On the 80/20 rule, production efficiency and the art of bodging

I've been thinking a lot about the 80/20 rule lately, and how it relates to the "S curve". You know, how once you reach of the top of the curve where it starts to flatten out, it's not worth your while pushing to make that last 20% perfect. 

A student of mine recently came to me for advice on writing his end of high school maths exploration paper on learning curves, and our conversation reminded me of this post from the blog of one of my favourite books of all time, "Early Retirement Extreme" (ERE) by Jacob Lund Fisker. The key takeaway from the post is that you want to spend most of your time in the middle of the curve, where the curve is the steepest and you get the most improvement in outcome (y-axis) per unit of "effort" (x-axis). This would seem to be an argument for getting pretty good at lots of things, rather than trying to be the best at one thing - at least if maximising return on effort is an axiom you subscribe to.

This is closely related to the book's discussion about the art of bodging or "improvising a working solution using whatever is on hand" as an optimisation strategy. Many readers will note the similarity of this definition to the one for the verb "to MacGyver". The two terms can usually be used interchangeably, although I'd suggest that while "MacGyvering" is usually done to solve an urgent problem or prevent a catastrophe, "bodging" is usually undertaken with the aim of saving money and/or avoiding having to buy a solution. This site suggests that MacGyver is used in US English, while bodging is a British English term. 

I just put this picture of MacGyver wearing aviators here to get you to click on it. 

I discovered Fisker's book in late 2012, and it's had a massive impact on the way I think. This book review on Wise Bread is a good summary if you have the time and inclination, but the 50000-foot summary is that being a consumer is a choice, and that it's possible to live off a fraction of what you earn, if you're willing to make the necessary lifestyle adjustments. The reason most people don't "retire" (read: reach a point where the income earned from your assets exceeds your expenses; this doesn't necessarily refer to retirement in the traditional sense of golf and cruise ship vacations) extremely early is because reducing your expenses to that level requires some extreme measures!

Of course, desired retirement income and desired level of comfort and lifestyle expenses all exist on sliding scales, so it's possible to get a lot out of the book without needing to be a hardcore minimalist who walks everywhere, takes cold showers and buys socks all of the same kind so they never have to deal with mismatching pairs (all of which are approaches suggested by Fisker in the book).

So while the book does have many examples of strategies and tactics that many would consider ridiculously extreme (and that would ruin most marriages, mine included), it's also full of gold, and is littered with hilarious, tongue-in-cheek figures and diagrams that look like they belong in a science or mathematics journal article, like this one from the section on bodging:

(Fisker, 2009)

Some representative quotes from the book include the following:

"The most effective option to save money on clothing clearly is not to buy any."

"You wouldn’t toss a pet either just because you lost interest or found something cuter, right? Ownership implies responsibility: You were responsible for digging raw resources out of the ground and now you’re responsible for getting the maximum use out of the object."

and

"I recommend getting rid of all the weird things in your cupboard. The best way is to not buy anything until your last strange ingredient is gone. Just imagine that there was an earthquake and the stores were closed for a week. How would you do?"

I was inspired to try out that last suggestion recently when our apartment complex was put under a 14-day lockdown as part of Covid-19 control measures. I lasted nearly a week until I ran out of milk. I had the brilliant idea of improvising some coffee with butter and salt that I'd heard about during a recent trip to Ethiopia. It tasted like the Vegemite soup that my mum used to give us when we were sick. I gave up and phoned for delivery.

Further investigation online revealed that you need a blender to make butter coffee properly, which got me thinking about the line on the above graph. I wasn't about to go and order an industrial blender just so I could make myself the occasional butter coffee, but there have been examples of actions that I've found myself doing more often during social distancing (read: while spending more time in my apartment), such as grinding coffee beans, filling up the ice cube tray, and hoiking those really heavy 20L water bottles onto the water dispenser, that have made me contemplate moving upwards and left on the line - maybe I should get an espresso machine? A water filter? Upgrade my fridge to one with an inbuilt ice cube maker? But then I look at that quote about tossing a pet (from the list above, which is one of many ERE quotes on my wall, by the way) and start having second thoughts. 

Fisker suggests that skill can shift the line down and to the left, but I'd also suggest that where the line lies for you is also a function of your attitude towards consumerism and sustainability and how much you value your time and labour at. For example, if we compared the lines for me and my wife on the matter of, say, what kind of coffee making device to own, they'd look something like this:

Figure 1: price of solution as a function of the reciprocal of use frequency, generalised with arbitrary units (produced by the author in Desmos, 2020) (to my maths teacher colleagues and IB maths students, excuse the screenshot - I couldn't get the labels to display when using the export feature)

For me, daily coffee-making warrants owning a plunger, whereas for my wife it justifies an espresso machine :-) 

Thinking about the physical interpretation of the x-axis units, we can modify the graph to be more intuitive and reflective of reality: "reciprocal of frequency of use" can be interpreted as "average time between uses", which can approach both zero and infinity but never reach either. This suggests that a reciprocal function might be a more appropriate model, with the expenditure level justified by the frequency of use approaching zero as the time between uses approaches infinity, and very high expenditures being justified for (almost) continuous use:

Figure 2: modified version of Fisker's 2009 model to account for asymptotic behaviour at very high and very low values of use frequency (produced by the author in Desmos, 2020)

What about you? Where does your line or curve lie on the spectrum? What are some examples of solutions you've improvised or "bodged" because you didn't want to buy something you weren't going to use very often? Share your stories in the comments!