Three-point estimating with PERT, with a worked example

The three estimates

• Optimistic (O): the duration if things go well. Not a miracle, but a realistic best case.
• Most likely (M): the duration you would expect most often if you did the work many times.
• Pessimistic (P): the duration if things go badly, short of a disaster that would change the project.

Asking for three numbers changes the conversation. A single estimate hides whether the estimator was cautious or hopeful. Three numbers show the shape of the uncertainty: an activity with O = 9, M = 10, P = 11 is predictable, while O = 5, M = 10, P = 30 is not, even though both have the same most likely value.

The PERT formulas

PERT uses a weighted average that gives the most likely value four times the weight of each extreme:

• Expected duration: E = (O + 4M + P) / 6
• Standard deviation: σ = (P − O) / 6
• Variance: σ² = ((P − O) / 6)²

The idea behind dividing the range by 6 is that the optimistic and pessimistic values sit roughly three standard deviations either side of the mean. It is an approximation, not a law. The simpler triangular average, (O + M + P) / 3, gives the extremes more weight and usually produces a longer expected duration when the pessimistic tail is long.

Worked example: a three-activity path

Three activities run in sequence on the critical path. Durations are in working days.

Notice three things. First, the sum of the most likely values is 21 days, but the expected path duration is 23 days, because A and B have long pessimistic tails. Planning on 21 days would be optimistic. Second, standard deviations do not add; variances do. The path variance is 2.78 + 2.78 + 0.44 = 6.00 (exactly 100/36 + 100/36 + 16/36 = 216/36), so the path σ is √6 ≈ 2.45 days. Third, if you treat the path total as roughly normal, you can read confidence levels:

• About 50% chance of finishing within 23.0 days.
• About 80% within 23.0 + 0.84 × 2.45 ≈ 25.1 days.
• About 95% within 23.0 + 1.645 × 2.45 ≈ 27.0 days.

So a commitment of 25 working days carries roughly 80% confidence, under the assumptions that the activities are independent and that this path stays critical.

How to run three-point estimating, step by step

1. Pick the activities that matter: the critical and near-critical path, and anything new, novel or dependent on outside parties.
2. Ask the people who will do the work for O, M and P, in that order of conversation: start with M, then ask "what could make it faster?" and "what could make it slower?".
3. Write down the reason behind each pessimistic value. Those reasons are often risks that belong in the register.
4. Compute E and σ for each activity and put E into the schedule.
5. For a single dominant path, add the variances and estimate confidence as above. For a network with parallel paths, run a Monte Carlo simulation instead.
6. Revisit estimates as work progresses; the range should narrow.

When PERT fits and when it does not

PERT estimating fits well when work is uncertain but understood: design, software development, commissioning, permits, anything the team has done before in a different form. It is also a good way to surface hidden risks, because the pessimistic value forces people to say what could go wrong.

It fits less well in three cases. For repetitive work with good historical data, use the data directly (for example, average rate per unit) rather than asking for opinions. For activities whose duration is fixed by contract or by a supplier's lead time, a single number is honest. And for a whole schedule with many parallel paths, path arithmetic understates the risk, so use the PERT ranges as inputs to a simulation rather than as the final answer.

Finally, remember that E is an expected value, not a promise. Half the time a single activity will take longer than E. Commit to a percentile such as P80 at project level, and hold the difference between E and that percentile as visible contingency.

Common mistakes

• Adding standard deviations. In the example, 1.67 + 1.67 + 0.67 = 4.01 days, far more than the correct 2.45. Add variances, then take the square root.
• Ignoring merge bias. When parallel paths join, the finish depends on the latest of them, so the real expected date is later than any single path suggests. Simulation captures this; path arithmetic does not.
• Narrow ranges. People anchor on M and give P values that are too close. Ask what happened last time.
• Padding M. If M already contains contingency, the formula double-counts it.
• Assuming independence when risks are shared. If the same supplier affects three activities, their overruns move together and the true spread is wider.

How to do this in Critova

For a quick answer, the free three-point estimate calculator computes E and σ from your O, M and P. Inside Critova, the Monte Carlo schedule risk analysis accepts triangular or PERT durations on activities, adds risk events, and runs the whole critical path network, so merge bias and parallel paths are handled. It reports P50, P80 and P90 dates and shows which activities drive the result. The Monte Carlo P80 guide explains the next step.