"Values change at scale"

Garret Hardin

Sometimes it's very easy to make people a lot more money.
Also, did you know that a mouse cannot be the size of an elephant?

Those two sentences are directly related. Hear me out.

Can you imagine the two animals standing next to each other and then, conceptually, scaling the mouse up to be the same size as the elephant? Hold that image.

While holding that image somewhere in your mind, let me present some sound mathematical reasoning as to why it's not possible from all the way back in the 17th-century courtesy of my homie Galileo:

"The weight of an animal goes up as the cube of its linear dimensions, whereas the strength of its supporting limbs goes up only as the square."

Below is an excerpt from Garret Hardin's Filters Against Folly with my snarky comments or additions in italics below.

Suppose we compare two identically shaped animals. Animal A is 3 units long, while animal B is 6 units long.*

Weight of A = 3 cubed = 3 x 3 x 3 = 27

Weight of B = 6 cubed = 6 x 6 x 6 = 216

We can see that 216 is 8 times as great as 27; though animal B is only 2 times a long as animal A, it is 8 times as heavy.

As for the strength of their legs:

Strength in A = 3 squared = 3 x 3 = 9
Strength in B = 6 squared = 6 x 6 = 36

So B’s legs can only bear 4 times as much weight as A's legs. But B is 8 times heavier (and has the same number of legs), so B's legs are only half as strong as they need to be (4 divided by 8). Clearly, something has to change as the length of the animal increases.

If the material of which the legs are composed is the same, then the cross-sectional area of the leg has to be doubled. The leg has to be thicker. This is not all.

Since heavier bones will require more powerful muscles, many secondary changes in appearance will also be necessary, not to mention the behavior which must correlate with the lightness or massiveness of the body. If mice evolved to be as big as elephants, their silhouette would be that of elephants. This simple maths proves the point that a mouse cannot be as big as an elephant.

* I can hear the detail people now, getting caught up in needing to know exactly what units of measurement are being used. This is why they remain blinded to patterns. Changing the unit of measure does not change the math or the implications of the math (effect of scale on values)

The mathematical difference is simple, but the practical conclusions that follow are profound.

In reaching the conclusion above, we have to do a little bit of calculation. But after that, we need only to remember the general pattern of the calculation to understand the general implications of this "scale effect."

You were likely able to scale a mouse to the size of an elephant in your head without any issues because our brains tend to fail to recognize patterns (nothing scales in a linear fashion).

• What works to govern 10 people will not work to govern 150 people.

• What works to govern 150 people will not work to govern a state, a country, or the world (see: the tragedy of the commons)

• What worked at $40,000 in revenue will not work at $400,000 in revenue

• What worked with 3 employees will not work with 30 employees

You can't just turn small things into larger versions of themselves. And you don't need fancy calculators or spreadsheets to understand this, just have to remember the general pattern of the calculation.

Years ago, I met a woman that expressed to me, on a zoom call, she felt lost in her business. Without sharing too many details; it was an e-comm business that she stumbled into by accident. Her buyers were raving fans and her product was amazing (I shared it with quite a few people). After realizing she had something great, she made the mistake most people in her position make: hired a bunch of coaches that don't understand general patterns or scale.

Unable to recognize the basic patterns of scale effect they all told her a version of the same thing:

"You are profitable selling 100 units a month from ads, so order 1,000 units for inventory and spend 10x as much on ads. After that, we will move to 10,000 units and 100x on ads. Simple, right? Just scale the mouse up to the size of an elephant."

Turns out a mouse cannot be the size of an elephant. [This is my surprised face].

Just 15 minutes into the call it was obvious (to me) I could help her. She was confused because I didn't do any math, no spreadsheets, calculators or detail-oriented questions, how could I already see that there was a better path forward? All of her coaches have elaborate spreadsheets with all the details and metrics and couldn't figure it out, how could I even know where to start?

(They were doing good computations, but using poor mathematics because they fail to see the general pattern of scale effects.)

I said: "You do not have to trust me or pay me anything, I will just tell you where to look so that you can do the proper math" We will call this process The Diagnostic.

So I did. And she did. She came back and joined my since-discontinued mastermind.

Step 1: The Solvable Problem
Q. Where are you now and what are you truly trying to accomplish?

A. Paraphrased: "I have X in inventory, Y in the bank account, and my husband has a great career I want to keep doing this because I love it and it's very important to me to contribute to my kid's school tuition. I don't need to pay for it, but it's important to me to do that, just so I feel good about how I am spending my time"

The total needed to pay for the kid's education was about $40,000 a year.

At the time we spoke the business had been profitable in the past but was operating at a small loss for the last few months.

Step 2: CASE
Compile, Analyze, Strategize, Execute

At first glance I had a gut feeling (pattern recognition) that she was already where she needed to be, ignorance to scale effect just caused her and everyone trying to help her to miss it, entirely.

She also said something along the lines of: "I have about 300-400 people that buy the monthly special every single month"

Because I am not a detail guy, I told my partner and COO at the time what I saw and asked him to go through all the data to validate what I thought was hidden in plain sight:

"I am pretty certain that there is a point that she could stop running ads and close the cart, my guess is that her ad performance tanks right around the time 300-400 units have sold and she throws the rest down a black hole. Can you check her ads data, and sales data and confirm? And then do the calculations showing what it would look like if she had only ordered 400 units and then turned off ads and shut down the cart after they were sold. Go back a year"

Understand: I didn't see her ads account or sales data a single time. We did need the details, but only after the pattern was recognized (good mathematics must come before accurate computations).

Sure enough, had she ordered 400 units and shut down the cart + turn off ads the moment the 400th unit sold, she would have averaged over $12,000 a month in profit.

That's $144,000 in profit, $104,000 more per year than what she was hoping to get to by trying to scale with poor math.

A mouse cannot be the size of an elephant.

Values change at scale.

Ratios change at scale.

Function changes at scale. (Technically, scale should be determined by function)

It depends.

Another rule straight from ecology:

"The scale of things determines what is functionally best"

or said another way; function must come before form.
"Should you scale your business?"

It depends on what function your business is meant to serve. In the scenario above the business is meant to be a source of joy, and fulfillment and to fund something important. The answer is no. Scaling her business would get it further away from being functional in her life.

If the answer, for you, is "yes, I should scale my business" be careful not to confuse accurate computations with good mathematics. Think of the elephant and the mouse and recall the underpinnings of the conclusion.

Or don't.

Your life, your rules.

Nic