In business consulting and competitor analysis, an important question that often arises is “what would happen if I were to open a new business here?” For one, it is a counterfactual question, and the consultant/analyst cannot directly find an answer from data analysis alone. This is because the relationships among variables would have been different had the new entrant existed, but by definition, the new entrant could not have been there when data was first collected, so the “naïve” patterns learned from historical data are subject to logical contradictions and poor generalizability.

In this article, I argue that with the help of a conceptual model, it may be possible to predict outcomes of a new entrant in a logically consistent way. I will use a simple example to show what this means.

Suppose I was a fitness franchisor and wanted to decide whether to open a new gym in the city. I gathered some market intelligence and found that there were L locations where customers might come from (e.g. the more affluent neighborhoods), and there were already G gyms in the city competing with each other. I also did some market research and got the total sales revenue of fitness for each of the L locations (e.g. from the Consumer Expenditure Surveys).

With all this information, I define a market penetration score (MPS): $$MPS_{lg}=frac{ISR_{lg}}{TSR_{l}},$$ where ISR is the individual sales revenue (of gym g at location l), and TSR is the total sales revenue (at l). While I cannot observe every g’s individual sales revenue, I do know the total sales revenue based on my market research, and I also know that $$TSR_{l}=sum_{g=1}^{G}ISR_{lg},$$ which is just a definition.

I then imagine opening a new gym somewhere in the city, and call it h. Instinctively, I would predict the ISR of the new entrant at l via a predicted MPS (by training a machine learning model, which I will describe later) together with my information on TSR: $$widehat{MPS}_{lh}times TSR_{l}.$$ However, because of the introduction of the new gym, the ISR of each current g at location l is expected to reduce by $$frac{widehat{MPS}_{lh}}{1+widehat{MPS}_{lh}}times ISR_{lg}.$$ As a result, the predicted ISR should be modified to $$frac{widehat{MPS}_{lh}}{1+widehat{MPS}_{lh}}times TSR_{l}.$$

This is what I mean by having a conceptual model: thinking clearly about the observed patterns being learned by machine learning models vs. the inner workings being applied to get logically consistent predictions.

Now comes the machine learning part. The predicted “raw” MPS can be acquired by fitting $$MPS_{lg}=MPSleft(D_{lg},A_{lg};Thetaright)$$ to past data in each of my other gym g at every location l in the same city or another area. Here, D is the distance-specific characteristics between g and l, and A represents other store-specific characteristics. There are a great many ways in machine learning to automatically find a function and parameter set for MPS, but oftentimes a traditional functional form specification such as the Huff model might work just as well (and is easy to interpret).

Finally, by changing site locations and store features, I can search for the best set of characteristics (subject to certain constraints) that maximize the sales revenue of my new gym. Sweet!