HomeTechniques and Tips@RISK Simulation: Numerical ResultsStatic Value of Input Differs from Simulated Mean

6.5. Static Value of Input Differs from Simulated Mean

Applies to:
@RISK, all releases
RISKOptimizer, all releases
@RISK Developer's Kit (RDK), all releases

Why is the expected value displayed in the spreadsheet cell that contains an @RISK input function different from the mean of the simulation results for that input?

The simulated mean of a distribution will typically be close to the theoretical mean, but not exactly the same. This is normal statistical behavior. And it's not just the mean, but the standard deviation, median, mode, percentiles, and all other statistics.

To illustrate, set up a simulation in the following way:

2. In cell A1, define an @RISK input as a normal distribution with mean of 10 and standard deviation of 1.

3. Click the Simulation Settings icon from the @RISK toolbar. On the Iterations tab, set the number of iterations to 10,000. On the Sampling tab, select Latin Hypercube for the sampling type and a fixed random generator seed of 1.

4. Run the simulation, click the cell, and click Browse Results in the @RISK toolbar. (In @RISK 4.x, open the @RISK–Results window.)

Statistical theory tells us that the expected distribution for the mean of the input is a normal distribution with a mean of 10 and a standard deviation (often called the standard error) of 1/√10000 = 0.01. Although the exact results will vary by version of @RISK, you should find that the mean of the simulated input is well within the interval 9.99 to 10.01, which is within one standard error of the theoretical mean. (The default Latin Hypercube sampling type does considerably better than classic Monte Carlo sampling.)

But the displayed value is not even close to the simulated mean of the input. How can that be?

Most likely this is a setting in your model. In the Simulation Settings dialog, look at When a Simulation is Not Running and verify that it is set to Static Values. Set Where RiskStatic is Not Defined, Use to True Expected Values.

As the dialog box implies, a RiskStatic property function in any distribution will make that distribution display the RiskStatic value instead of the statistic you select in Static Values.

Is there any way to get the exact mean of the distribution in my worksheet?

We'd say "theoretical mean" rather than exact mean, and that's the key to the answer. Where RiskMean returns the mean of the last simulation that was run, RiskTheoMean returns the mean of the theoretical distribution. There's also RiskTheoStdDev, RiskTheoPercentile, and so forth. In @RISK, click Insert Function » Statistic Functions » Theoretical to see all of them.