Plans based on averages are wrong, on average. So says "the flaw of averages," as coined by Sam. L. Savage, a consulting professor in the Department of Management Science and Engineering at Stanford and discussed in the May 2003 feature, "How to Take Risks in a Time of Anxiety." Unfortunately, many business owners make business decisions based on averages -- the average length of a selling season, the average number of X sold over a period of time, the average cost of selling X last year. Basing decisions on averages doesn't account for the many variables that can disrupt the best-laid plans. For instance, what if the selling season for X is shortened by unexpected conditions, what if the demand for X decreases, what if the cost of selling X rises due to a suppliers' shortage? To rely solely on averages means ignoring the inevitability of factors you can't control.

Fortunately, computers and probability modeling software can play a pivotal role in helping business owners better project the outcome of their decisions. One popular tool is Monte Carlo simulation, which bombards a model with a range of inputs that represent any number of uncertain values. In doing this, owners can witness the outcomes of a number of scenarios to make the best decision possible.

Senior writer Leigh Buchanan provides an example of Monte Carlo simulation in detail in the sidebar "The Parka Problem." Here, offers an interactive example of "The Parka Problem," providing a trial version of Savage's simulation software, XLSim®, and two lessons that allow you to see Monte Carlo simulations in action. Note, if you are already doing simulation with @Risk or Crystal Ball®, the lessons contain notes for use with these two popular packages as well.

Monte Carlo Simulation


To start your test drive of Monte Carlo simulation you will need simulation software. You may download the trial version of Sam Savage's probability modeling software, XLSim®, this version of which requires a PC with Microsoft Windows 95 or higher as well as Microsoft Excel 97 or higher. Simply click on the below link and follow the instructions.

Next, download the lessons and save them on your hard drive. Parka Lesson 1.xls simulates projected profit while Parka Lesson 2.xls helps determine how the business in the example should purchase for maximum profit.

Once you've downloaded the necessary pieces, click on XLSim2e.exe to install the program. Then go to START PROGRAMS XLSim2e and click on XLSim 2.0. This will launch Microsoft Excel, if it is not already open, and will load the simulation software. A Simulate menu should appear in the Excel tool bar. If the menu does not appear, make sure that the Macro Security level is not set to high (use Tools -- Macro Security to change the security level).

With your simulation software loaded into Excel, open Parka Lesson 1.xls and proceed with the self contained instructions. You may then proceed to Parka Lesson 2.xls. If you wish to learn more about simulation after going through the two lessons, it is suggested that you execute the Tutorial command from the Simulate menu.

Monte Carlo Resources

XLSim® ( is a relatively simple add-in, designed to get people up to speed quickly in the area of Monte Carlo simulation.

@RISK ( and Crystal Ball® ( are two popular industrial simulation packages which provide additional features for modeling and simulating uncertainty.