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· 4 min read
How to Run a Monte Carlo Simulation
Manesh Jayawardhana
CIO & Co-founder
A project plan built on best estimates gives you one number. Someone asks how confident you are, and the honest answer is “moderately”, which isn’t a useful thing to put in a board pack.
Monte Carlo simulation replaces that with a distribution: not “the outcome is 42,300” but “there’s a 71% chance of clearing the 30,000 target, and a one-in-ten chance of coming in under 18,900”. That’s a different conversation.
How it works
The method is almost embarrassingly simple.
For each uncertain input, define a range and a distribution instead of a single value. Then run the model thousands of times, sampling each input at random from its distribution and computing the outcome. Collect all the outcomes and you have an empirical distribution to read percentiles from.
No clever mathematics — just repetition. The insight is that the shape of the output distribution is what you actually want, and simulation gets it without needing the model to be analytically tractable.
Why the average of the inputs isn’t the answer
The most important reason to do this: the function of an average is not the average of the function, whenever the model does anything other than add.
Take your best estimate for each input, compute once, and you get one number that can be nowhere near the median outcome. This happens whenever values multiply, whenever there’s a cap or a floor, and whenever a threshold changes behaviour. It’s known as the flaw of averages, and it’s why single-point estimates systematically mislead in one direction.
A concrete version: a project needs three things to go right, each 80% likely. The “average” case is that everything goes fine. The actual probability of all three is 51%.
Choosing distributions
Triangular — a low, most likely and high estimate. This is the right default for most business cases, because it’s exactly what people can actually estimate.
Normal — when the quantity is the sum of many small independent effects. Reaches for symmetry, so don’t use it for anything bounded at zero with a long upper tail.
Uniform — only when you genuinely know nothing except the bounds. It’s a strong claim, not a neutral one.
| Trials | Good For | Notes |
|---|---|---|
| 1,000 | A quick look | Percentiles still wobble |
| 10,000 | Most decisions | Median and quartiles stable |
| 100,000+ | Tail probabilities | Needed for rare events |
Why people get stuck here
- Precise-looking outputs from vague inputs. The result is only as good as the ranges you supplied.
- Ignoring correlation. Sampling costs and demand independently when they move together produces an unrealistically narrow distribution.
- Too few trials for tails. Estimating a 1-in-100 outcome from a thousand runs gives ten data points.
- Reading the mean. Which is often exactly the number the simulation was run to avoid.
Common mistakes to avoid
- Treating a simulation as more rigorous than the assumptions behind it.
- Using uniform distributions everywhere because they feel neutral.
- Sampling correlated inputs independently.
- Quoting the mean when the distribution is skewed.
- Running once and not checking whether the percentiles are stable across runs.
How to do it with Monte Carlo Simulator
The Monte Carlo Simulator samples your inputs and reports the outcome distribution, in your browser.
- Define each uncertain input as a range with a distribution rather than a single guess.
- Run at least ten thousand trials.
- Run it twice — if the percentiles agree closely, you have enough trials.
- Read the percentiles and the probability of hitting your target, not the average.
Other statistical tools are in the tools directory.
Frequently asked questions
How many trials do I need?
Enough that the answer stops moving. Ten thousand twice; if the percentiles agree, that’s sufficient. Tail probabilities need considerably more than medians do.
Which distribution should I use?
Triangular for most business cases, since low, likely and high is what people can actually estimate. Normal when the quantity is a sum of many small effects. Uniform only when you truly know nothing but the bounds.
Why not just average the inputs?
Because the average of a function isn’t the function of the averages once anything multiplies or is capped. That gap is precisely what the simulation exposes.
Final thought
Report the tenth percentile alongside the median. The downside case is what decisions actually hinge on, and it’s the number a single-point estimate can never show you.