Three-Point Estimation (PERT): Formula and Worked Example
Three-point estimation forces estimators to express the uncertainty in their estimate, not just the best-case number. It is the simplest probabilistic estimating technique and the foundation of PERT scheduling.
The PERT formula
where O is the optimistic estimate (best case), M is the most likely estimate, and P is the pessimistic estimate (worst case). The PERT formula assumes a beta distribution, which puts more weight on the most-likely value than a simple arithmetic mean would.
A simpler triangular-distribution variant uses E = (O + M + P) / 3, which gives a slightly higher expected value because it weights the tail more.
Worked example
You are estimating the cost of building a custom data migration module. The team gives:
- Optimistic (O): 30,000 USD (everything fits, no edge cases)
- Most likely (M): 50,000 USD
- Pessimistic (P): 120,000 USD (legacy schema is a mess, two months of cleanup)
So the PERT expected cost is ~58,333 USD with one standard deviation of ~15,000 USD. A budget set at E + 1 SD = 73,333 USD gives roughly 84% probability of staying within budget; E + 2 SD = 88,333 USD gives roughly 97.5% probability.
Crucially, the most-likely estimate alone was 50,000 USD. PERT recommends 58,333 USD just to break even, and a confidence-weighted budget closer to 73,000 USD. A single-point budget at the most-likely value would have under-funded the work.
Sources
- Project Management Institute (2017). A Guide to the Project Management Body of Knowledge (PMBOK Guide), 6th edition. PMI, Newtown Square PA. See section 6.4.2.4 on estimation.
- Malcolm D.G., Roseboom J.H., Clark C.E., Fazar W. (1959). Application of a technique for research and development program evaluation. Operations Research 7(5).