@RISK: Static Value of Output Differs from Simulated Mean

Output means differ because outputs show calculated static values, not their distribution means. Use RiskMean or RiskPtoX to display true output stats.

Jan 20, 2026
Knowledge

Title

Answer

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

After running a simulation, input means match expectations, but output means are very different. What is wrong?

Answer:
Nothing is wrong. This is normal behavior.

When a simulation is not running, @RISK shows static values.

For inputs, these static values are their means.
For outputs, however, the displayed values are calculated from the static input values, not the mean of the output distribution.

In general, the mean of a calculated result is not equal to the result calculated from the mean inputs.

This is true for means, percentiles, and modes, especially in non-linear models.
If you want to see the simulated mean of an output in the worksheet, use RiskMean().
For percentiles (including the median), use RiskPtoX().

Example:

If an input has mean 0, the mean of its square is 1, not 0.

If an input has mean 5, the mean of its reciprocal is 5/9, not 1/5.

This difference occurs because “the mean of a function is not the function of the mean.”

When you run a simulation, you’ll see that output distributions usually have different shapes from input distributions.