Visualizing Impacts of KPIs on Business

In performance driven businesses we want to not only define how revenues increased or decreased, but also understand why this happened. By understanding impact of all components of revenues we can truly understand reasons of revenue movements. Only by doing this we can define actionable solutions to decrease negative impact and improve positive impact even further to push company growth.

In this blog post we will present a practical solution to reduce pressing business questions into actionable KPI-insights.

Written by Günay Aliyeva and Dominik Kirst.

Simple Example
Let’s start with simple KPIs for revenue which are average revenue per customer and the number of customers. Multiplied these give the revenue:

where we observe the following data:

Here we can see that daily revenues have dropped by 600$. Successful business decision makers should be asking themselves the following questions and try to find answers:

• What was the revenue impact of decreased average revenues per customer?
• What was the revenue impact of an increased number of customers?
• How much revenue loss would we suffer if number of users would not increase?
• How much revenue increase would we have if average revenue per user would not drop?

In our example it is easy to derive actions by spending few minutes to think. Since the revenue is increasing even though the number of costumer is decreasing we should try to increase the average revenue even more. In real business situations revenues never consist of only 2 basic components. Usually we can count 4–5 complex components where each can be broken down into several basic variables that need to be analyzed.

We came up with a general approach that can be adjusted to the needs of your business case. You can use this approach for any type of business and add as many new component KPIs as needed.

General Approach
Just as in the simple case above we aim for numbers and plots that immediately give us actionable insights of our changing KPI. In a perfect world these are generated automatically and available with ease. This can be achieved by the plot below, where we have a decomposition of our observed revenue change into chosen component KPIs attached. Consider the revenue formula of a retailer:

that contains the number of costumers, the conversion rate, the average purchase value and the average purchase discount.

Here the retailer can immediately conclude, which component had the highest positive impact and that even though our revenue increases, there are components where she should initiate actions.

Let’s get back to her observed data:

Imagine you want to answer the question which component had the most positive or negative impact on revenue by simply looking at the given data. Even though you might have some good guesses, you’ll face the problem that there is no reasonable unifying scale on which to compare them.
Our approach to this problem uses the idea of marginal cost calculations to determine the impacts of each component, a method that MBAs might recall from their microeconomics courses. We can apply this approach to determine the influence on a given revenue function if a component changes by calculating its derivative.
For example the derivative of her revenue function in respect to the average purchase value is given by

To compute the impact of a component we scale the derivative by our observed difference. Since the derivative is not constant in general, we need to specify at which point we’re calculating the gradient.

In our approach we use a point where the derivative is similar to the slope of the secant between both measurements. While there exists an exact solution, we use a heuristic where we choose the midpoint of both measurements as approximation.

Thus the impact of the average purchase value is given by

For the other components we determine the following impact:

Furthermore we can calculate how accurate our approximation is by comparing the sum of all impacts and the observed difference of our revenue. In our example:

which is 1% off compared to the actual observed difference of 2500$ between both measurements of her revenue function. By applying this method we can automatically generate the plot presented above easily:

In addition this information enables us to get further insights into trade offs between different components and ideally tune them in a way that yields optimal revenue. Here the retailer can collect additional information about the trade off between the amount of costumers and the observed conversion rate with respect to her revenue, using observed component impacts.

While there are higher order approximations to increase the quality of the method, we observed that the first order approach is sufficient for our daily KPIs. Furthermore, the midpoint of both measurements might not always be a useful approximation and you could try to either directly solve for the secant or use one of the endpoints.

Summary
By using a simple mathematical method based on the idea of marginal costs, we are able to decompose KPI changes into preselected components and visualize them with ease. This gives us the ability to immediately understand positive and negative developments of our KPI in terms of simpler actionable components. Furthermore we can gain further insights into trade offs between KPI components that have conflicting trends, like higher costumer numbers, that often tend to decrease the conversion rate and vice versa.

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