Not 1% better every day

Getting better 1% every day is an idea that is almost always disconnected from the reality of making improvements in life/industry.

Unfortunately I keep seeing this idea everywhere (and by everywhere I mean mostly LinkedIn) and it’s driving me crazy so I have to write something about it.

Atomic Habits #

In James Clear’s New York Times Bestselling Atomic Habits, he describes the principle of improving by “aggregation of marginal gains”:

Here’s how the math works out: if you can get 1 percent better each day for one year, you’ll end up thirty-seven times better by the time you’re done

https://jamesclear.com/marginal-gains

The math is right. But it’s not really how skill acquisition works in the real world. The fundamental problem with it is that it implies that you can improve more quickly as time goes on.

In general, I have had the exact opposite experience trying to acquire skills and knowledge in my life.

In my experience:

• first you improve quickly
• then you improve slowly

Reducing the idea to absurdity #

Let’s demonstrate the ridiculousness of the “1 percent better every day” model of improvement by extending it across more than 1 year:

If you compound your improvements by 1% every day for 365 days, indeed you will end up 37 times better by the time you’re done.

But if you do it every day for five years, you will be 1.01^(365*5) = more than 77 million times better than where you started.

Do it for ten years, and you will be 1.01^(365*10) = 5.9 quadrillion times better than where you started.

Or, looking at it within the scale of just the first year:

• If you improve by 1% every single day for a year, then on the last day of the year, you will have to improve 37 times as much on the last day of the year, as you did on the first day of the year.

For example #

Let’s say you have never lifted weights before and you decide you are going to begin. Your goal is to improve your single repetition maximal strength on a barbell back squat.

The first time you get into the gym, you are able to squat 100 lbs. That may not be much, but, 1% every day – right?

The first session, you only gain 1.0 lbs of strength. This is very reasonable, and actually untrained individuals may indeed be able to gain 1lb of strength per day in their first week of training back squats.

But since you are a LinkedIn 1-percenter, on the last week of the year, you will be adding more than 30 lbs a day to your back squat, every day, for the last seven days! In fact you will be squatting 3700 pounds.

If you simply work diligently and patiently, that 1% can really add up. After 20 years of dedicated lifting, you’ll be able to lift the sun itself (math).

A better model #

Skill acquisition and physiological adaptations to exercise tend to follow logarithmic rather than exponential curves.

The first week of back squats, you might gain 10 lbs of maximal strength. On your 52nd week of squatting, your mileage may vary, but I think most people will be happy to continue going up “just” 1 lb per week.

After many years of lifting, you may stop getting stronger in your squat altogether, or otherwise be happy to add 1 lb of maximal strength per month.

As an algebra refresher, here’s a chart showing a logarithmic and an exponential curve on it – notice the “plateau” effect we see in the logarithmic curve:

I think this is probably why the “80/20” rule (another LinkedIn cheerleading concept) is also popular.

The Pareto 80/20 principle has been stated in various ways but it’s something like “you can get 80% of the value of doing something by spending only 20% of the effort on it” or, rephrasing, “eking out the final 20% of value requires quadrupling your efforts”.

This is closer to making sense to me re: skill acquisition, and as a bonus it seems pretty close to how logarithmic growth can work as well:

• If you improve at something logarithmically (say e.g. log base 2) for a year, and you start at zero, you will get 80% of the way there at around 30% of the way through the year, day 112 (math).

Exponential growth as a valid model for other things #

I’ve been specifically mentioning skill and physical strength acquisition, but there are other things we sometimes want to model or to improve that do grow exponentially.

For example, if you are a long-term investor in the US stock market, you may reasonably expect compounding gains of 7% real growth per year over the course of a 50+ year investing period. That’s closer to 0.02% every day rather than 1% every day, but it’s still something that is actually exponential.

Actually, I am unable to think of other things in life that improve exponentially.

Other curves #

There are other curves, too, that may model skill acquisition even better than logarithmic curves. Power law curves come to mind. For an algebra refresher, ask your favorite LLM: “what are the differences between these curves: power law, exponential, logarithmic, polynomial”.

It’s also worth noting you can approximate any curve as closely as you like with a sufficiently high degree polynomial.

But I don’t think it’s super important to closely and accurately model improvements in skill for ourselves. In general, I think it’s just psychologically helpful to keep in mind that you may not improve more quickly as time goes on. Know that when you start that you may improve quickly at first, and that before you know it you may be fighting a plateau. Sanity that way lies.