# Counteracting Law of Large Numbers

All,

Throughout the years I have seen many mentions of the law of large numbers and how it shouldn’t be surprising that YoY revenue growth decreases as revenue increases. I have been using a metric to counteract that and get an idea of how the companies look no matter which stage they are in. My goal in all the metrics I use is to normalize things across companies for direct comparison. This will be a short post on it and I would appreciate any feedback.

Rev Trajectory = sqrt(Revenue)*YoY_Revenue_Growth_Rate

The idea behind this is that revenue grows exponentially while revenue growth rate decreases linearly. In order to make them both linear, you can take the square root of revenue (you can use yearly or quarterly). I expect (hope) to see Rev Trajectory stable or increasing. If the metric starts to decrease, then I know that the revenue growth rate decrease is outpacing the revenue growth.

An interesting takeaway from the metric is that Crowdstrike is one of the only companies that is still showing an increasing Rev Strength. They are insanely consistent and I have been pleased with the latest ER.

-Junomean2

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The idea behind this is that revenue grows exponentially while revenue growth rate decreases linearly. In order to make them both linear, you can take the square root of revenue (you can use yearly or quarterly). I expect (hope) to see Rev Trajectory stable or increasing. If the metric starts to decrease, then I know that the revenue growth rate decrease is outpacing the revenue growth.<<<

Juno,
It’s been too long since I was competent at even the lower part of higher math, but here’s my \$0.02:

If you look at ln(Revenue) over time and fit a line to it, you can easily see if exponential growth is being achieved as the natural log of an exponential function will graph as a straight line.

Another thing might be to fit a line to the observed revenue and take the first derivative of the resulting function. If the first derivative is positive, then positive revenue growth is achieved. Then I would think you would look for a decline in the slope of the first derivative - the second derivative. In my terms, the first derivative is slope of the revenue function, the second is acceleration. As acceleration slows, you get concerned.

I’m sure there is a more seasoned mathematician on here who can clean up my mess.

Thanks for making me use a neglected part of my brain!
Vince

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Hi Junomean,

If I understand what you’re looking for, I think you can get a more meaningful answer and with increased accuracy, by doing the following:

• Row 1: List Revenue for each period

• Row 2: Calculate the Rev Growth Rate for the latest period: CurrRev/PrevRev-1
o Copy that formula to each successive date-column.

• Row 3: Calculate the Growth Rate of Growth Rates: Divide the Growth Rate of the latest date-column by the Growth Rate of the previous date-column and subtract 1 (just like you calculate a stock-price gain from one period to the current period, it makes no difference that these are percent.) Format as percent.
• Copy that formula to each successive date-column.

These results have the benefits of being directly comparable between any size companies, and increased accuracy because they are a direct calculation rather than a derivative.

Or, as mentioned, maybe I’m missing the comparison you are attempting to make.

I hope that helps. If not, please hand me my teddy bear and tuck me in.

Dan

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Or, as mentioned, maybe I’m missing the comparison you are attempting to make.

My goal with this metric is to see how impressive the growth rate is given the absolute revenue of a company. How can we compare Datadog’s revenue growth rate with Monday.com’s when Datadog has \$406M of revenue and Monday.com has \$124M? For me this metric normalizes the growth rate across businesses with different sizes (revenue). It is not perfect but it is better than saying Monday.com and Datadog are about the same because they are both growing revenue ~75% YoY. Datadog’s growth rate is much more impressive because they have >3x the revenue.

As stated there are many ways to derive something for normalizing this effect and I wanted to present one way. I also have to make the same caveat I do every time I post a metric: this is ONE tool in the toolbox and should never be taken in isolation.

-Junomean2

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