What is Monte Carlo project forecasting?
Monte Carlo project forecasting is a simulation technique that answers "when will this finish?" with a probability distribution instead of a date. The method: run the entire project on paper thousands of times. In each run, draw every task's duration at random from that task's estimated range, resolve every uncertain branch by its odds, and walk the dependency graph to see when (and how) the project ends. The thousands of simulated endings, taken together, are the forecast.
The name comes from the casino: the method's currency is random draws, and it was developed in the 1940s for physics problems too tangled for exact equations. Project schedules are exactly such a problem.
Why simulation, instead of just adding the estimates#
Because plans do arithmetic that point estimates get wrong. Three effects in particular:
Parallel branches merge at the slowest one. A milestone waiting on three branches starts when the last arrives, and the maximum of uncertain quantities is later and more skewed than any of them. Adding estimates misses this entirely; simulation reproduces it run by run.
Uncertainty compounds along chains. Each task's spread feeds the next task's start. A chain of ten roughly-right estimates produces a wide finish distribution, and only the simulation knows how wide (why estimates need ranges).
Branches split the future. A review that fails 20% of the time sends one future in five down a different path. A single-date forecast silently assumes the happy branch; the simulation runs both in proportion.
Reading the output#
The result is typically summarised as quantiles and end-state odds:
| Number | Meaning |
|---|---|
| P50 | Half the simulated futures finish by this date (the median) |
| P80 / P95 | 80% / 95% of futures finish by these dates (commitment-grade) |
| P(success) | The fraction of futures that ended in the success state |
A concrete example with real engine output (a four-task plan whose estimates sum to 44 hours: P50 of 42, P95 of 65, and a 20% chance of ending in rework rather than launch) is walked through in the completion spectrum essay.
Two properties make a Monte Carlo forecast trustworthy in practice. Determinism: seeded runs give the same answer twice, so the number is stable enough to argue with. Structure-awareness: because every run walks the real dependency graph, by-products fall out free, like how often each chain decided the finish (criticality rates) and what the cash balance did along the way.
The honest limits#
The simulation propagates exactly the uncertainty you give it. Optimistic ranges in, optimistic distribution out; the method removes the arithmetic errors of single-date planning, not the estimation errors of humans (that takes calibration against actuals). And the output is a forecast, not a promise: a P95 is a date you will still miss one time in twenty. The gain is that, for the first time, you know which twenty.
In Topolog, every plan gets this treatment automatically (8,000 simulated futures by default, recomputed on every edit), rendered as the spectrum view: the spectrum docs show the surface.