Comparing Simulations with a Box Plot

A box plot, aka box and whisker chart, is a simple way to show the results of a Monte Carlo simulation.  It's also a useful way to visualize the differences between several simulations in one plot.

Typically the results of a single simulation is shown as a histogram.  This a good tool for visualizing outcomes, but when comparing among simulations it loses its appeal and doesn't do well showing differences in a clear manner.  This limitation can be overcome with a simple box plot.

Box Plot Basics

There are several different flavors, but we'll limit our discussion to how box plots are implemented in Simulation Master.  The box portion indicates the simulation output from the first quartile to the third quartile.  The line through the box is the median value.

The lower whisker extends to the minimum value, and the upper whisker extends to the maximum value.

Comparing Simulations

The simplicity of the box plot lends itself to plotting several simulations on one chart.  This is a simple way to compare alternatives, such as competing projects.  In the box plot below, we have simulated the net present value for three projects.

We can now compare the projects in a logical manner.  Depending on your risk criteria, you can compare each quartile as well as best case and worst case scenarios.

For example, if we want to limit the downside, project B would likely be ruled out because it's minimum value is the least and the q1 and median values are less than project A.  Project C would likely be ruled out as well since its minimum, q1, and median values are less than project A.  Also note that the second and third quartiles of project A is in a tighter range than the other projects which indicates less risk.  Therefore, we would likely choose project A.

Now let's say we have a higher risk tolerance.  Project C has the highest upside potential at the maximum and q3 levels.  Note that the second and third quartiles have a greater range than the other projects so there is an indication of higher risk.  Project B has a lower minimum value while not having as much upside potential so it would likely not be chosen.  Project A has the least risk, but limited upside.  Therefore, we would likely choose project C.