No, the title of this post is not hyperbolic.
By the end of this article, I will prove to you that the absurd proposition that most of what happens in the world can be explained by only three simple graphs is not as ridiculous as it seems.
Of course, I’m always open to the notion that I could be off.
Hurl as much as you can at my hypothesis. Try to break it with examples that seem to be exceptions.
There is a chance that a great deal of exceptions are similar enough that there is a fourth graph that could tie them all together. Then I’d just edit this post and include that fourth graph. Or fifth.
You get the point.
Let’s get started with the one that most people are familiar with.
The Bell Curve
Here is the graph in its detailed form.
If you’re not familiar with what standard deviations are, they are measures that demonstrate how spread out a data set is.
68% of data points are within + or – 1 standard deviations of the mean in a normal distribution/bell curve. This means the data does not vary to an extreme extent.
Here is the graph in its simplest form.
One way or the other, you have surely encountered this graph at some point in your life.
It is primarily used to describe the normal distribution of some trait across populations or samples. The x-axis represents the measure of whatever trait, and the y-axis represents the frequency within a population.
The most common example is that of the distribution of IQ’s (the traditional measure of intelligence) across populations.
It’s fairly self explanatory, but 68% of people have an IQ that falls in between 85 and 115.
This goes back to our conversation on standard deviation. Within plus or minus one standard deviation from the mean, so 100+15 and 100-15, you can find 68% of the entire population. Most people are average.
Below 85 is what would be considered dumb. Above 115 is what would be considered smart. 100 is the exact average IQ.
These cut offs are not perfect. You would be hard-pressed to pinpoint the difference between someone with an IQ of 110, and an IQ of 120.
IQ also does not demonstrate itself outwardly 100%. There are people who are successful, well-read, and extremely hard-working that would come across as someone with a high IQ, but are surprisingly average or even below. Conversely, you might come across ignorant, lazy, and uneducated people who technically are intelligent on paper.
Both tails are extremely rare. It is unlikely you will meet many people who are actual geniuses, to the same proportion that you would meet people who are mentally handicapped.
The IQ example should be straightforward, and I imagine many of you will agree that the bell curve would describe the relative intelligences of the people you have, or meet in your life really well. Most people you know or come across will be somewhat average.
If you grow up in a more affluent area, or attend a prestigious institution there might be a skew to your graph. That being said, no matter how elite the sample of the population may seem, I’ve still personally seen the bell curve play out—with tighter standard deviations (a narrower and taller bell in the bell curve), with the shape remaining the same.
Let’s move away from IQ, so that I can show you what else the bell curve may apply to.
The first example seems to be a natural transition from IQ—performance in the workplace. For those of you that have or have had a job or internship, again, your wheels ought to be turning.
There are the overperformers at work. These people go above and beyond to impress the boss, or are just that efficient and talented at what they do that they cannot help but stand out. Perhaps you are one yourself. There are not many of these.
There are the underperformers or slackers at work. These people actively avoid doing their work, or complete their tasks in a way that calls attention to how incompetent they are. There are not many of these.
Then there are the majority of people—the average workers. There is a slight deviation here, from those that do the bare minimum to not be reprimanded, to those that could work just a little harder and overperform.
Most workers are middle of the pack, replaceable drones that are too scared to pitch new ideas or take risks that overperformers can pull off. Conversely, these same workers care enough about their jobs, and are smart enough that they will never sink to the level of an underperformer.
Interestingly enough, there may be a specific reason that the bell curve is especially prominent in the workplace.
Consider this regarding the scarcity of the above average tail end: overperformers do not remain in their positions for long because they often get promoted, or jump ship to another company where they receive a higher pay and/or title.
Now that they’ve moved up a level and have new responsibilities, they are now part of a group of people who were also previously overperformers—making it harder for them to stand out.
Eventually, most overperformers max out their overpeformance and end up becoming an average person within a smaller group. Even at the very top, there are mainly average CEOs (think Mark Hurd, Tim Armstrong), some incompetent or corrupt CEOs (Ken Lay, John Sculley), and some rockstar CEOs (Jeff Bezos, Tim Cook).
This is why even in elite samples, you’ll see the bell curve still applies. Look around at your college classmates. These people were likely the overperformers at their high schools, but now are languishing in the average range at a good university. Those that are overperformers at good universities then go on to good graduate schools where they are competing with fellow overperformers from other universities, and the fierce competition likely relegates them to average status.
You get the picture.
Now, consider this regarding the scarcity of the above average tail end: underperformers get fired. It may take a while, but eventually, any halfway decent company will get rid of its underperformers.
Once those underperformers are gone, the bottom range of the average people are now in the hot seat. They either shape up and move back off the chopping block into safely average, or are unable to, therefore getting them fired.
Meanwhile, the replacements that come in are likely average (according to the probability of the bell curve), so that the middle continues to crowd.
You’re probably thinking: “Okay Matt, so far you’ve given me IQ, college students performance, and worker performance. They’re solid examples, but their connection to the bell curve seems to be fairly obvious. I need some more.”
Let’s move to the athletic.
Here is a graph of average marathon completion times.
Hmm, looks familiar.
Here is a graph of the distribution of height, separated by gender.
Interesting. Let’s try to delve to the more outlandish.
Here is a graph of how our body responds to stress.
Not a perfect one to one, but very similar.
This graph merits an explanation. It depicts the way in which the body reacts to stress. The x-axis depicts the three phases in which the body undergoes when dealing with a stressful event (these events can be daily stressors or chronic stressors). The y-axis depicts the resistance the body has to the stress.
As you can see the body slowly builds up resistance to stress, but if the stressor remains for a long enough time, the body becomes exhausted. This is known as burn-out. And burn out ends at the tail.
Here is a user-generated graph of the distribution of diets in the US.
This one is more discretionary but still fits. Think to your self how many vegans you know, and how many people you know on a strict Keto diet.
Here is a zoomed in graph of repeat foreclosures in the US.
Here is a graph of Yerkes-Dodson Law—the law essentially states that you perform best when you have a healthy amount of stress or anxiety towards the action you are performing. Too little stress and you won’t care enough to try, too much and you’ll be too crippled with panic to perform.
So what gives? What’s the explanation here? How can this shape of graph work for different instances across radically different topics?
The first graphs are easier to explain, as they represent what the curve was literally invented for—given a large enough sample, you can map the frequency of a continuous variable in a bell shape.
This is due to central limit theorem, which approximately says that a bunch of independent random variables combined together into one variable will result in a normal distribution. The probability that the loosely or non-correlated combinations of all these variables converges in a strongly defined average range is high.
Perhaps this graph of the probability of how many heads you will get after 100 coin flips will help clarify the initial explanation.
Well what about the other weirder variables? This explanation is less scientific, but I believe satisfactory.
Balance. Our body has adopted an approach to neither trying too hard nor too little, because this preserves our health and energy, while still producing acceptable results.
Our body enjoys being in homeostasis, and when it exits homeostasis for whatever reason, it enjoys reverting back to it ASAP.
That explains General Adaption Syndrome, along with Yerkes-Dodson, and the dietary preference curve.
But what about the repeat foreclosure curve? A sudden explosion of a phenomenon across a timespan, before a reversion to the mean? Our next graph will better explain that one.
The Exponential Growth
Okay, I’ll admit this one is kind of cheating. It technically is two graphs—both starting the same, but two different variations of the end.
Here is the first graph (ignore labels for now).
Best summarized as exponential growth with a sudden crash (J-curve is also another name).
Here is the other variation.
Technically this is labeled as logistic growth, but I would classify it more as exponential growth with leveling off (S-curve is another name).
Either way, these graphs both feature some variable exploding in frequency at a breakneck rate after a temporary period of gradual stagnation/slight increase.
The first type has a sudden decrease that mirrors the exponential increase in its speed, meanwhile the second has a prolonged stagnation (could be temporary or permanent).
Let’s look at the most common example of the first type (growth and crash).
First we see the stagnation—investors are wary or unaware of the opportunities presented to them, or they simply don’t have enough cash to invest. A few people get in at this early stage, but most stay out or don’t even have it on their radar.
Then we see a steady gradual increase as a few smart investors start to catch wind of the opportunity. The opportunity is still relatively unknown and unproven, so there’s a definite risk to investing this early—which keeps most out. Also to be fair, the general public is usually kept in the dark about opportunities this early on.
Then we have the initial explosion, where buyer sentiment increases suddenly because of some mainstream news or precipitating event. All of a sudden some of the average people warm up to the idea and realize they stand to make a lot of money.
Then comes the manic phase. By now, the actual price of the opportunity is above its fair valuation. Sure, it was a good idea with a fair price, but now it’s a good idea with a fucking outrageously expensive price. The people who get in late at this stage think there’s still room to grow, so they don’t mind paying this premium (if they even think they are paying on). They assume they’ll surely find a buyer at a higher price soon enough.
The smart money has usually gotten out somewhere near the peak. These experienced investors see the warning signs flashing and desire to cash out their massive profits. They take their cash and sit on it till the crash, or start seeking other ideas that are also in their infancies.
The opportunity may also start receiving more scrutiny as it is now wildly popular, and people may start finding flaws. These two actions result in a reasonable dip.
Those that bought at the top see a little crash and start panicking. They were in it for a quick buck and cannot tolerate even minute losses. They aren’t professionals and are largely driven by emotion. This panic selling piles on and drives the prices sharply downward, as there is no one legitimate propping up the buyer sentiment.
Eventually, if the idea was worth anything from the start, and wasn’t a scam, the price will settle down and stop falling like a sharp knife. Investors will buy a bit, as they believe the valuation is now fairer than it was at the peak, but the public that was burned heavily will stay out. Until the opportunity evolves/progresses and is brought back into the mainstream.
Here is the bubble repeated over and over in recent history.
Th crashes are the dot-com bubble of the early 2000s, the housing bubble of the late 2000s, and the author’s prediction of an impending crash after the current longest bull market of all-time.
Here is a graph of how your blood glucose levels react after a sugary meal.
Here is a graph of reported cases of polio.
Here is a graph of the average pay in the financial industry. Small dips and peaks, but the broader trends mirror the previous graphs.
And if you really wanted to, you could zoom in and argue that the smaller peaks and dips are just scaled down versions of the larger graphs.
Here is a graph of cigarette consumption in the US.
Here is a graph of melatonin production.
These two also somewhat resemble a bell curve, in the same way that the mortgage example is similar to the exponential growth and crash.
This last graph should be familiar to college students. Not too sure about the all nighter part though…
Now let’s move on to the S curve example, where we see sudden growth and then leveling off.
The best example is similar to the St. Matthew reindeer herd one. Except in the St. Matthew reindeer herd, the reindeer had no predator or competing species, and therefore grew far beyond their carrying capacity.
The earliest members of the species have it hardest at first. They must pioneer survival in a new environment, and fend for themselves with limited numbers.
There are plenty of resources for them to compete for, but they still have trouble managing survival and organization.
As births steadily begin to outpace deaths, the species sees rapid success. They’re now acclimated to their environment, and have carved a respectable niche that allows them to take full advantage of the resources around them.
Now we have uncontrollable reproduction. Resources are beginning to be limited. Previously, cohesion was high because there was little to no competition for resources. Now, it’s eat or get eaten. Eventually, enough animals die to establish a healthy population limit.
If significantly more species are born, then you see a rise in deaths. When there is a rise in deaths, you see a significant rise in births. The species reaches a sustaining equilibrium eventually.
Here is another example, in the number of new reported AIDS cases in the US up until the mid 90s.
Here is a graph of Gmail’s market share in 2010 (2018 would just be further stagnation).
Notice the other two competing lines are just an inversion of the S curve.
Here is a graph of the U.S.’s incarceration rate up until 2008.
Here is a graph of what it looks like to master a new skill or hobby.
Now back to the important question once more—why? Why are exponential growth graphs so widely applicable?
In the case of the population related graphs, the answer is that there are simply a finite amount of people or resources.
AIDS can only infect so many people before we educate people about avoiding it. Polio can only infect only so many people before we find a cure and eradicate it.
Software solutions can only convert so many existing customers before there is only a tiny dribble of new customers to keep them growing. You can only get so good at a new skill before you’ve maxed out how good someone can be at a particular skill.
With the more prolific crashes like glucose levels and stock prices, the answer seems to be about momentum. A force that rises quickly must be rising quickly because of some fundamentally sound reason—if it isn’t then it will fall as quickly, for its own good.
Think of when things are restrained for a while, but gaining steam. They slowly amass potential energy, which explodes out of the gate when let free—but is just as quickly exhausted when it is converted to kinetic energy.
Again, these explanations are not scientific by nature, but I’d say the intuitions are correct. Feel free to chime in if you feel that I’m missing something, or are completely missing the point.
The Pareto Principle
I’m positive that my readers have heard of the first two graphs: the bell curve, and the exponential growth with its two variations.
The third graph is more unknown, however once you’ve seen it, you’ll realize it’s everywhere in your life.
It is actually less commonly displayed a graph and is more often discussed as a rule of thumb, but it still makes sense in graphic form.
Think quickly about the work you’ve accomplished today. Chances are 80% of the actual productive work you’ve done has come from 20% of your total effort.
Within a company, 80% of your productivity comes from 20% of your workers.
How do these two work?
Well for an individual, so much time is lost on mindless activities (checking emails, reading articles, being on social media, eating lunch/snacks, going to the bathroom), and even more time is lost on meetings and general workplace chatter.
Given our short attention spans, we usually complete work in bursts. It takes all the hours of dicking around, synthesizing information, and prepping, before you actually end up producing something.
This is observable in a company, just at a larger scale. Particularly in a larger organization, many jobs are non-essential. They can be very important to squeezing out every last margin of profit, but the company would not suffer dearly if it chopped off a toe or a finger.
Meanwhile, the most essential jobs drive your core business. In tech, your software engineers and salespeople are critical. Without them, your business would completely collapse. In finance, your investment bankers and traders are generating the bulk of your revenues. Without them, there is no way you could stay open.
But if you scrapped your policy teams (yes I’m aware of the irony), or your compliance teams, or your marketing teams—and not all at once—you’d suffer some sort of decline but it would be minor.
Now, here are some more examples of the Pareto Principle in effect.
Take a look at this, another business centric example.
Sit down and calculate your own personal expenses. You’ll likely find that 20% of the things you spend your money on result in 80% of your overall costs (for me it was ~25% generating ~75%).
Make a list of your friends. You likely spend 80% of your free time with 20% of the people on the list.
I could keep going but you get the point.
Here is where I tie it all together.
Everything is connected. Some of you with keener eyes may have already noticed that the three types of graphs are linked in various ways.
This is how I see it, with an example.
The tail ends of a bell curve consistently under or overperform. Most people in the financial services industry are on the positive tail end of the bell curve when it comes to IQ, and/or GPA’s and educational achievements.
They overperform until they reach a role where they have outsized influence on their corporation, a corporation which has an outsized influence on the rest of the industry, an industry which has an outsized influence on the world economy. That is the Pareto Principle in action.
They continue to do their work that has an element of leverage in its impact, trying to cater to their corporation’s bottom line—but knowing this is only largely possible if they target average people (think relaxing standards of creditworthiness so that more people can afford a mortgage i.e. 2008 housing bubble).
The fat part of the bell curve (filled with average people) pile in quickly once given the opportunity, but think little about the consequences or long term effects. Once the negative tail end of the curve (people with terrible jobs, no credit etc.) start participating (buying homes in this example), you can bet the fun is over.
It all comes crashing down rapidly, as the market and our individual selves search for a regression to the mean, or a stable equilibrium.
Then our attention cycle moves to something new. More people are born. More people join the workforce. Everyone forgets and keeps living life.
And then we repeat the same cycles.
Aim to prioritize your 20%. Do everything you can to be above average. Embrace the mania but expect the crash.
Consider this post perpetually unfinished.
I’m going to start off with a few examples I’ve found that do not fit in to any of the three categories, along with a few comments.
If you come across any others, I’ll be happy to add them.
Here is a graph of the nationwide distribution of credit scores.
The argument could be made that this is a warped bell curve, or an exponential growth graph. The ambiguity makes me place it here though.
Here is a graph detailing the average weight loss journey.
No sudden drop, just a steady decrease with a plateau.
Here is a graph of the billions lost in hurricane damage in the US.
No clear trend here.