Does the Law of Large Numbers Apply to Software-as-a-Service (SaaS)?

When analyzing your Software-as-a-Service (SaaS) business growth, there are multiple different ways to plan. One thing all businesses must keep in mind the law of large numbers. The law of large numbers began in probability and statistics but also applied in business growth and development. What you need to consider here, and what we will discuss in this article, is if you doubled revenue in one year, can you projected that you will increase again next year.

The Law of Large Numbers

The law of large numbers in regards to probability and statistics states that as the sample size grows, it gets closer to the average of the whole population. Now, this idea may seem pretty common sense; of course, when you build a sample size, the result will be closer to the average population. But, let’s not shrug this concept off so easily. There are many instances that this law becomes a crucial way of thinking. 

History of the law of large numbers

The law of large numbers was first proved by the mathematician Jakob Bernoulli in 1713. He and his team were developing a process in which they could use probability theory to analyze games of chance. 

The law of large numbers is similar to the law of averages. In coin tossing, the law of large numbers says the outcome of heads eventually is ½. So, if out of the first 10 tosses only 3 are heads, the law of large numbers says it can take a very long time to approach ½. For instance, for probability to hit 95% that the fraction of heads is between 0.47 and 0.53, the number of tosses must surpass 1,000. This means, only having heads appear 3 times out of 10 is dwarfed by the remaining 990 tosses.

Where The Law of Large Numbers Applies

In financial terms, this indicates that when a large business proliferates, it cannot sustain this growth pace forever. In business and finance, the rule of large numbers refers to the fact that exponential growth rates often do not scale. Technically, this is not related to the law of large numbers but is a result of the law of marginal returns or diseconomies of scale. For example, when looking at two different companies with two very different prior year revenue figures but both with the same goal to increase revenue by 50%. The law of large numbers dictates that the company with the higher prior-year revenue will struggle more than the other company to achieve this goal. 

The Law and SaaS

As I am sure you are wondering, “okay, this is great and all, but what does this probability equation have to do with my SaaS business?”. Multiple studies have taken a more in-depth look at this correlation. SaaS Capital – a provider of venture debt compiled data from approx. 950 SaaS companies in 2017, determined what you might be thinking. The law of large numbers applies in such that as revenue grows, percentage growth in revenue tends to decline.

In a survey from SaaS Capital, the median growth rate for companies with an Annual Run Rate (ARR) of less than $1 million was approx. 60%. Compared to companies with an ARR greater than $50 million sharply declined to approx -27%. Now, as the word “median” dictates, this hides the best and worst-performing companies. This is not to be taken as a blanket statement but a statement that will affect the vast majority of companies. 

Why The Law Applies to SaaS

The law of large numbers will apply to SaaS businesses in many ways. When you are a growing company, you can use these statistical views to understand your growth and plan around it. It has been observed and well documented that businesses in the early to middle stages ($30 – $50 million and sometimes earlier) have adopted the law of large numbers and have added enough small to medium-sized customers. This adoption helps with rapid growth but is challenging to sustain over the long term. This forces the support staff, account managers and sales members to adapt quickly to the needs of enterprise customers. 

Why The Law Doesn’t Always Apply to SaaS

Now, the law of large numbers will not apply to everyone in every scenario. If you are a new business and are slowly building your customer base, it is more than likely you are building with small to medium size businesses. Not only are you working with smaller companies, but you are also typically spending more time on each customer as you try to ensure everything is working correctly and collecting feedback. In this scenario, the law of large numbers would not apply. If you were to introduce the law of large numbers in this scenario, you would not collect the feedback needed to improve your software; your customers would have high turnover as you are not able to meet their requirements, and you would not develop those longer-lasting relationships with your customers. 

 Theory of Constraints

The theory of constraints refers to a methodology of identifying the top limiting factor and systematically improving it in hopes of eliminating it. Through the understanding of the theory of constraints, we can determine where the “bottleneck” is and allows us to resolve this issue. To fix an aspect of this nature, we must address the issue itself, not the flow before or after, hoping to increase the flow but to solve the actual problem.

In regards to the theory of large numbers, this goes to show that adding more volume to an issue does not solve the issue. Whether this issue is converting sales or generating leads, adding more numbers (within their respective criteria) does not fix these issues. You must identify why this bottleneck is happening and address it. You may be experiencing it due to a lack of sales staff, in which adding throwing more customers at them will not solve the issue. Address the issue of a low sales force by adding more trained members to your sales team to work as a unit to convert sales. 

The law of large numbers affects every business in different ways. No matter which approaches to business you take, the law will follow you, but it is how you manage the number of customers you have to maintain growth. It is important to remember the faster you grow, the faster it becomes harder to sustain this growth, and it must be accounted for.