ModelRisk example · General techniques
Random Sales with a Competitor That May Enter
What is it worth to keep a competitor out? Monthly sales when a rival may enter the market.
From the model’s saved run
Sales over 100 months
Units sold with the competitor's possible entry, against the sales without it.
| Measure | Unit | Value |
|---|---|---|
| Expected units without any competitor | units | 15,365 |
| Mean units sold | units | 12,587 |
| Mean units lost to the competitor | units | 2,779 |
| Mean margin lost | US$k | 1,250 |
| Chance that the competitor never enters | probability | 20.0% |
| Margin per month of delay to its entry | US$k | 18.0 |
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| Units sold | units | 11,433 | 12,039 | 15,369 | 12,587 |
| Units lost to the competitor | units | 0 | 3,317 | 3,930 | 2,779 |
Line chart: 90th percentile, Median, Mean, 10th percentile.
Histogram of Units sold over 100 months from the saved simulation.
The business question
A company sells about 88 units a month of a niche product, and sales grow by about 1.3 units a month. Sales arrive at random, so each month's number is Poisson.
A competitor is preparing a similar product: there is an 80% chance it launches, in a month somewhere between the 20th and the 50th, and from then on it is expected to take 30% of the company's sales. Each unit earns a margin of US$450.
The company wants its sales forecast for the next 100 months, the sales at risk, and a value for actions that would delay the competitor, such as locking in key customers.
- Who it is for
- Planners forecasting sales that a single uncertain event could change: a competitor, a substitute, a regulation, a price war.
- Main outputs
- Units sold over 100 months at P10 / median / P90 · units and margin lost to the competitor · the chance that it never enters · the value of each month of delay · monthly bands.
How the model works
Three sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
Current monthly sales and their growth, the competitor's chance of entering, its window and the share of sales it takes, and the margin per unit.
Months sheet
VoseBernoulli decides whether the competitor enters and VoseStepUniform in which month. From that month on, each month's expected sales are 30% lower. Sales are Poisson around the expected number. The sales lost are the expected sales the competitor takes.
Results sheet
Units sold over 100 months, the units and margin lost, the value of each month of delay, and the monthly bands.
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The results in detail
How to read these results
- Without a competitor the company would sell about 15,400 units over the 100 months. With the competitor's 80% chance of entering, it sells about 12,600 on average and loses about 2,800 units, or about US$1.2 million of margin.
- The histogram has two humps: the iterations in which the competitor enters, and the one in five in which it never does. That is why the 90th percentile of units sold is close to the no-competitor figure while the median is far below it.
- Each month the competitor's entry is delayed keeps about 40 units, worth about US$18,000 of margin in the middle of the window: the budget to set against actions that would hold it off.
- A Poisson rate cut by 30% gives the same distribution as removing each sale with a 30% chance, so this model and GU-11, which thins the deaths with a binomial, use two equivalent forms of the same step change.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
Sales now 2 inputs
The current monthly sales and their trend.
| Assumption | Unit | Value |
|---|---|---|
| Units sold per month now | units | 88 |
| Increase in units per month, each month | units | 1.3 |
The competitor 4 inputs
Whether it enters, when, and what it takes.
| Assumption | Unit | Value |
|---|---|---|
| Chance that it enters | probability | 80% |
| Earliest month it could enter | month | 20 |
| Latest month it could enterEach month in the window equally likely. | month | 50 |
| Share of sales it takes once it is in | share | 30% |
Value 1 input
| Assumption | Unit | Value |
|---|---|---|
| Margin per unit soldAdded here to put a value on the sales. | US$ | 450 |
Units and conventions
- Money
- US$ thousand (US$k), except the margin per unit in US$.
- Sales lost
- The expected sales the competitor takes in this iteration: 30% of the expected sales from its entry month on.
Key assumptions and limitations
- Poisson
- Sales arrive independently at a steady rate within a month.
- Competitor
- If it enters, it takes the same share every month from its first month on; no ramp-up and no response from the company.
- Trend
- Linear growth, as in the original example, with or without the competitor.
- Data
- The sales, growth, chance of entry, window and share are those of ModelRisk's earlier Poisson Sales with Competitor example; the margin is added here.
How to use it
- Set sales, growth, the competitor and the margin on the Inputs sheet.
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Compare the value of a month's delay with the cost of actions that would cause it.
ModelRisk functions used
- VoseBernoulli
- Whether the competitor enters.
- VoseStepUniform
- The month it enters: each month from 20 to 50 equally likely. The original example rounded VoseUniform(19.5, 50.5), which gives the same.
- VosePoisson
- Each month's sales around the expected number, lower once the competitor is in.
- VoseOutput
- Monthly sales as an output range, and the totals.
- VoseSimMean, VoseSimPercentile
- Statistics of the simulation, the monthly means and bands.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley: forecasting random events and the effect of a competitor.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.