Exponential Growth: Myth, Reality, and Strategic Considerations

July 4, 2024

We’ve all heard the Indian story of the man who asked for his reward to be 1 grain of wheat placed on the 1st square of a chessboard and doubling the number of grains on each subsequent square. While there are only 64 squares, you’d need 2,000 times the world’s wheat production to provide that reward. This famous story shows our lack of intuition about exponential growth and its power.

Similarly, James Clear’s often shared picture shows that a daily 1% improvement will result in ~38X by year-end. This is the same as compounding interest, which shows exponential growth behavior, too.

These stories are powerful. I’m a big proponent of continuous improvement myself. At the same time, since exponential growth is hard to imagine, I often see people misuse it and reach the wrong conclusion. Exponential growth isn’t magic, and if you don’t do the math to verify it, you may find yourself in a situation where continuous improvement won’t allow you to win. But how so? Let’s dig in to see.

There are two parts here:

  1. How significant is the growth at every step (100% in the wheat case, 1% in James Clear’s story)?
  2. How long do you sustain that growth (64 iterations in the wheat case, 365 iterations in James Clear’s story)?

The numbers in the above stories were chosen to show the potential of exponential growth. But the results really depend on these numbers, and they may not be something you have control over in reality.

What if you improve by 1% each week instead of each day? It’s no longer the 3,778% improvement you’re looking at, but 68% instead. It’s still more significant than most would imagine, but it’s not even doubling! And that assumes the improvement you’re making compound. If you don’t have focus and improve in different areas, it will be less than that.

Let’s try a small exercise. If a startup has to double its Annual Recurring Revenue (ARR) (from 2M to 4M) to get its next round of funding, how long does it take to get there if its new ARR doubles every quarter? Only 1 quarter? It’s a trick question since you need to know the new ARR (not the total existing ARR) to calculate. Let’s assume it was adding 50k new ARR in the first quarter; how to get to the new 2M ARR needed to double? It would take 16 months to get there. A lot longer than 3 months. And this assumes doubling is sustained. Just one quarter with a little less new ARR, and the time it takes will be much longer.

So, while exponential growth is incredible, it’s essential to put that into perspective and ask the appropriate questions:

  1. Can we sustain that growth rate? What’s the data to date telling us? Is the growth rate slowing down, even just a tiny bit? What’s the “honest” growth rate we can expect to sustain?
  2. How much time do we have to achieve our goal? Can we get there in time with that honest growth rate? If the answer is no, then continuous improvement won’t help you.

Again, this isn’t magic. Instead, it would be best to look at high-risk / high-reward tactics. They aren’t the first choice. Since they have a high chance of failure, you’d pick a less risky alternative (like continuous improvement) if it would allow you to win. However, if the less risky approach is guaranteed insufficient, the high-risk option is the only viable one.

If you have only 10$ and need to make millions by the end of the day, buying lottery tickets (or other form of gambling) is the only way to have a chance of achieving that goal. Even if you’re almost guaranteed to lose, at least you have a chance.  If you invest it in stocks (or any other form of investment where the odds of losing all money are low), you have a good chance of ending the day with more money but 0 chances of making millions. 0.000000072 is greater than 0.

So, while continuous improvement is excellent, and you should focus on it for many things, remember that it isn’t magic. Sometimes, it isn’t enough. Look at the current state, the goal, the timeframe you have, the current growth, and any deviation from the required growth. Then, don’t guess; do the actual math. We’re bad at guessing exponential growth; minor variations have significant impacts, so be careful.