Explore how uncertainty propagates through business outcomes using simulation. See how to set inputs, run trials, and interpret risk percentiles with confidence.
Monte Carlo simulation estimates outcome distributions by
repeatedly sampling inputs and propagating them through a model
averaging a single historical scenario
solving closed-form integrals symbolically
filtering to only best‑case records
A common stability rule of thumb is that simulation error drops roughly with
the cube of the number of inputs
the square root of the number of trials
the number of CPU cores
calendar time since project start
To make trials reproducible across runs you should set
the percentile of interest to 50%
all inputs to their means
a fixed random seed
the time step to zero
When inputs are correlated, a sound approach is to
shuffle inputs independently each time
ignore it since percentiles are unchanged
replace distributions with constants
model dependence explicitly, for example via a copula or correlated draws
Latin hypercube sampling is used to
cover input spaces more evenly than naive random draws
fit parameters via maximum likelihood
convert discrete outcomes into continuous ones
eliminate the need for sensitivity analysis
Interpreting results for executives typically involves sharing
source code line counts
P5, P50, and P95 outcomes and the probability of shortfall against a target
only the mean without dispersion
only the single best trial
A tornado chart ranks inputs by
how frequently they are sampled
their data type in the schema
their impact on the outcome when varied over plausible ranges
alphabetical order
Compared with bootstrapping, Monte Carlo typically
always produces narrower intervals
requires less information about inputs
cannot estimate percentiles
uses parametric or expert‑elicited distributions instead of resampling rows
Convergence diagnostics in simulation are used to
check that summary estimates stabilize as trials increase
remove outliers from inputs
guarantee true causality
compress storage of runs
Scenario design should include
hidden assumptions left implicit
documented assumptions, ranges, and rationale for each uncertain input
excluding downside cases to boost morale
only historical averages with no uncertainty
Starter
Begin by defining inputs and simple ranges before running thousands of trials.
Solid
Nice—incorporate dependence and share percentiles plus shortfall risk in exec summaries.
Expert!
Excellent—your simulations balance variance reduction, sensitivity, and clear governance.
