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Math meets B2B SaaS: Who says data analysis and gut feel don't go together?



You’ve hired a stellar Account Executive who you believe will achieve 90% of their quota. Following a 3-month ramp up period, you’ve assigned them a £100k sales target for Q2. It’s May, and you’re yet to see any results… How likely is the Account Exec to hit their target now? Well, Bayesian statistics has the answers for you.


Bayesian statistics is an approach to data analysis and parameter estimation that shows that being data-driven doesn’t mean ignoring your gut feel or experience. On the contrary, the Bayesian approach encourages us to bring the beliefs we have about the businesses we manage and the sectors we operate in, into the equation. At the core of this approach lies the very intuitive principle that we should be updating our beliefs and expectations as we uncover new information, instead of starting from a position of ‘no view’.


In business, this methodology can help you understand whether a launch in a new geography is going well or not, whether an Account Executive is ramping up as expected, or how a specific demo is contributing to demo-to-close conversion rates. Curious to find out how?


Welcome to the third edition of Math theorems meet B2B SaaS, where I’ll cover how you can leverage Bayesian statistics to ensure your Go-to-Market Strategy stays adaptive and data-driven! (And spoiler alert, despite its scary name, it’s very simple to implement 🤓)


‘Math theorems meet B2B SaaS’ is a mini-series where I discuss how math theorems can help explain and address some strategic as well as operational topics in the world of B2B SaaS.


The first edition of "Math meets B2B SaaS" covered how Poisson processes can help you think about your GTM strategy from a new perspective.


The second edition covered how you can leverage the optimal stopping theory to land on the best Ideal Customer Profile (ICP).



Let’s start with the basics: What is Bayesian statistics?


Bayesian statistics is a way of analysing and interpreting data that is particularly useful in situations where there is existing knowledge or beliefs about a topic, or when the available data is limited. In essence, it provides a mathematical framework for updating and revising beliefs based on new evidence.


Let’s start with the terminology: in Bayesian statistics, your current belief (think of it as your market knowledge, experience, etc.) is called a prior. Then, as new information (e.g. new sales information, marketing campaign performance, etc.) becomes available, you update your belief, making it more accurate. This updated belief is called a posterior.





Footnote: This is an iterative process where you update your current belief (prior) with new information at each step, and your updated belief (posterior) becomes your new current belief (prior) at the next iteration.


How’s this relevant to my go-to-market strategy?


Product and tech teams have been leveraging Bayesian statistics for various use cases from A/B testing product feature releases, to anomaly detection in data, to building predictive models. For instance, Latana, a brand performance analytics company we are proud to partner with, uses Bayesian inference to construct statistically significant findings from large sets of question-level data. With this technique, they are able to provide rich and accurate insights on brand performance that they wouldn’t be able to otherwise.


However, this methodology doesn’t need to be confined to the use cases of product and tech teams. As a business leader, you can also leverage Bayesian statistics to combine your expertise and gut feel with real-time data to update your predictions and ensure your commercial decisions remain adaptive and data-driven.


For instance, as Head of Sales, you already have an idea as to where you’re likely to close this quarter. As a marketing professional, you already have an initial hypothesis as to which marketing channel is going to perform better. Using Bayesian statistics, you can bring those views into your data analysis in a legitimate and systematic way.


From a commercial decision making standpoint, Bayesian statistics is particularly helpful as it:

  • Allows you to not only account for your existing beliefs but also how confident you are about those beliefs.

    • In Bayesian statistics, high confidence corresponds to a strong prior, and low confidence to a weak prior.

    • High level of uncertainty (meaning low confidence/weak prior) is quantified using wide probability distributions. As more data is collected or stronger evidence is obtained, the posterior distribution becomes narrower, indicating reduced uncertainty.

  • Enables data-driven decisions based on probabilities rather than just statistical significance.

  • Works even with small datasets.


Case in point: Assessing whether a launch in a new market is going well using Bayesian statistics


The simplest way to explain this is by using examples. Let’s say that you're an SME software business with a strong presence in three countries, and that you have started expanding into a new country. You’re looking for early signs to assess whether the launch is a success. Tracking monthly demo-to-close rate as a leading commercial indicator results in the graph below:




As you can see, by this graph, it is very hard to judge how the new launch is performing. With all the peaks and troughs, it’s hard to separate between what is valuable information and what is noise.


Let’s try to make sense of the same data but this time using Bayesian Statistics and bringing our gut feel and experience into the picture. Having previously launched in three countries, you believe that during the initial ramp up period your demo-to-close conversion rate should be around 30%. This is your prior.


A) Interpreting demo-to-close rate using Bayesian statistics with a strong prior


Step 1: Bringing your expertise into the equation, a.k.a setting a prior

  • This 30% conversion rate can be a strongly held view, so a number that you feel very confident about, maybe based on how well you know the local market and competitive dynamics or the high calibre team that you recruited.

  • The way to translate this high level of confidence into your Bayesian equation is by setting 30% as a prior based on a large data sample (e.g. 3,000 closes in 10,000 demos).

    • This should make intuitive sense as if you’ve arrived at this conversion rate based on recurring evidence from thousands of demos, you would hold onto your initial view more strongly.


Step 2: Combining your expertise with real-time data, a.k.a. updating your belief

  • Let’s say that the first month you do 100 demos, and 28 of them successfully convert.

  • Your prior was 30% based on 3,000 closes in 10,000 demos.

  • You need to update your prior with this new information, as you now have 3,028 closes in 10,100 demos, instead of 3,000 closes in 10,000 demos that you’ve started with.

  • So your posterior becomes 29.98% (3,028/10,100).

  • And the second month you do 100 demos and 21 of them successfully convert. With this new information, your posterior becomes 29.90% (3,049 closes in 10,200 demos.) and so on…



Using Bayesian statistics with a strong prior with exactly the same monthly performance as in the example above, your demo-to-close rate looks like this:



Since we’ve started with a very strong prior, it is less reactive to new information, and slower to change.


B) Interpreting demo-to-close rate using Bayesian statistics with a weak prior

  • Your hypothesis of 30% demo-to-close conversion rate can also be a rough number you are not particularly confident about. That’s absolutely fine. A weak initial view is better than no view.

  • The way to translate this low level of confidence into your Bayesian equation is by setting 30% as a prior based on a small data sample (e.g. 30 closes in 100 demos)

  • You then update your beliefs in exactly the same way as you’ve done with a strong prior.


Using Bayesian statistics with a weak prior with exactly the same monthly performance, your demo-to-close rate looks like this:

You’ll realise that the weaker the prior, the quicker it changes as new data becomes available.



Conclusion


A founder's life is notoriously known to be a rollercoaster, with many emotional peaks and bottoms. Whilst the Bayesian approach may not help smoothen that emotional roller coaster, it will help smoothen the noisy, seasonal, random empirical data so that you're not (overly) reacting to the latest information that becomes available.


VCs highly value serial entrepreneurs and always look for Founder-Market-Fit, because those founders have better instincts and strongly held views about the markets they operate in. So why not marry your highly valued gut feel and a data-driven approach to get the best of both worlds?


This is exactly the reason why the Bayesian approach is better than other smoothing techniques such as moving averages, as it offers a simple yet powerful framework for you to bring your views of the world into data-driven decision making, instead of purely relying on empirical data. It allows you to better analyse new information in a systematic way and quickly assess the direction of travel (i.e. whether performance is better or worse than originally thought), without requiring a degree in data science!


You can also apply this very same methodology to make more informed decisions about your Account Executive's performance and financial projections based on evolving information.


Intrigued to find out more about ‘Bayesian Statistics’? I highly recommend:


Get in touch!

I’m always happy to discuss math theorems and how they are applied to the day-to-day business world! If you’d like to connect, you can find me on LinkedIn, or you can drop me an email at gc@oxx.vc.



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