Sales modeling has long been used by clients and media agencies around the world to create insights regarding their historical performance. Most of the efforts have been focused around retrospective projects measuring soft KPI’s, e.g., awareness, liking, penetration etc. In this white paper we’re introducing a new paradigm for implementing a real-time continuous sales modeling setup which can deliver updated learnings and clear-cut recommendations at the time where they’re needed.

Background

In todays media market, with an abundance of data yet few inferred actionable insights, there’s no longer a question of whether or not you should do sales modeling. Rather, it’s a question of how to get started. To the modern CMO the concept of sales modeling, along it’s obvious benefits, is well known. Since it’s based on the scientific method, an implemented sales model can function as a fact based decision support tool for marketeers. Yet, most businesses today does not currently use a sales modeling agency. The reasons for this are many but most of them can be nailed down to the following key hurdles:

Cost: Building a sales model requires a lot of resources in the shape of staff, data wrangling, and key stakeholders. Often you as a client is required to collect, consolidate, clean and deliver diverse data sources across your organization.
Complexity: The statistical modeling theory behind validating a model can be, to say the least, overwhelming for non specialists. For this reason you need dedicated fully trained data scientists to develop useful models.
Time consuming: Every useful model have a lot of parameters to tune. In traditional sales models these are tuned by experts every time a new project is launched. Tuning these parameters, while maintaining model robustness, is hard and usually requires weeks of the data scientist’s time.
Slow time-to-market: Typically a realistic sales modeling project takes between 4-6 weeks to deliver the results after the data has been aquired and validated. It’s not uncommon that by the time the CMO reads the report with the modeling insights the results are over 6 months old.

We live in exciting times. There’s more data, as well as affordable computational power, available than ever before. As a consequence a new statistical learning paradigm has started to blossom. This new paradigm is called being Bayesian and basically refers to the way we make inferences from existing data. Now what’s really neat about this approach is that it enables us to make explicit predictions taking all the uncertainty into account from our parameters.

Being Bayesian is good

The ever increasing interest in Bayesian statistics has led not only to extensive research in Bayesian methodology but also to the use of the Bayesian paradigm to address tough challenges in rather diverse domains such as astrophysics, weather forecasting, health care policy, and of course media.

The hypotheses related to these challenges in media are typically expressed through probability distributions for observable domain specific data. These probability distributions depend on a set of unknown quantities called parameters. Let’s call all of these parameters $\theta$ . In the Bayesian paradigm, current knowledge about the model parameters is expressed by placing a probability distribution on the parameters. This distribution is known as the “prior distribution”, which is mathematically denoted by $p(\theta)$ . The word stems from the fact that it expresses our beliefs about the parameters prior to observing any evidence(data) that supports it.

As data $y$ become available, the information they bring to the table about the nature of the model parameters is expressed in something called the “likelihood,” which is proportional to the distribution of the observed data given the model parameters, written as $p(y\vert\theta)$ . In more plain English the likelihood tells us something about how likely we are to observe that specific data given the set of parameter values. As the data is fixed the only thing we can vary are the parameters $\theta$ , which means that the larger the likelihood the more consistent our parameter choice is with the observed data.

This information is then combined with the prior to produce an updated probability distribution called the “posterior distribution,” on which all Bayesian inference is based. Bayes’ Theorem, an elementary identity in probability theory, states how the update is done mathematically: the posterior is proportional to the prior times the likelihood, or more precisely,

$p\left(\theta\vert y\right)=\frac{p\left(\theta\right)p\left(y\vert\theta\right)}{\int_\theta p\left(\theta\right)p\left(y\vert\theta\right)d\theta}$

Eventhough the posterior distribution is in principle always available, the resulting analytic computations are often intractable in any realistically complex model. It has been realized that the ability to sample from this distribution is what we really want to be doing.

The remedy

So far I hope you’ve all jumped on the Bayesian train and agree with me that this provides us with an intuitive and scientifically correct approach. There can be no inference without assumption. So how does all of this help existing businesses jump the sales modeling hurdle? Well, to be fair, the Bayesian approach is only part of the solution. Let’s attach the obstacles one by one.

Cost

Truth be told, there is no skipping the initial phase of consolidating your data and chasing down the right people in your business intelligence department. The key to keeping the costs to a minimum is automation. This automation should consist of an ETL process running continuously in your environment. This makes sure that data is gathered and consolidated as often as you need withouth manual intervention. It could, and should, also contain the responsibility of sending the data to the right place. Never, ever assign the task, of sending data to your analytics partner, to a human. Us humans are wonderful beings and excel at so many things. Keeping track of data and being consistent however, is not one of them. Keep this in mind.

Complexity

Before diving into the remedy and the solution let’s revisit why I claim that building a predictive model is a complex process. After all, there are numerous statistical softwares around that are able to produce a model given any kind of data you throw at it, right? Well, not quite. It’s true that all of that software can produce a model. It’s just that without an expert tuning that model, what comes out of the process is pure nonsense. Consider this; Any reasonably sized sales model contains at least 30 to 60 variables accompanied by at least 60 to 180 parameters. Most sales models operate on weekly numbers allowing us to get access to 156 observation points given that we collect the last three years of history. Best case scenario you have 2.6 data points per parameter providing a rather poor evidence base for your inference. Worst case you end up with an underdetermined problem. Underdetermination refers to situations where the evidence available is insufficient to identify which belief we should hold about that evidence. Basically it means that mathematically this problem is not possible to solve. All of this can be solved today but it requires years of training in the domain of statistical learning theory and machine learning. Therefor it is wise to leave it to the experts.

Time consuming

Remember all of those parameters we talked about before? Well there’s more to it and of why they are massively difficult to tune.

They are mostly continuous parameters meaning that they have an infinite amount of values to assume. In practice they are not infinite though as they can be diveded into ranges that are for all purposes equal. This is called region of practical equivalence (ROPE).
They are not independent which is short for saying that the specific value of one of them depends on one or several of the other parameters. This is not good news since it means that we cannot optimize them one by one.
They introduce the curse of dimensionality into the mix. To understand what this is imagine we have one variable which can assume 10 possible values. This is known as a one dimensional problem and all we have to do is to evaluate each of the 10 values and select the best one. Easy enough. Now suppose we have another variable which can also assume 10 possible values. Now we have $10\times10=100$ possible configurations to search through. Following the same logic, imagine that we have $M$ variables each featuring D possible values. This would result in $D^M$ possible configurations. Plugging our situation into this equation would yield $10^{30}$ possibilities. That’s 100 billion times as many configurations as there are grains of sand on earth.

Due to these challenges and the vast experience required to tune statistical models it is something best left outsourced unless you have a large team of highly skilled data scientists inhouse.

Slow time-to-market

Any running sales model is only as good as the just-in-time learnings it can deliver. For this reason you need a platform where you can leverage the insights from the model and turn it into actionable conclusions. This platform should enable you to do the following:

Explaining what happened to sales last week and why by presenting you with a decomposition of the total sales into all the responsible sales drivers
Track the performance of your current campaigns in real hard core KPI’s such as sales, profit and revenue
Plan your future campaigns based on the predicted effect of your running sales model
Submit your campaign plan for execution

This requires that data is updated and delivered on a daily basis and that the platform is able to refit, test and deploy the updated model quickly. Then and only then are you truly sitting in your KPI cockpit with an actionable overview of your media performance.

Conclusion

In this paper we discussed the major hurdles most companies are facing today when implementing predictive sales modeling. These hurdles can be overcome by replacing a lot of manual processes by automatic ETL jobs and clever Bayesian modeling setups. Hopefully you’re convinced that introducing sales modeling into your everyday decison making process is a good idea. Trust me, it’ll be the smartest decision you’ll ever make.