Presenting Simulation Results

Presenting the results of a Monte Carlo simulation can be challenging when your audience isn't inclined to receive probabilistic information.  Decision makers often want a single number for net present value, project completion date, or profit.

How do we as the modeler/analyst present this information so it is understood and appreciated for the extra information that a simulation provides?  In this article we'll look at some graphic and non-graphic ways to convey the results.


Graphic Methods

We'll start with some graphical ways of presenting simulation results.


A histogram is probably the most common way to present simulation results.  Simulation outcomes are placed in bins and represented on the horizontal axis.  Each column represents the frequency of outcomes for each bin.  This gives a good view of where the most probable outcomes are located and the total range of possibilities.

The drawback to histograms is that if you're not used to interpreting them, they can be confusing.  It's also hard to compare alternative simulations in a meaningful way.

Box Plot

A box plot is a simple representation of each quartile of outcomes.  The simplicity of the box plot may be valuable when dealing with an audience that wants a single number.  Another key benefit of box plots are that multiple simulations can be plotted together for comparison.  To learn more about box plots and comparing simulations, check out a previous blog article on this topic.  Again, this is useful to illustrate risks to an audience in a simple graphic.

Cumulative Frequency Plot

The cumulative frequency plot simply starts at the lowest outcome and plots the cumulative frequency count vs. outcome.  While not as simple as the box plot, it conveys probabilities as well as the histogram.  It also is easily adapted for comparing multiple alternative simulations in one plot.

Non-Graphic Methods

While the graphic methods show the most information, your audience may not want or be able to fully interpret them.  If the target audience is used to single point estimates, this is especially true.  We'll discuss some ways to present information in a way that illustrates risk while keeping it simple.


Presenting one or more percentiles of the output is the most straightforward way of communicating results without a chart.  This could be shown as a table of output vs. percentile.

Output Percentile
-4334 1st
447 10th
3461 25th
6794 50th
10267 75th
15162 90th
18635 99th

Speak in Terms of Failure or Success

Speaking in terms of failure or success can drive home the risks involved in a more impactful way than giving percentiles.

For example, if a project critical path is simulated, we could give a 50th percentile value.  What may be lost is that there is a 50% chance that the project is late!  Presenting this information in that light changes its meaning at a more emotional level.

Alternatively, you could present the 90th percentile value and say this is the time with a 90% chance that the project will be completed on time.

When Losses Are Involved, Give the Risk of Loss

When the simulation output is profit, net present value, or some other gain/loss measure it may be appropriate to state the chance of loss.  The graphic methods shown earlier are for the net present value of a project.  As you can see from the charts, there is a possibility for a negative net present value.  In fact, the simulation shows that the project has a 8.5% chance of being negative.


We've shown some ways for presenting simulation results to audiences that aren't well versed on probabilistic information.  Hopefully these will give you some ideas for tailoring your presentation to your audience.