Framework library · Risk management and assessment

Monte Carlo simulation

A single estimate hides how uncertain it is. Monte Carlo simulation gives each uncertain quantity a range, draws from those ranges thousands of times, and adds them up each time, so the answer is a distribution: how likely the project is to come in under budget, and how much contingency it really needs.

LevelAdvanced
TimeAn hour to set up the ranges, and seconds for the runs
Who to involveWhoever owns the estimate, with the people who know each cost or duration best.
Also calledMonte Carlo analysis, probabilistic cost estimate, quantitative risk analysis

Use it when

  • A budget, schedule or forecast is the sum of several uncertain pieces and you need to know how much contingency to hold.
  • A board asks "how confident are you?" and a single number cannot answer.
  • You want to know which uncertainty drives the spread, so the effort to reduce it goes to the right place.

Avoid it when

  • You cannot give honest ranges. A simulation of guesses is a precise-looking guess.
  • The pieces move together (for example, every cost rises with one contractor's rates). This tool draws them independently, which understates the spread. Model the common driver as its own quantity instead.
  • The risk is a single event, not a spread of outcomes. Put it in the risk register.

How to run it

  1. Break the total into pieces

    Five to fifteen pieces, each one that someone can estimate: civil works, equipment, labour, permits.

  2. Give each piece three numbers

    The lowest it could plausibly be, the most likely, and the highest it could plausibly be. Plausible means a one-in-twenty chance of being outside, not the worst imaginable.

  3. Ask the people who know

    Ranges from the engineer who has built it before are worth more than ranges from the spreadsheet. Ask for the highest number first; people anchor on the most likely.

  4. Set the target

    The budget or deadline you are testing against.

  5. Read the distribution

    P50 is the median; P80 or P90 is what most organisations budget to. The chance of exceeding the target is the number the board wants.

  6. Work on the drivers

    The chart of what drives the spread shows which ranges matter. Narrow those with better information, or carry the contingency.

Work through it

Answer the questions below, or load the worked example to see a finished one. The drawing updates as you type. Export the result as a PowerPoint deck, a Word document, an Excel workbook, a PDF or plain text.

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Mistakes to avoid

  • Ranges that are too narrow. People are overconfident. Widen anything that has never been done before.
  • Adding the "most likely" values and calling it the estimate. The sum of most-likely values is usually below the P50.
  • Treating the output as fact. It is only as good as the ranges, and it ignores anything you did not list.

Where it comes from

Developed at Los Alamos in the 1940s by Stanislaw Ulam, John von Neumann and Nicholas Metropolis, and named in Metropolis and Ulam, "The Monte Carlo Method", Journal of the American Statistical Association 44(247), 1949. Brought into business investment decisions by David B. Hertz, "Risk Analysis in Capital Investment", Harvard Business Review, January to February 1964. Source.

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