How do you build a Monte Carlo simulation for a marketing decision?

What distribution of a decision outcome follows from declared input assumptions, and what is the probability of crossing a threshold?

The unit is scenario × draw × period. Distributions describe uncertainty about one price-volume-margin decision, not 20,000 observed markets.

The target is the conditional distribution of ΔΠ=f(X), especially median, 5th/95th percentiles and Pr(ΔΠ<0), under fixed distributions and dependencies.

For every input declare distribution, parameters, unit, source, horizon and dependencies. MSC-010 has fixed price, correlated normal volume and elasticity at −0.20, triangular costs and fixed price change.

Assume distributions represent relevant uncertainty, linear correlation is adequate, the model remains valid over all draws, and truncations or constraints are explicit.

For each draw s: P₁=P₀(1+d), Q₁=Q₀(1+d)^ε and ΔΠₛ=(P₁−VC)Q₁−(P₀−VC)Q₀−ΔFC.

The script reads the base scenario, generates 20,000 draws with a fixed seed, imposes ρ=−0.20 using two normals, applies triangular distributions and sorts ΔΠ to calculate quantiles.

Mean €10,437.88, median €10,538.92, P5 −€357.20, P95 €21,066.54 and Pr(ΔΠ<0)=5.555%.

For estimated risk p̂, MC_SE=√[p̂(1−p̂)/S]=0.1620 percentage point. This simulation error covers neither model error nor misspecified distributions.

Repeat with more draws and multiple seeds, track median, quantiles and risk, then vary distributions, dependencies and parameters. Numerical convergence alone does not validate assumptions.

Check impossible values, support, realised correlations, quantile stability, each input’s contribution, extreme scenarios and unit consistency.

Common errors are confusing draws with observations, choosing convenient distributions, ignoring dependencies, reporting only the mean, hiding the seed or treating simulated probability as observed frequency.

Under MSC-010, the scenario is usually positive but its lower tail crosses zero. The 5.555% figure is risk conditional on distributions, not known real-world risk.

Compare threshold risk across consistently defined scenarios, target data collection and set a conditional escalation or test rule.

Do not claim an objective probability, guarantee profit, validate a distribution through numerical convergence or ignore unencoded structural uncertainty.

Deliver an assumption register, dependencies, seed, draws, code, quantiles, threshold risk, Monte Carlo error, convergence, sensitivity and supported/unsupported decision.