How sure are we?

01The problem

The baseline said Friday 5 March, one working day before the promise. But that date is a single path through a plan whose tasks vary a great deal. Some tasks overrun far more than they underrun, and when several paths run in parallel, the project finishes when the slowest one does. That makes the real finish later than any single estimate suggests.

The managing director doesn't need a date. They need to know how likely the promised date is, and what date they could commit to if they wanted to be reasonably sure. Both come from simulation.

02The concept

Monte Carlo simulation

For each of thousands of runs, draw a duration for every task from a distribution shaped by its three estimates (a triangular distribution: minimum, most likely, maximum), run the schedule, and record the finish. After 10,000 runs you have 10,000 possible finish days. The spread tells you how uncertain the plan is.

From the results you can read:

• The chance of meeting a date: the share of runs that finish by it.
• P50: the day half the runs beat. A coin toss.
• P80: the day 80% of runs beat. A date you could commit to with reasonable confidence.
• The reserve: the gap between the baseline and P80, which is the schedule contingency the plan needs and doesn't have.

Why the simulated finish is later than the plan

Take two parallel paths of equal length. Each has a 50% chance of finishing on time. The project is on time only when both do: about 25%. A project with many near-critical paths loses more still. This is the "merge bias" of project networks, and it's why a plan built on likely durations is almost always optimistic.

03Example

Reload the plan, then simulate. This version draws all the durations at once and works through the tasks in order, so 10,000 runs take a moment:

Mean finish: day 103.6
Chance of finishing by day 91: 2.8%
P50: day 103.4
P80: day 109.6
P90: day 112.9

On the plan's own estimates, the chance of making the promised date was under 3%. The date was never likely, and it was promised before the plan was simulated. Convert the P50 and P80 days to dates:

Baseline: 2027-03-05
P50:      2027-03-25
P80:      2027-04-02
Reserve needed for P80: 20 working days

A date the sponsor could commit to with 80% confidence is Friday 2 April, about 20 working days after the baseline. And this is the plan from before week 10. Nothing in this lesson knows yet that the analysers are stuck in customs. That's lesson 5.

04Walkthrough

1. Define simulate() and run it for 10,000 runs with seed 42.
2. Calculate the probability of finishing by day 91.
3. Calculate P50, P80 and P90, and convert them to dates.
4. Calculate the reserve in working days between the baseline (day 90) and P80.
5. Plot the finish days as a histogram with the baseline, the promise and P80 marked (optional, but sponsors remember pictures).
6. Write the schedule risk note (the task below).

05Practice

06Check your understanding