Many of our clients want to know what the outcome of any price change will be in advance. That is understandable. Pricing is a critical part of any business and any changes to pricing and bundling can be nerve wracking.
How will the change impact sales?
Will we be able to bring our existing customers along with us and convert them to the new pricing?
How will our competitors react?
Any one of these questions can be difficult to answer. The future is by its nature undecided and for every major decision a range of outcomes is possible. What makes pricing predictions especially difficult is the interactions between the different factors.
To take a simple example, an increase in prices cascades through to results in a number of ways. Below is a simplified causal diagram (we have started to use causal diagrams in our pricing work and will be writing more on this in the future, meanwhile, if you are interested, see Judea Pearl’s work in this area - which is quite technical but very important).
The price increase changes the reference price (which frames value perceptions) and may well provoke a competitive response, which will also impact the reference price. The competitive response could be that the competitor also increase their prices, or they could hold, or they could even reduce prices in response to your price increase. Any of these will change the reference price and therefore the perceived value.
It is this perceived value that impacts revenue, and it can do this in two different ways. It can change the customer’s buying process, which often impacts pipeline velocity. For example, when a price exceeds a certain threshold, procurement processes can become more stringent (in a complete model this would be made explicit). The change in perceived value can also impact conversion rates along the sales process. Reframing perceived value at a higher level could actually improve conversions in certain cases. We frequently see cases where higher prices lead to higher unit sales (What does that tell you about the price elasticity of demand?).
It is the Interactions between the different causal vectors that makes prediction so difficult. But fortunately there are advanced statistical techniques emerging to tease these out (for a good introduction see Causal Diagrams and Causal Models by Eliezer Yudkowsky). A lot of our work these days is teasing out these pricing interactions and working out how to model them.
Note that in the above diagram we have drawn a box around value. Understanding how value is created, understood, delivered and measured for different market segments is at the heart of the Ibbaka approach. In the coming months we will be sharing more of our work in this area.
I described this as a simple model, and it is , but ‘simple’ is not a bad thing. All models are a lot simpler than the reality they are meant to reflect and predict. They have to be. A good model abstracts out the most important factors that influence outcomes, especially those there is some control over.
A line in a diagram is not enough to get to prediction. In fact, each of the lines above gets represented as a set of equations. In pricing, the outcomes are never certain. The approach we are taking at Ibbaka uses Monte Carlo simulations to evaluate our models.
Monte Carlo approaches were invented by the scientists working on nuclear weapons at Los Alamos in the late 1940s. The basic idea is pretty simple.
Define a set of decision rules (we take these from the causal diagrams)
Estimate a range of possible outcomes
Estimate a range of confidence in these outcomes
Apply the decision rules to a randomized set of inputs
Generate a range of outcomes at different levels of confidence (the higher the confidence the wider the range)
What does a decision rule look like? We write these out in natural language and then translate them into code.
Given engagement levels at -1 standard deviation, there is a 20% to 30% probability that the customer will accept the price increase.
Given engagement levels at +1 standard deviation, there is a 25% to 50% probability that the customer will accept the price increase.
Given engagement levels at -2 standard deviation, there is a 0% to 20% probability that the customer will accept the price increase.
Given engagement levels at +2 standard deviation, there is a 45% to 80% probability that the customer will accept the price increase.
and so on …
Our models can include anywhere from three to twenty such statements. We code these and run the Monte Carlo to get the range of outcomes. We found it easier to code on our own application than to use one of the more general solutions (though if you want to do this yourself try Solver). It is important to test the models against the actual results so that you can constantly improve your models. Judea Pearl’s approach, as set out in Causal Inference in Statistics, provides a way to untangle the web of causality. The main thing is to:
Show your assumptions in a causal model and investigate the range of outcomes in a Monte Carlo model
Test the model against outcomes and evolve it
Identify the critical risk factors and the outcomes they impact
Devise a plan to manage the risks
The parameters in the models can differ from segment to segment. We apply our customer segmenting technology to find the different segments. In a recent project we helped a customer understand how to bring its current customers over into a new pricing model. We began by analyzing data about the size of the price change for each customer, usage patterns, when the original contracts were signed and so on. We identified three different segments from this data (legacy customer who are resistant to change, engaged customers who are likely to change and marginal customers who are very price sensitive). We then used different parameters for each segment in the Monte Carlo model. This gave a lot more insight on how to carry these customers across to the new pricing model and the probability of success. It allowed us to provide very granular advice on how to proceed.
To see another way to use causal diagrams, check out our post on OpenView Labs, Should you raise your prices when your costs go up?
Concerned about how your price change will impact revenues, what the critical risk factors are, and how to optimize for success? Contact us at firstname.lastname@example.org. We can help you to understand the probability of success and to manage the risks.