent of herbs show up in twenty percent of prescriptions and twenty percent in eighty percent of prescriptions.  This means I need to keep a lot of herbs in stock just in case, but a few herbs I will constantly need to order and reorder.  The same presumably applies to pharmacies and pure drugs.  I imagine they get through a lot of NSAIDs and steroids and relatively little thyroxin and cisplatin, for example.

This all appears to be a law of nature.  I have no idea how it operates but there it is.  It may have widespread practical use but again, I can only think of a couple of applications.  It is, however, interesting and one clear use is that knowledge of it means you don't invest much time in trying to "fix" it.