Spider plot

 

The following is an example of the Conditional Mean version of a Spider plot. It was created by running the NPV of a capital investment model:

 

The horizontal axis shows the cumulative percentile of the input variable, and the vertical axis shows the selected statistics (in this case the mean) for the output if the input variable was around the percentile value of the horizontal axis. The horizontal line in the middle marks the unconditional statistic (in this case the mean NPV). So, for example, by hovering over the graph at a certain point a tool tip shows the following information:

It says that if the input variable, Market Growth, was around its 85th percentile, the NPV would be around $42 million. How precisely around the 85th percentile depends on the number of tranches. This plot was made with 10 tranches, meaning that the cumulative probability is split into 10 equal sections: 0-10%, 10-20%, …, 80-90%, 90-100% with mid points 5%, 15%, …, 85%, 95%.

This chart was generated using 100,000 samples, so 10,000 samples were used to calculate each conditional mean, which is a lot, and we can afford to use more tranches. The following plot is the same analysis using 50 tranches (so 50 points to each line, 2,000 samples being analyzed to create each point):

The value of this type of plot is that it gives more precise information about the nature of the relationship between the input variables and the output. Two input variables in the above plot have pretty flat lines (Unit Cost and Product development cost) so we can remove them and focus on the others:

The market growth variable is most influencing the NPV because it covers the largest vertical range, and as it increases, so the NPV increases. Sales Price has a similar relationship but slightly less influence.

Market growth has a more interesting relationship. At low values the greater the market growth, the greater the NPV – which one would expect when selling a product. But at about the 70th percentile the mean NPV drops dramatically. If you look into the model this comes from you will see why: if the market attains a certain size it is assumed that a competitor will appear and take away a lot of sales.

The Conservatives get in? variable has a different effect. This is a flag (either 0 or 1) and when equal to 1 there is a corporate tax cut increasing the NPV. Thus the line is a step showing either the mean NPV when there is no tax cut, or the mean NPV when the tax cut occurs.

The format of the plot can be comprehensively adjusted by clicking on the various control buttons in the Spider Options tab:

The following editing tabs are available:

 

 

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